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Commit 68e59d61 authored by Olexa Bilaniuk's avatar Olexa Bilaniuk
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[RHO] Initial commit of RHO algorithm for rapid homography estimation. 

Implements the RHO algorithm as presented in

Paper: Bilaniuk, Olexa, Hamid Bazargani, and Robert Laganiere. "Fast
Target Recognition on Mobile Devices: Revisiting Gaussian Elimination
for the Estimation of Planar Homographies." In Computer Vision and
Pattern Recognition Workshops (CVPRW), 2014 IEEE Conference on, pp.
119-125. IEEE, 2014.

- Complete, heavily documented reference C implementation, as well as
temporarily disabled dirty SSE2 port.
- Enabled tests for RHO in test_homography; Currently these fail
presumably due to too-stringent accuracy requirements.
- Refinement and final refinement are not yet functional; Do not pass
their corresponding flags to RHO.
parent 32348604
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Showing with 4329 additions and 15 deletions
modules/calib3d/include/opencv2/calib3d.hpp
View file @ 68e59d61
......@@ -53,7 +53,8 @@ namespace cv
//! type of the robust estimation algorithm
enum { LMEDS = 4, //!< least-median algorithm
RANSAC = 8 //!< RANSAC algorithm
RANSAC = 8, //!< RANSAC algorithm
RHO = 16 //!< RHO algorithm
};
enum { SOLVEPNP_ITERATIVE = 0,
......
modules/calib3d/src/fundam.cpp
View file @ 68e59d61
......@@ -41,6 +41,10 @@
//M*/
#include "precomp.hpp"
#include "rhorefc.h"
#if CV_SSE2
#include "rhosse2.h"
#endif
#include <iostream>
namespace cv
......@@ -273,6 +277,73 @@ public:
}
namespace cv{
static bool createAndRunRHORegistrator(double confidence, int maxIters, double ransacReprojThreshold, int npoints, InputArray _src, InputArray _dst, OutputArray _H, OutputArray _tempMask){
Mat src = _src.getMat();
Mat dst = _dst.getMat();
Mat tempMask = _tempMask.getMat();
bool result;
/* Run RHO. Needs cleanup or separate function to invoke. */
Mat tmpH = Mat(3, 3, CV_32FC1);
tempMask = Mat(npoints, 1, CV_8U);
double beta = 0.35;/* 0.35 is a value that often works. */
#if CV_SSE2 && 0
if(useOptimized()){
RHO_HEST_SSE2 p;
rhoSSE2Init(&p);
rhoSSE2EnsureCapacity(&p, npoints, beta);
result = !!rhoSSE2(&p,
(const float*)src.data,
(const float*)dst.data,
(char*) tempMask.data,
npoints,
ransacReprojThreshold,
maxIters,
maxIters,
confidence,
4,
beta,
RHO_FLAG_ENABLE_NR,
NULL,
(float*)tmpH.data);
rhoSSE2Fini(&p);
}else
#endif
{
RHO_HEST_REFC p;
rhoRefCInit(&p);
rhoRefCEnsureCapacity(&p, npoints, beta);
result = !!rhoRefC(&p,
(const float*)src.data,
(const float*)dst.data,
(char*) tempMask.data,
npoints,
ransacReprojThreshold,
maxIters,
maxIters,
confidence,
4,
beta,
RHO_FLAG_ENABLE_NR,
NULL,
(float*)tmpH.data);
rhoRefCFini(&p);
}
tmpH.convertTo(_H, CV_64FC1);
/* Maps non-zero maks elems to 1, for the sake of the testcase. */
for(int k=0;k<npoints;k++){
tempMask.data[k] = !!tempMask.data[k];
}
return result;
}
}
cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
int method, double ransacReprojThreshold, OutputArray _mask,
const int maxIters, const double confidence)
......@@ -317,10 +388,12 @@ cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
result = createRANSACPointSetRegistrator(cb, 4, ransacReprojThreshold, confidence, maxIters)->run(src, dst, H, tempMask);
else if( method == LMEDS )
result = createLMeDSPointSetRegistrator(cb, 4, confidence, maxIters)->run(src, dst, H, tempMask);
else
else if( method == RHO ){
result = createAndRunRHORegistrator(confidence, maxIters, ransacReprojThreshold, npoints, src, dst, H, tempMask);
}else
CV_Error(Error::StsBadArg, "Unknown estimation method");
if( result && npoints > 4 )
if( result && npoints > 4 && method != RHO)
{
compressPoints( src.ptr<Point2f>(), tempMask.ptr<uchar>(), 1, npoints );
npoints = compressPoints( dst.ptr<Point2f>(), tempMask.ptr<uchar>(), 1, npoints );
......
modules/calib3d/src/rhorefc.cpp 0 → 100644
View file @ 68e59d61
/*
IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
By downloading, copying, installing or using the software you agree to this license.
If you do not agree to this license, do not download, install,
copy or use the software.
BSD 3-Clause License
Copyright (C) 2014, Olexa Bilaniuk, Hamid Bazargani & Robert Laganiere, all rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistribution's of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistribution's in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* The name of the copyright holders may not be used to endorse or promote products
derived from this software without specific prior written permission.
This software is provided by the copyright holders and contributors "as is" and
any express or implied warranties, including, but not limited to, the implied
warranties of merchantability and fitness for a particular purpose are disclaimed.
In no event shall the Intel Corporation or contributors be liable for any direct,
indirect, incidental, special, exemplary, or consequential damages
(including, but not limited to, procurement of substitute goods or services;
loss of use, data, or profits; or business interruption) however caused
and on any theory of liability, whether in contract, strict liability,
or tort (including negligence or otherwise) arising in any way out of
the use of this software, even if advised of the possibility of such damage.
*/
/**
* Bilaniuk, Olexa, Hamid Bazargani, and Robert Laganiere. "Fast Target
* Recognition on Mobile Devices: Revisiting Gaussian Elimination for the
* Estimation of Planar Homographies." In Computer Vision and Pattern
* Recognition Workshops (CVPRW), 2014 IEEE Conference on, pp. 119-125.
* IEEE, 2014.
*/
/* Includes */
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <stddef.h>
#include <limits.h>
#include <float.h>
#include <math.h>
#include "rhorefc.h"
/* Defines */
#define MEM_ALIGN 32
#define HSIZE (3*3*sizeof(float))
#define MIN_DELTA_CHNG 0.1
#define REL_CHNG(a, b) (fabs((a) - (b))/(a))
#define CHNG_SIGNIFICANT(a, b) (REL_CHNG(a, b) > MIN_DELTA_CHNG)
#define CHI_STAT 2.706
#define CHI_SQ 1.645
#define RLO 0.25
#define RHI 0.75
#define MAXLEVMARQITERS 10
#define m 4 /* 4 points required per model */
#define SPRT_T_M 25 /* Guessing 25 match evlauations / 1 model generation */
#define SPRT_M_S 1 /* 1 model per sample */
#define SPRT_EPSILON 0.1 /* No explanation */
#define SPRT_DELTA 0.01 /* No explanation */
/* For the sake of cv:: namespace ONLY: */
#ifdef __cplusplus
namespace cv{/* For C support, replace with extern "C" { */
#endif
/* Data Structures */
/* Prototypes */
static inline void* almalloc(size_t nBytes);
static inline void alfree(void* ptr);
static inline int sacInitRun(RHO_HEST_REFC* p);
static inline void sacFiniRun(RHO_HEST_REFC* p);
static inline int sacHaveExtrinsicGuess(RHO_HEST_REFC* p);
static inline int sacHypothesize(RHO_HEST_REFC* p);
static inline int sacVerify(RHO_HEST_REFC* p);
static inline int sacIsNREnabled(RHO_HEST_REFC* p);
static inline int sacIsRefineEnabled(RHO_HEST_REFC* p);
static inline int sacIsFinalRefineEnabled(RHO_HEST_REFC* p);
static inline int sacPROSACPhaseEndReached(RHO_HEST_REFC* p);
static inline void sacPROSACGoToNextPhase(RHO_HEST_REFC* p);
static inline void sacGetPROSACSample(RHO_HEST_REFC* p);
static inline int sacIsSampleDegenerate(RHO_HEST_REFC* p);
static inline void sacGenerateModel(RHO_HEST_REFC* p);
static inline int sacIsModelDegenerate(RHO_HEST_REFC* p);
static inline void sacEvaluateModelSPRT(RHO_HEST_REFC* p);
static inline void sacUpdateSPRT(RHO_HEST_REFC* p);
static inline void sacDesignSPRTTest(RHO_HEST_REFC* p);
static inline int sacIsBestModel(RHO_HEST_REFC* p);
static inline int sacIsBestModelGoodEnough(RHO_HEST_REFC* p);
static inline void sacSaveBestModel(RHO_HEST_REFC* p);
static inline void sacInitNonRand(double beta,
unsigned start,
unsigned N,
unsigned* nonRandMinInl);
static inline void sacNStarOptimize(RHO_HEST_REFC* p);
static inline void sacUpdateBounds(RHO_HEST_REFC* p);
static inline void sacOutputModel(RHO_HEST_REFC* p);
static inline void sacOutputZeroH(RHO_HEST_REFC* p);
static inline double sacInitPEndFpI(const unsigned ransacConvg,
const unsigned n,
const unsigned s);
static inline void sacRndSmpl(unsigned sampleSize,
unsigned* currentSample,
unsigned dataSetSize);
static inline double sacRandom(void);
static inline unsigned sacCalcIterBound(double confidence,
double inlierRate,
unsigned sampleSize,
unsigned maxIterBound);
static inline void hFuncRefC(float* packedPoints, float* H);
static inline int sacCanRefine(RHO_HEST_REFC* p);
static inline void sacRefine(RHO_HEST_REFC* p);
static inline void sacCalcJtMats(float (* restrict JtJ)[8],
float* restrict Jte,
float* restrict Sp,
const float* restrict H,
const float* restrict src,
const float* restrict dst,
const char* restrict inl,
unsigned N);
static inline void sacChol8x8 (const float (*A)[8],
float (*L)[8]);
static inline void sacTRInv8x8(const float (*L)[8],
float (*M)[8]);
static inline void sacTRISolve8x8(const float (*L)[8],
const float* Jte,
float* dH);
static inline void sacScaleDiag8x8(const float (*A)[8],
float lambda,
float (*B)[8]);
static inline void sacSub8x1(float* Hout, const float* H, const float* dH);
/* Functions */
/**
* Initialize the estimator context, by allocating the aligned buffers
* internally needed.
*
* Currently there are 5 per-estimator buffers:
* - The buffer of m indexes representing a sample
* - The buffer of 16 floats representing m matches (x,y) -> (X,Y).
* - The buffer for the current homography
* - The buffer for the best-so-far homography
* - Optionally, the non-randomness criterion table
*
* @param [in/out] p The uninitialized estimator context to initialize.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoRefCInit(RHO_HEST_REFC* p){
memset(p, 0, sizeof(*p));
p->ctrl.smpl = (unsigned*)almalloc(m*sizeof(*p->ctrl.smpl));
p->curr.pkdPts = (float*) almalloc(m*2*2*sizeof(*p->curr.pkdPts));
p->curr.H = (float*) almalloc(HSIZE);
p->curr.inl = NULL;
p->curr.numInl = 0;
p->best.H = (float*) almalloc(HSIZE);
p->best.inl = NULL;
p->best.numInl = 0;
p->nr.tbl = NULL;/* By default this table is not computed. */
p->nr.size = 0;
p->nr.beta = 0.0;
int areAllAllocsSuccessful = p->ctrl.smpl &&
p->curr.H &&
p->best.H &&
p->curr.pkdPts;
if(!areAllAllocsSuccessful){
rhoRefCFini(p);
}
return areAllAllocsSuccessful;
}
/**
* Ensure that the estimator context's internal table for non-randomness
* criterion is at least of the given size, and uses the given beta. The table
* should be larger than the maximum number of matches fed into the estimator.
*
* A value of N of 0 requests deallocation of the table.
*
* @param [in] p The initialized estimator context
* @param [in] N If 0, deallocate internal table. If > 0, ensure that the
* internal table is of at least this size, reallocating if
* necessary.
* @param [in] beta The beta-factor to use within the table.
* @return 1 if successful; 0 if an error occured.
*
* Reads: nr.*
* Writes: nr.*
*/
int rhoRefCEnsureCapacity(RHO_HEST_REFC* p, unsigned N, double beta){
unsigned* tmp;
if(N == 0){
/* Deallocate table */
alfree(p->nr.tbl);
p->nr.tbl = NULL;
p->nr.size = 0;
}else{
/* Ensure table at least as big as N and made for correct beta. */
if(p->nr.tbl && p->nr.beta == beta && p->nr.size >= N){
/* Table already correctly set up */
}else{
if(p->nr.size < N){
/* Reallocate table because it is too small. */
tmp = (unsigned*)almalloc(N*sizeof(unsigned));
if(!tmp){
return 0;
}
/* Must recalculate in whole or part. */
if(p->nr.beta != beta){
/* Beta changed; recalculate in whole. */
sacInitNonRand(beta, 0, N, tmp);
alfree(p->nr.tbl);
}else{
/* Beta did not change; Copy over any work already done. */
memcpy(tmp, p->nr.tbl, p->nr.size*sizeof(unsigned));
sacInitNonRand(beta, p->nr.size, N, tmp);
alfree(p->nr.tbl);
}
p->nr.tbl = tmp;
p->nr.size = N;
p->nr.beta = beta;
}else{
/* Might recalculate in whole, or not at all. */
if(p->nr.beta != beta){
/* Beta changed; recalculate in whole. */
sacInitNonRand(beta, 0, p->nr.size, p->nr.tbl);
p->nr.beta = beta;
}else{
/* Beta did not change; Table was already big enough. Do nothing. */
/* Besides, this is unreachable. */
}
}
}
}
return 1;
}
/**
* Finalize the estimator context, by freeing the aligned buffers used
* internally.
*
* @param [in] p The initialized estimator context to finalize.
*/
void rhoRefCFini(RHO_HEST_REFC* p){
alfree(p->ctrl.smpl);
alfree(p->curr.H);
alfree(p->best.H);
alfree(p->curr.pkdPts);
alfree(p->nr.tbl);
memset(p, 0, sizeof(*p));
}
/**
* Estimates the homography using the given context, matches and parameters to
* PROSAC.
*
* @param [in/out] p The context to use for homography estimation. Must
* be already initialized. Cannot be NULL.
* @param [in] src The pointer to the source points of the matches.
* Must be aligned to 4 bytes. Cannot be NULL.
* @param [in] dst The pointer to the destination points of the matches.
* Must be aligned to 16 bytes. Cannot be NULL.
* @param [out] inl The pointer to the output mask of inlier matches.
* Must be aligned to 16 bytes. May be NULL.
* @param [in] N The number of matches.
* @param [in] maxD The maximum distance.
* @param [in] maxI The maximum number of PROSAC iterations.
* @param [in] rConvg The RANSAC convergence parameter.
* @param [in] cfd The required confidence in the solution.
* @param [in] minInl The minimum required number of inliers.
* @param [in] beta The beta-parameter for the non-randomness criterion.
* @param [in] flags A union of flags to control the estimation.
* @param [in] guessH An extrinsic guess at the solution H, or NULL if
* none provided.
* @param [out] finalH The final estimation of H, or the zero matrix if
* the minimum number of inliers was not met.
* Cannot be NULL.
* @return The number of inliers if the minimum number of
* inliers for acceptance was reached; 0 otherwise.
*/
unsigned rhoRefC(RHO_HEST_REFC* restrict p, /* Homography estimation context. */
const float* restrict src, /* Source points */
const float* restrict dst, /* Destination points */
char* restrict inl, /* Inlier mask */
unsigned N, /* = src.length = dst.length = inl.length */
float maxD, /* Works: 3.0 */
unsigned maxI, /* Works: 2000 */
unsigned rConvg, /* Works: 2000 */
double cfd, /* Works: 0.995 */
unsigned minInl, /* Minimum: 4 */
double beta, /* Works: 0.35 */
unsigned flags, /* Works: 0 */
const float* guessH, /* Extrinsic guess, NULL if none provided */
float* finalH){ /* Final result. */
/**
* Setup
*/
p->arg.src = src;
p->arg.dst = dst;
p->arg.inl = inl;
p->arg.N = N;
p->arg.maxD = maxD;
p->arg.maxI = maxI;
p->arg.rConvg = rConvg;
p->arg.cfd = cfd;
p->arg.minInl = minInl;
p->arg.beta = beta;
p->arg.flags = flags;
p->arg.guessH = guessH;
p->arg.finalH = finalH;
if(!sacInitRun(p)){
sacOutputZeroH(p);
sacFiniRun(p);
return 0;
}
/**
* Extrinsic Guess
*/
if(sacHaveExtrinsicGuess(p)){
sacVerify(p);
}
/**
* PROSAC Loop
*/
for(p->ctrl.i=0; p->ctrl.i < p->arg.maxI; p->ctrl.i++){
sacHypothesize(p) && sacVerify(p);
}
/**
* Teardown
*/
if(sacIsFinalRefineEnabled(p) && sacCanRefine(p)){
sacRefine(p);
}
sacOutputModel(p);
sacFiniRun(p);
return sacIsBestModelGoodEnough(p) ? p->best.numInl : 0;
}
/**
* Allocate memory aligned to a boundary of MEMALIGN.
*/
static inline void* almalloc(size_t nBytes){
if(nBytes){
unsigned char* ptr = (unsigned char*)malloc(MEM_ALIGN + nBytes);
if(ptr){
unsigned char* adj = (unsigned char*)(((intptr_t)(ptr+MEM_ALIGN))&((intptr_t)(-MEM_ALIGN)));
ptrdiff_t diff = adj - ptr;
adj[-1] = diff - 1;
return adj;
}
}
return NULL;
}
/**
* Free aligned memory.
*
* If argument is NULL, do nothing in accordance with free() semantics.
*/
static inline void alfree(void* ptr){
if(ptr){
unsigned char* cptr = (unsigned char*)ptr;
free(cptr - (ptrdiff_t)cptr[-1] - 1);
}
}
/**
* Initialize SAC for a run given its arguments.
*
* Performs sanity-checks and memory allocations. Also initializes the state.
*
* @returns 0 if per-run initialization failed at any point; non-zero
* otherwise.
*
* Reads: arg.*, nr.*
* Writes: curr.*, best.*, ctrl.*, eval.*
*/
static inline int sacInitRun(RHO_HEST_REFC* p){
/**
* Sanitize arguments.
*
* Runs zeroth because these are easy-to-check errors and unambiguously
* mean something or other.
*/
if(!p->arg.src || !p->arg.dst){
/* Arguments src or dst are insane, must be != NULL */
return 0;
}
if(p->arg.N < m){
/* Argument N is insane, must be >= 4. */
return 0;
}
if(p->arg.maxD < 0){
/* Argument maxD is insane, must be >= 0. */
return 0;
}
if(p->arg.cfd < 0 || p->arg.cfd > 1){
/* Argument cfd is insane, must be in [0, 1]. */
return 0;
}
/* Clamp minInl to 4 or higher. */
p->arg.minInl = p->arg.minInl < m ? m : p->arg.minInl;
if(sacIsNREnabled(p) && (p->arg.beta <= 0 || p->arg.beta >= 1)){
/* Argument beta is insane, must be in (0, 1). */
return 0;
}
if(!p->arg.finalH){
/* Argument finalH is insane, must be != NULL */
return 0;
}
/**
* Optional NR setup.
*
* Runs first because it is decoupled from most other things (*) and if it
* fails, it is easy to recover from.
*
* (*) The only things this code depends on is the flags argument, the nr.*
* substruct and the sanity-checked N and beta arguments from above.
*/
if(sacIsNREnabled(p) && !rhoRefCEnsureCapacity(p, p->arg.N, p->arg.beta)){
return 0;
}
/**
* Inlier mask alloc.
*
* Runs second because we want to quit as fast as possible if we can't even
* allocate the up tp two masks.
*
* If the calling software wants an output mask, use buffer provided. If
* not, allocate one anyways internally.
*/
p->best.inl = p->arg.inl ? p->arg.inl : (char*)almalloc(p->arg.N);
p->curr.inl = (char*)almalloc(p->arg.N);
if(!p->curr.inl || !p->best.inl){
return 0;
}
/**
* Reset scalar per-run state.
*
* Runs third because there's no point in resetting/calculating a large
* number of fields if something in the above junk failed.
*/
p->ctrl.i = 0;
p->ctrl.phNum = m;
p->ctrl.phEndI = 1;
p->ctrl.phEndFpI = sacInitPEndFpI(p->arg.rConvg, p->arg.N, m);
p->ctrl.phMax = p->arg.N;
p->ctrl.phNumInl = 0;
p->ctrl.numModels = 0;
if(sacHaveExtrinsicGuess(p)){
memcpy(p->curr.H, p->arg.guessH, HSIZE);
}else{
memset(p->curr.H, 0, HSIZE);
}
p->curr.numInl = 0;
memset(p->best.H, 0, HSIZE);
p->best.numInl = 0;
p->eval.Ntested = 0;
p->eval.Ntestedtotal = 0;
p->eval.good = 1;
p->eval.t_M = SPRT_T_M;
p->eval.m_S = SPRT_M_S;
p->eval.epsilon = SPRT_EPSILON;
p->eval.delta = SPRT_DELTA;
sacDesignSPRTTest(p);
return 1;
}
/**
* Finalize SAC run.
*
* Deallocates per-run allocatable resources. Currently this consists only of
* the best and current inlier masks, which are equal in size to p->arg.N
* bytes.
*
* Reads: arg.bestInl, curr.inl, best.inl
* Writes: curr.inl, best.inl
*/
static inline void sacFiniRun(RHO_HEST_REFC* p){
/**
* If no output inlier mask was required, free both (internal) masks.
* Else if an (external) mask was provided as argument, find the other
* (the internal one) and free it.
*/
if(p->arg.inl){
if(p->arg.inl == p->best.inl){
alfree(p->curr.inl);
}else{
alfree(p->best.inl);
}
}else{
alfree(p->best.inl);
alfree(p->curr.inl);
}
p->best.inl = NULL;
p->curr.inl = NULL;
}
/**
* Hypothesize a model.
*
* Selects randomly a sample (within the rules of PROSAC) and generates a
* new current model, and applies degeneracy tests to it.
*
* @returns 0 if hypothesized model could be rejected early as degenerate, and
* non-zero otherwise.
*/
static inline int sacHypothesize(RHO_HEST_REFC* p){
if(sacPROSACPhaseEndReached(p)){
sacPROSACGoToNextPhase(p);
}
sacGetPROSACSample(p);
if(sacIsSampleDegenerate(p)){
return 0;
}
sacGenerateModel(p);
if(sacIsModelDegenerate(p)){
return 0;
}
return 1;
}
/**
* Verify the hypothesized model.
*
* Given the current model, evaluate its quality. If it is better than
* everything before, save as new best model (and possibly refine it).
*
* Returns 1.
*/
static inline int sacVerify(RHO_HEST_REFC* p){
sacEvaluateModelSPRT(p);
sacUpdateSPRT(p);
if(sacIsBestModel(p)){
sacSaveBestModel(p);
if(sacIsRefineEnabled(p) && sacCanRefine(p)){
sacRefine(p);
}
sacUpdateBounds(p);
if(sacIsNREnabled(p)){
sacNStarOptimize(p);
}
}
return 1;
}
/**
* Check whether extrinsic guess was provided or not.
*
* @return Zero if no extrinsic guess was provided; non-zero otherwiseEE.
*/
static inline int sacHaveExtrinsicGuess(RHO_HEST_REFC* p){
return !!p->arg.guessH;
}
/**
* Check whether non-randomness criterion is enabled.
*
* @return Zero if non-randomness criterion disabled; non-zero if not.
*/
static inline int sacIsNREnabled(RHO_HEST_REFC* p){
return p->arg.flags & RHO_FLAG_ENABLE_NR;
}
/**
* Check whether best-model-so-far refinement is enabled.
*
* @return Zero if best-model-so-far refinement disabled; non-zero if not.
*/
static inline int sacIsRefineEnabled(RHO_HEST_REFC* p){
return p->arg.flags & RHO_FLAG_ENABLE_REFINEMENT;
}
/**
* Check whether final-model refinement is enabled.
*
* @return Zero if final-model refinement disabled; non-zero if not.
*/
static inline int sacIsFinalRefineEnabled(RHO_HEST_REFC* p){
return p->arg.flags & RHO_FLAG_ENABLE_FINAL_REFINEMENT;
}
/**
* Computes whether the end of the current PROSAC phase has been reached. At
* PROSAC phase phNum, only matches [0, phNum) are sampled from.
*
* Accesses:
* Read: i, phEndI, phNum, phMax.
*/
static inline int sacPROSACPhaseEndReached(RHO_HEST_REFC* p){
return p->ctrl.i >= p->ctrl.phEndI && p->ctrl.phNum < p->ctrl.phMax;
}
/**
* Updates unconditionally the necessary fields to move to the next PROSAC
* stage.
*
* Not idempotent.
*
* Accesses:
* Read: phNum, phEndFpI, phEndI
* Write: phNum, phEndFpI, phEndI
*/
static inline void sacPROSACGoToNextPhase(RHO_HEST_REFC* p){
double next;
p->ctrl.phNum++;
next = (p->ctrl.phEndFpI * p->ctrl.phNum)/(p->ctrl.phNum - m);
p->ctrl.phEndI += ceil(next - p->ctrl.phEndFpI);
p->ctrl.phEndFpI = next;
}
/**
* Get a sample according to PROSAC rules. Namely:
* - If we're past the phase end interation, select randomly 4 out of the first
* phNum matches.
* - Otherwise, select match phNum-1 and select randomly the 3 others out of
* the first phNum-1 matches.
*/
static inline void sacGetPROSACSample(RHO_HEST_REFC* p){
if(p->ctrl.i > p->ctrl.phEndI){
sacRndSmpl(4, p->ctrl.smpl, p->ctrl.phNum);/* Used to be phMax */
}else{
sacRndSmpl(3, p->ctrl.smpl, p->ctrl.phNum-1);
p->ctrl.smpl[3] = p->ctrl.phNum-1;
}
}
/**
* Checks whether the *sample* is degenerate prior to model generation.
* - First, the extremely cheap numerical degeneracy test is run, which weeds
* out bad samples to the optimized GE implementation.
* - Second, the geometrical degeneracy test is run, which weeds out most other
* bad samples.
*/
static inline int sacIsSampleDegenerate(RHO_HEST_REFC* p){
unsigned i0 = p->ctrl.smpl[0], i1 = p->ctrl.smpl[1], i2 = p->ctrl.smpl[2], i3 = p->ctrl.smpl[3];
typedef struct{float x,y;} MyPt2f;
MyPt2f* pkdPts = (MyPt2f*)p->curr.pkdPts, *src = (MyPt2f*)p->arg.src, *dst = (MyPt2f*)p->arg.dst;
/**
* Pack the matches selected by the SAC algorithm.
* Must be packed points[0:7] = {srcx0, srcy0, srcx1, srcy1, srcx2, srcy2, srcx3, srcy3}
* points[8:15] = {dstx0, dsty0, dstx1, dsty1, dstx2, dsty2, dstx3, dsty3}
* Gather 4 points into the vector
*/
pkdPts[0] = src[i0];
pkdPts[1] = src[i1];
pkdPts[2] = src[i2];
pkdPts[3] = src[i3];
pkdPts[4] = dst[i0];
pkdPts[5] = dst[i1];
pkdPts[6] = dst[i2];
pkdPts[7] = dst[i3];
/**
* If the matches' source points have common x and y coordinates, abort.
*/
if(pkdPts[0].x == pkdPts[1].x || pkdPts[1].x == pkdPts[2].x ||
pkdPts[2].x == pkdPts[3].x || pkdPts[0].x == pkdPts[2].x ||
pkdPts[1].x == pkdPts[3].x || pkdPts[0].x == pkdPts[3].x ||
pkdPts[0].y == pkdPts[1].y || pkdPts[1].y == pkdPts[2].y ||
pkdPts[2].y == pkdPts[3].y || pkdPts[0].y == pkdPts[2].y ||
pkdPts[1].y == pkdPts[3].y || pkdPts[0].y == pkdPts[3].y){
return 1;
}
/* If the matches do not satisfy the strong geometric constraint, abort. */
/* (0 x 1) * 2 */
float cross0s0 = pkdPts[0].y-pkdPts[1].y;
float cross0s1 = pkdPts[1].x-pkdPts[0].x;
float cross0s2 = pkdPts[0].x*pkdPts[1].y-pkdPts[0].y*pkdPts[1].x;
float dots0 = cross0s0*pkdPts[2].x + cross0s1*pkdPts[2].y + cross0s2;
float cross0d0 = pkdPts[4].y-pkdPts[5].y;
float cross0d1 = pkdPts[5].x-pkdPts[4].x;
float cross0d2 = pkdPts[4].x*pkdPts[5].y-pkdPts[4].y*pkdPts[5].x;
float dotd0 = cross0d0*pkdPts[6].x + cross0d1*pkdPts[6].y + cross0d2;
if(((int)dots0^(int)dotd0) < 0){
return 1;
}
/* (0 x 1) * 3 */
float cross1s0 = cross0s0;
float cross1s1 = cross0s1;
float cross1s2 = cross0s2;
float dots1 = cross1s0*pkdPts[3].x + cross1s1*pkdPts[3].y + cross1s2;
float cross1d0 = cross0d0;
float cross1d1 = cross0d1;
float cross1d2 = cross0d2;
float dotd1 = cross1d0*pkdPts[7].x + cross1d1*pkdPts[7].y + cross1d2;
if(((int)dots1^(int)dotd1) < 0){
return 1;
}
/* (2 x 3) * 0 */
float cross2s0 = pkdPts[2].y-pkdPts[3].y;
float cross2s1 = pkdPts[3].x-pkdPts[2].x;
float cross2s2 = pkdPts[2].x*pkdPts[3].y-pkdPts[2].y*pkdPts[3].x;
float dots2 = cross2s0*pkdPts[0].x + cross2s1*pkdPts[0].y + cross2s2;
float cross2d0 = pkdPts[6].y-pkdPts[7].y;
float cross2d1 = pkdPts[7].x-pkdPts[6].x;
float cross2d2 = pkdPts[6].x*pkdPts[7].y-pkdPts[6].y*pkdPts[7].x;
float dotd2 = cross2d0*pkdPts[4].x + cross2d1*pkdPts[4].y + cross2d2;
if(((int)dots2^(int)dotd2) < 0){
return 1;
}
/* (2 x 3) * 1 */
float cross3s0 = cross2s0;
float cross3s1 = cross2s1;
float cross3s2 = cross2s2;
float dots3 = cross3s0*pkdPts[1].x + cross3s1*pkdPts[1].y + cross3s2;
float cross3d0 = cross2d0;
float cross3d1 = cross2d1;
float cross3d2 = cross2d2;
float dotd3 = cross3d0*pkdPts[5].x + cross3d1*pkdPts[5].y + cross3d2;
if(((int)dots3^(int)dotd3) < 0){
return 1;
}
/* Otherwise, accept */
return 0;
}
/**
* Compute homography of matches in gathered, packed sample and output the
* current homography.
*/
static inline void sacGenerateModel(RHO_HEST_REFC* p){
hFuncRefC(p->curr.pkdPts, p->curr.H);
}
/**
* Checks whether the model is itself degenerate.
* - One test: All elements of the homography are added, and if the result is
* NaN the homography is rejected.
*/
static inline int sacIsModelDegenerate(RHO_HEST_REFC* p){
int degenerate;
float* H = p->curr.H;
float f=H[0]+H[1]+H[2]+H[3]+H[4]+H[5]+H[6]+H[7];
/* degenerate = isnan(f); */
degenerate = f!=f;/* Only NaN is not equal to itself. */
/* degenerate = 0; */
return degenerate;
}
/**
* Evaluates the current model using SPRT for early exiting.
*
* Reads: arg.maxD, arg.src, arg.dst, curr.H, eval.*
* Writes: eval.*, curr.inl, curr.numInl
*/
static inline void sacEvaluateModelSPRT(RHO_HEST_REFC* p){
unsigned i;
unsigned isInlier;
double lambda = 1.0;
float distSq = p->arg.maxD*p->arg.maxD;
const float* src = p->arg.src;
const float* dst = p->arg.dst;
char* inl = p->curr.inl;
const float* H = p->curr.H;
p->ctrl.numModels++;
p->curr.numInl = 0;
p->eval.Ntested = 0;
p->eval.good = 1;
/* SCALAR */
for(i=0;i<p->arg.N && p->eval.good;i++){
/* Backproject */
float x=src[i*2],y=src[i*2+1];
float X=dst[i*2],Y=dst[i*2+1];
float reprojX=H[0]*x+H[1]*y+H[2]; /* ( X_1 ) ( H_11 H_12 H_13 ) (x_1) */
float reprojY=H[3]*x+H[4]*y+H[5]; /* ( X_2 ) = ( H_21 H_22 H_23 ) (x_2) */
float reprojZ=H[6]*x+H[7]*y+1.0; /* ( X_3 ) ( H_31 H_32 H_33=1.0 ) (x_3 = 1.0) */
/* reproj is in homogeneous coordinates. To bring back to "regular" coordinates, divide by Z. */
reprojX/=reprojZ;
reprojY/=reprojZ;
/* Compute distance */
reprojX-=X;
reprojY-=Y;
reprojX*=reprojX;
reprojY*=reprojY;
float reprojDist = reprojX+reprojY;
/* ... */
isInlier = reprojDist <= distSq;
p->curr.numInl += isInlier;
*inl++ = isInlier;
/* SPRT */
lambda *= isInlier ? p->eval.lambdaAccept : p->eval.lambdaReject;
p->eval.good = lambda <= p->eval.A;
/* If !p->good, the threshold A was exceeded, so we're rejecting */
}
p->eval.Ntested = i;
p->eval.Ntestedtotal += i;
}
/**
* Update either the delta or epsilon SPRT parameters, depending on the events
* that transpired in the previous evaluation.
*
* If a "good" model that is also the best was encountered, update epsilon,
* since
*/
static inline void sacUpdateSPRT(RHO_HEST_REFC* p){
if(p->eval.good){
if(sacIsBestModel(p)){
p->eval.epsilon = (double)p->curr.numInl/p->arg.N;
sacDesignSPRTTest(p);
}
}else{
double newDelta = (double)p->curr.numInl/p->eval.Ntested;
if(newDelta > 0 && CHNG_SIGNIFICANT(p->eval.delta, newDelta)){
p->eval.delta = newDelta;
sacDesignSPRTTest(p);
}
}
}
/**
* Numerically compute threshold A from the estimated delta, epsilon, t_M and
* m_S values.
*
* Epsilon: Denotes the probability that a randomly chosen data point is
* consistent with a good model.
* Delta: Denotes the probability that a randomly chosen data point is
* consistent with a bad model.
* t_M: Time needed to instantiate a model hypotheses given a sample.
* (Computing model parameters from a sample takes the same time
* as verification of t_M data points)
* m_S: The number of models that are verified per sample.
*/
static inline double designSPRTTest(double delta, double epsilon, double t_M, double m_S){
double An, C, K, prevAn;
unsigned i;
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Eq (2)
*/
C = (1-delta) * log((1-delta)/(1-epsilon)) +
delta * log( delta / epsilon );
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Eq (6)
* K = K_1/K_2 + 1 = (t_M*C)/m_S + 1
*/
K = t_M*C/m_S + 1;
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Paragraph below Eq (6)
*
* A* = lim_{n -> infty} A_n, where
* A_0 = K1/K2 + 1 and
* A_{n+1} = K1/K2 + 1 + log(A_n)
* The series converges fast, typically within four iterations.
*/
An = K;
i = 0;
do{
prevAn = An;
An = K + log(An);
}while((An-prevAn > 1.5e-8) && (++i < 10));
/**
* Return A = An_stopping, with n_stopping < 10
*/
return An;
}
/**
* Design the SPRT test. Shorthand for
* A = sprt(delta, epsilon, t_M, m_S);
*
* Idempotent, reentrant, thread-safe.
*
* Reads: eval.delta, eval.epsilon, eval.t_M, eval.m_S
* Writes: eval.A, eval.lambdaAccept, eval.lambdaReject
*/
static inline void sacDesignSPRTTest(RHO_HEST_REFC* p){
p->eval.A = designSPRTTest(p->eval.delta, p->eval.epsilon, p->eval.t_M, p->eval.m_S);
p->eval.lambdaReject = ((1.0 - p->eval.delta) / (1.0 - p->eval.epsilon));
p->eval.lambdaAccept = (( p->eval.delta ) / ( p->eval.epsilon ));
}
/**
* Return whether the current model is the best model so far.
*/
static inline int sacIsBestModel(RHO_HEST_REFC* p){
return p->curr.numInl > p->best.numInl;
}
/**
* Returns whether the current-best model is good enough to be an
* acceptable best model, by checking whether it meets the minimum
* number of inliers.
*/
static inline int sacIsBestModelGoodEnough(RHO_HEST_REFC* p){
return p->best.numInl >= p->arg.minInl;
}
/**
* Make current model new best model by swapping the homography, inlier mask
* and count of inliers between the current and best models.
*/
static inline void sacSaveBestModel(RHO_HEST_REFC* p){
float* H = p->curr.H;
char* inl = p->curr.inl;
unsigned numInl = p->curr.numInl;
p->curr.H = p->best.H;
p->curr.inl = p->best.inl;
p->curr.numInl = p->best.numInl;
p->best.H = H;
p->best.inl = inl;
p->best.numInl = numInl;
}
/**
* Compute NR table entries [start, N) for given beta.
*/
static inline void sacInitNonRand(double beta,
unsigned start,
unsigned N,
unsigned* nonRandMinInl){
unsigned n = m+1 > start ? m+1 : start;
double beta_beta1_sq_chi = sqrt(beta*(1.0-beta)) * CHI_SQ;
for(; n < N; n++){
double mu = n * beta;
double sigma = sqrt(n)* beta_beta1_sq_chi;
unsigned i_min = ceil(m + mu + sigma);
nonRandMinInl[n] = i_min;
}
}
/**
* Optimize the stopping criterion to account for the non-randomness criterion
* of PROSAC.
*/
static inline void sacNStarOptimize(RHO_HEST_REFC* p){
unsigned min_sample_length = 10*2; /*(p->N * INLIERS_RATIO) */
unsigned best_n = p->arg.N;
unsigned test_n = best_n;
unsigned bestNumInl = p->best.numInl;
unsigned testNumInl = bestNumInl;
for(;test_n > min_sample_length && testNumInl;test_n--){
if(testNumInl*best_n > bestNumInl*test_n){
if(testNumInl < p->nr.tbl[test_n]){
break;
}
best_n = test_n;
bestNumInl = testNumInl;
}
testNumInl -= !!p->arg.inl[test_n-1];
}
if(bestNumInl*p->ctrl.phMax > p->ctrl.phNumInl*best_n){
p->ctrl.phMax = best_n;
p->ctrl.phNumInl = bestNumInl;
p->arg.maxI = sacCalcIterBound(p->arg.cfd,
(double)p->ctrl.phNumInl/p->ctrl.phMax,
m,
p->arg.maxI);
}
}
/**
* Classic RANSAC iteration bound based on largest # of inliers.
*/
static inline void sacUpdateBounds(RHO_HEST_REFC* p){
p->arg.maxI = sacCalcIterBound(p->arg.cfd,
(double)p->best.numInl/p->arg.N,
m,
p->arg.maxI);
}
/**
* Ouput the best model so far to the output argument.
*/
static inline void sacOutputModel(RHO_HEST_REFC* p){
if(sacIsBestModelGoodEnough(p)){
memcpy(p->arg.finalH, p->best.H, HSIZE);
}else{
sacOutputZeroH(p);
}
}
/**
* Ouput a zeroed H to the output argument.
*/
static inline void sacOutputZeroH(RHO_HEST_REFC* p){
memset(p->arg.finalH, 0, HSIZE);
}
/**
* Compute the real-valued number of samples per phase, given the RANSAC convergence speed,
* data set size and sample size.
*/
static inline double sacInitPEndFpI(const unsigned ransacConvg,
const unsigned n,
const unsigned s){
double numer=1, denom=1;
unsigned i;
for(i=0;i<s;i++){
numer *= s-i;
denom *= n-i;
}
return ransacConvg*numer/denom;
}
/**
* Choose, without repetition, sampleSize integers in the range [0, numDataPoints).
*/
static inline void sacRndSmpl(unsigned sampleSize,
unsigned* currentSample,
unsigned dataSetSize){
/**
* If sampleSize is very close to dataSetSize, we use selection sampling.
* Otherwise we use the naive sampling technique wherein we select random
* indexes until sampleSize of them are distinct.
*/
if(sampleSize*2>dataSetSize){
/**
* Selection Sampling:
*
* Algorithm S (Selection sampling technique). To select n records at random from a set of N, where 0 < n ≤ N.
* S1. [Initialize.] Set t ← 0, m ← 0. (During this algorithm, m represents the number of records selected so far,
* and t is the total number of input records that we have dealt with.)
* S2. [Generate U.] Generate a random number U, uniformly distributed between zero and one.
* S3. [Test.] If (N – t)U ≥ n – m, go to step S5.
* S4. [Select.] Select the next record for the sample, and increase m and t by 1. If m < n, go to step S2;
* otherwise the sample is complete and the algorithm terminates.
* S5. [Skip.] Skip the next record (do not include it in the sample), increase t by 1, and go back to step S2.
*
* Replaced m with i and t with j in the below code.
*/
unsigned i=0,j=0;
for(i=0;i<sampleSize;j++){
double U=sacRandom();
if((dataSetSize-j)*U < (sampleSize-i)){
currentSample[i++]=j;
}
}
}else{
/**
* Naive sampling technique. Generate indexes until sampleSize of them are distinct.
*/
unsigned i, j;
for(i=0;i<sampleSize;i++){
int inList;
do{
currentSample[i]=dataSetSize*sacRandom();
inList=0;
for(j=0;j<i;j++){
if(currentSample[i] == currentSample[j]){
inList=1;
break;
}
}
}while(inList);
}
}
}
/**
* Generates a random double uniformly distributed in the range [0, 1].
*/
static inline double sacRandom(void){
#ifdef _WIN32
return ((double)rand())/RAND_MAX;
#else
return ((double)random())/INT_MAX;
#endif
}
/**
* Estimate the number of iterations required based on the requested confidence,
* proportion of inliers in the best model so far and sample size.
*
* Clamp return value at maxIterationBound.
*/
static inline unsigned sacCalcIterBound(double confidence,
double inlierRate,
unsigned sampleSize,
unsigned maxIterBound){
unsigned retVal;
/**
* Formula chosen from http://en.wikipedia.org/wiki/RANSAC#The_parameters :
*
* \[ k = \frac{\log{(1-confidence)}}{\log{(1-inlierRate**sampleSize)}} \]
*/
double atLeastOneOutlierProbability = 1.-pow(inlierRate, (double)sampleSize);
/**
* There are two special cases: When argument to log() is 0 and when it is 1.
* Each has a special meaning.
*/
if(atLeastOneOutlierProbability>=1.){
/**
* A certainty of picking at least one outlier means that we will need
* an infinite amount of iterations in order to find a correct solution.
*/
retVal = maxIterBound;
}else if(atLeastOneOutlierProbability<=0.){
/**
* The certainty of NOT picking an outlier means that only 1 iteration
* is needed to find a solution.
*/
retVal = 1;
}else{
/**
* Since 1-confidence (the probability of the model being based on at
* least one outlier in the data) is equal to
* (1-inlierRate**sampleSize)**numIterations (the probability of picking
* at least one outlier in numIterations samples), we can isolate
* numIterations (the return value) into
*/
retVal = ceil(log(1.-confidence)/log(atLeastOneOutlierProbability));
}
/**
* Clamp to maxIterationBound.
*/
return retVal <= maxIterBound ? retVal : maxIterBound;
}
/**
* Given 4 matches, computes the homography that relates them using Gaussian
* Elimination. The row operations are as given in the paper.
*
* TODO: Clean this up. The code is hideous, and might even conceal sign bugs
* (specifically relating to whether the last column should be negated,
* or not).
*/
static void hFuncRefC(float* packedPoints,/* Source (four x,y float coordinates) points followed by
destination (four x,y float coordinates) points, aligned by 32 bytes */
float* H){ /* Homography (three 16-byte aligned rows of 3 floats) */
float x0=*packedPoints++;
float y0=*packedPoints++;
float x1=*packedPoints++;
float y1=*packedPoints++;
float x2=*packedPoints++;
float y2=*packedPoints++;
float x3=*packedPoints++;
float y3=*packedPoints++;
float X0=*packedPoints++;
float Y0=*packedPoints++;
float X1=*packedPoints++;
float Y1=*packedPoints++;
float X2=*packedPoints++;
float Y2=*packedPoints++;
float X3=*packedPoints++;
float Y3=*packedPoints++;
float x0X0=x0*X0, x1X1=x1*X1, x2X2=x2*X2, x3X3=x3*X3;
float x0Y0=x0*Y0, x1Y1=x1*Y1, x2Y2=x2*Y2, x3Y3=x3*Y3;
float y0X0=y0*X0, y1X1=y1*X1, y2X2=y2*X2, y3X3=y3*X3;
float y0Y0=y0*Y0, y1Y1=y1*Y1, y2Y2=y2*Y2, y3Y3=y3*Y3;
/**
* [0] [1] Hidden Prec
* x0 y0 1 x1
* x1 y1 1 x1
* x2 y2 1 x1
* x3 y3 1 x1
*
* Eliminate ones in column 2 and 5.
* R(0)-=R(2)
* R(1)-=R(2)
* R(3)-=R(2)
*
* [0] [1] Hidden Prec
* x0-x2 y0-y2 0 x1+1
* x1-x2 y1-y2 0 x1+1
* x2 y2 1 x1
* x3-x2 y3-y2 0 x1+1
*
* Eliminate column 0 of rows 1 and 3
* R(1)=(x0-x2)*R(1)-(x1-x2)*R(0), y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
* R(3)=(x0-x2)*R(3)-(x3-x2)*R(0), y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
*
* [0] [1] Hidden Prec
* x0-x2 y0-y2 0 x1+1
* 0 y1' 0 x2+3
* x2 y2 1 x1
* 0 y3' 0 x2+3
*
* Eliminate column 1 of rows 0 and 3
* R(3)=y1'*R(3)-y3'*R(1)
* R(0)=y1'*R(0)-(y0-y2)*R(1)
*
* [0] [1] Hidden Prec
* x0' 0 0 x3+5
* 0 y1' 0 x2+3
* x2 y2 1 x1
* 0 0 0 x4+7
*
* Eliminate columns 0 and 1 of row 2
* R(0)/=x0'
* R(1)/=y1'
* R(2)-= (x2*R(0) + y2*R(1))
*
* [0] [1] Hidden Prec
* 1 0 0 x6+10
* 0 1 0 x4+6
* 0 0 1 x4+7
* 0 0 0 x4+7
*/
/**
* Eliminate ones in column 2 and 5.
* R(0)-=R(2)
* R(1)-=R(2)
* R(3)-=R(2)
*/
/*float minor[4][2] = {{x0-x2,y0-y2},
{x1-x2,y1-y2},
{x2 ,y2 },
{x3-x2,y3-y2}};*/
/*float major[8][3] = {{x2X2-x0X0,y2X2-y0X0,(X0-X2)},
{x2X2-x1X1,y2X2-y1X1,(X1-X2)},
{-x2X2 ,-y2X2 ,(X2 )},
{x2X2-x3X3,y2X2-y3X3,(X3-X2)},
{x2Y2-x0Y0,y2Y2-y0Y0,(Y0-Y2)},
{x2Y2-x1Y1,y2Y2-y1Y1,(Y1-Y2)},
{-x2Y2 ,-y2Y2 ,(Y2 )},
{x2Y2-x3Y3,y2Y2-y3Y3,(Y3-Y2)}};*/
float minor[2][4] = {{x0-x2,x1-x2,x2 ,x3-x2},
{y0-y2,y1-y2,y2 ,y3-y2}};
float major[3][8] = {{x2X2-x0X0,x2X2-x1X1,-x2X2 ,x2X2-x3X3,x2Y2-x0Y0,x2Y2-x1Y1,-x2Y2 ,x2Y2-x3Y3},
{y2X2-y0X0,y2X2-y1X1,-y2X2 ,y2X2-y3X3,y2Y2-y0Y0,y2Y2-y1Y1,-y2Y2 ,y2Y2-y3Y3},
{ (X0-X2) , (X1-X2) , (X2 ) , (X3-X2) , (Y0-Y2) , (Y1-Y2) , (Y2 ) , (Y3-Y2) }};
/**
* int i;
* for(i=0;i<8;i++) major[2][i]=-major[2][i];
* Eliminate column 0 of rows 1 and 3
* R(1)=(x0-x2)*R(1)-(x1-x2)*R(0), y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
* R(3)=(x0-x2)*R(3)-(x3-x2)*R(0), y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
*/
float scalar1=minor[0][0], scalar2=minor[0][1];
minor[1][1]=minor[1][1]*scalar1-minor[1][0]*scalar2;
major[0][1]=major[0][1]*scalar1-major[0][0]*scalar2;
major[1][1]=major[1][1]*scalar1-major[1][0]*scalar2;
major[2][1]=major[2][1]*scalar1-major[2][0]*scalar2;
major[0][5]=major[0][5]*scalar1-major[0][4]*scalar2;
major[1][5]=major[1][5]*scalar1-major[1][4]*scalar2;
major[2][5]=major[2][5]*scalar1-major[2][4]*scalar2;
scalar2=minor[0][3];
minor[1][3]=minor[1][3]*scalar1-minor[1][0]*scalar2;
major[0][3]=major[0][3]*scalar1-major[0][0]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][0]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][0]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][4]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][4]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][4]*scalar2;
/**
* Eliminate column 1 of rows 0 and 3
* R(3)=y1'*R(3)-y3'*R(1)
* R(0)=y1'*R(0)-(y0-y2)*R(1)
*/
scalar1=minor[1][1];scalar2=minor[1][3];
major[0][3]=major[0][3]*scalar1-major[0][1]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][1]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][1]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][5]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][5]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][5]*scalar2;
scalar2=minor[1][0];
minor[0][0]=minor[0][0]*scalar1-minor[0][1]*scalar2;
major[0][0]=major[0][0]*scalar1-major[0][1]*scalar2;
major[1][0]=major[1][0]*scalar1-major[1][1]*scalar2;
major[2][0]=major[2][0]*scalar1-major[2][1]*scalar2;
major[0][4]=major[0][4]*scalar1-major[0][5]*scalar2;
major[1][4]=major[1][4]*scalar1-major[1][5]*scalar2;
major[2][4]=major[2][4]*scalar1-major[2][5]*scalar2;
/**
* Eliminate columns 0 and 1 of row 2
* R(0)/=x0'
* R(1)/=y1'
* R(2)-= (x2*R(0) + y2*R(1))
*/
scalar1=minor[0][0];
major[0][0]/=scalar1;
major[1][0]/=scalar1;
major[2][0]/=scalar1;
major[0][4]/=scalar1;
major[1][4]/=scalar1;
major[2][4]/=scalar1;
scalar1=minor[1][1];
major[0][1]/=scalar1;
major[1][1]/=scalar1;
major[2][1]/=scalar1;
major[0][5]/=scalar1;
major[1][5]/=scalar1;
major[2][5]/=scalar1;
scalar1=minor[0][2];scalar2=minor[1][2];
major[0][2]-=major[0][0]*scalar1+major[0][1]*scalar2;
major[1][2]-=major[1][0]*scalar1+major[1][1]*scalar2;
major[2][2]-=major[2][0]*scalar1+major[2][1]*scalar2;
major[0][6]-=major[0][4]*scalar1+major[0][5]*scalar2;
major[1][6]-=major[1][4]*scalar1+major[1][5]*scalar2;
major[2][6]-=major[2][4]*scalar1+major[2][5]*scalar2;
/* Only major matters now. R(3) and R(7) correspond to the hollowed-out rows. */
scalar1=major[0][7];
major[1][7]/=scalar1;
major[2][7]/=scalar1;
scalar1=major[0][0];major[1][0]-=scalar1*major[1][7];major[2][0]-=scalar1*major[2][7];
scalar1=major[0][1];major[1][1]-=scalar1*major[1][7];major[2][1]-=scalar1*major[2][7];
scalar1=major[0][2];major[1][2]-=scalar1*major[1][7];major[2][2]-=scalar1*major[2][7];
scalar1=major[0][3];major[1][3]-=scalar1*major[1][7];major[2][3]-=scalar1*major[2][7];
scalar1=major[0][4];major[1][4]-=scalar1*major[1][7];major[2][4]-=scalar1*major[2][7];
scalar1=major[0][5];major[1][5]-=scalar1*major[1][7];major[2][5]-=scalar1*major[2][7];
scalar1=major[0][6];major[1][6]-=scalar1*major[1][7];major[2][6]-=scalar1*major[2][7];
/* One column left (Two in fact, but the last one is the homography) */
scalar1=major[1][3];
major[2][3]/=scalar1;
scalar1=major[1][0];major[2][0]-=scalar1*major[2][3];
scalar1=major[1][1];major[2][1]-=scalar1*major[2][3];
scalar1=major[1][2];major[2][2]-=scalar1*major[2][3];
scalar1=major[1][4];major[2][4]-=scalar1*major[2][3];
scalar1=major[1][5];major[2][5]-=scalar1*major[2][3];
scalar1=major[1][6];major[2][6]-=scalar1*major[2][3];
scalar1=major[1][7];major[2][7]-=scalar1*major[2][3];
/* Homography is done. */
H[0]=major[2][0];
H[1]=major[2][1];
H[2]=major[2][2];
H[3]=major[2][4];
H[4]=major[2][5];
H[5]=major[2][6];
H[6]=major[2][7];
H[7]=major[2][3];
H[8]=1.0;
}
/**
* Returns whether refinement is possible.
*
* NB This is separate from whether it is *enabled*.
*/
static inline int sacCanRefine(RHO_HEST_REFC* p){
/**
* If we only have 4 matches, GE's result is already optimal and cannot
* be refined any further.
*/
return p->best.numInl > m;
}
/**
* Refines the best-so-far homography.
*
* BUG: Totally broken for now. DO NOT ENABLE.
*/
static inline void sacRefine(RHO_HEST_REFC* p){
int i, j;
float S; /* Sum of squared errors */
float L = 1;/* Lambda of LevMarq */
for(i=0;i<MAXLEVMARQITERS;i++){
float dH[8];
sacCalcJtMats(p->lm.JtJ, p->lm.Jte, &S, p->best.H, p->arg.src, p->arg.dst, p->arg.inl, p->arg.N);
sacScaleDiag8x8(p->lm.JtJ, L, p->lm.JtJ);
sacChol8x8(p->lm.JtJ, p->lm.JtJ);
sacTRInv8x8(p->lm.JtJ, p->lm.JtJ);
sacTRISolve8x8(p->lm.JtJ, p->lm.Jte, dH);
sacSub8x1(p->best.H, p->best.H, dH);
}
}
/**
* Compute directly the JtJ, Jte and sum-of-squared-error for a given
* homography and set of inliers.
*
* This is possible because the product of J and its transpose as well as with
* the error and the sum-of-squared-error can all be computed additively
* (match-by-match), as one would intuitively expect; All matches make
* contributions to the error independently of each other.
*
* What this allows is a constant-space implementation of Lev-Marq that can
* nevertheless be vectorized if need be.
*
* @param JtJ
* @param Jte
* @param Sp
* @param H
* @param src
* @param dst
* @param inl
* @param N
*/
static inline void sacCalcJtMats(float (* restrict JtJ)[8],
float* restrict Jte,
float* restrict Sp,
const float* restrict H,
const float* restrict src,
const float* restrict dst,
const char* restrict inl,
unsigned N){
unsigned i;
float S;
/* Zero out JtJ, Jte and S */
memset(JtJ, 0, 8*8*sizeof(*JtJ));
memset(Jte, 0, 8*1*sizeof(*Jte));
S = 0.0f;
/* Additively compute JtJ and Jte */
for(i=0;i<N;i++){
/* Skip outliers */
if(!inl[i]){
continue;
}
/**
* Otherwise, compute additively the upper triangular matrix JtJ and
* the Jtd vector within the following formula:
*
* LaTeX:
* (J^{T}J + \lambda \diag( J^{T}J )) \beta = J^{T}[ y - f(\Beta) ]
* Simplified ASCII:
* (JtJ + L*diag(JtJ)) beta = Jt e, where e (error) is y-f(Beta).
*
* For this we need to calculate
* 1) The 2D error (e) of the homography on the current point i
* using the current parameters Beta.
* 2) The derivatives (J) of the error on the current point i under
* perturbations of the current parameters Beta.
* Accumulate products of the error times the derivative to Jte, and
* products of the derivatives to JtJ.
*/
/* Compute Squared Error */
float x = src[2*i+0];
float y = src[2*i+1];
float X = dst[2*i+0];
float Y = dst[2*i+1];
float W = (H[6]*x + H[7]*y + 1.0f);
float iW = W<FLT_EPSILON ? 1.0f/W : 0;
float reprojX = (H[0]*x + H[1]*y + H[2]) * iW;
float reprojY = (H[3]*x + H[4]*y + H[5]) * iW;
float eX = reprojX - X;
float eY = reprojY - Y;
float e = eX*eX + eY*eY;
S += e;
/* Compute Jacobian */
float dxh11 = x * iW;
float dxh12 = y * iW;
float dxh13 = iW;
float dxh21 = 0.0f;
float dxh22 = 0.0f;
float dxh23 = 0.0f;
float dxh31 = -reprojX*x * iW;
float dxh32 = -reprojX*y * iW;
float dyh11 = 0.0f;
float dyh12 = 0.0f;
float dyh13 = 0.0f;
float dyh21 = x * iW;
float dyh22 = y * iW;
float dyh23 = iW;
float dyh31 = -reprojY*x * iW;
float dyh32 = -reprojY*y * iW;
/* Update Jte: X Y */
Jte[0] += eX *dxh11 + eY *dyh11;
Jte[1] += eX *dxh12 + eY *dyh12;
Jte[2] += eX *dxh13 + eY *dyh13;
Jte[3] += eX *dxh21 + eY *dyh21;
Jte[4] += eX *dxh22 + eY *dyh22;
Jte[5] += eX *dxh23 + eY *dyh23;
Jte[6] += eX *dxh31 + eY *dyh31;
Jte[7] += eX *dxh32 + eY *dyh32;
/* Update JtJ: X Y */
JtJ[0][0] += dxh11*dxh11 + dyh11*dyh11;
JtJ[1][0] += dxh11*dxh12 + dyh11*dyh12;
JtJ[1][1] += dxh12*dxh12 + dyh12*dyh12;
JtJ[2][0] += dxh11*dxh13 + dyh11*dyh13;
JtJ[2][1] += dxh12*dxh13 + dyh12*dyh13;
JtJ[2][2] += dxh13*dxh13 + dyh13*dyh13;
JtJ[3][0] += dxh11*dxh21 + dyh11*dyh21;
JtJ[3][1] += dxh12*dxh21 + dyh12*dyh21;
JtJ[3][2] += dxh13*dxh21 + dyh13*dyh21;
JtJ[3][3] += dxh21*dxh21 + dyh21*dyh21;
JtJ[4][0] += dxh11*dxh22 + dyh11*dyh22;
JtJ[4][1] += dxh12*dxh22 + dyh12*dyh22;
JtJ[4][2] += dxh13*dxh22 + dyh13*dyh22;
JtJ[4][3] += dxh21*dxh22 + dyh21*dyh22;
JtJ[4][4] += dxh22*dxh22 + dyh22*dyh22;
JtJ[5][0] += dxh11*dxh23 + dyh11*dyh23;
JtJ[5][1] += dxh12*dxh23 + dyh12*dyh23;
JtJ[5][2] += dxh13*dxh23 + dyh13*dyh23;
JtJ[5][3] += dxh21*dxh23 + dyh21*dyh23;
JtJ[5][4] += dxh22*dxh23 + dyh22*dyh23;
JtJ[5][5] += dxh23*dxh23 + dyh23*dyh23;
JtJ[6][0] += dxh11*dxh31 + dyh11*dyh31;
JtJ[6][1] += dxh12*dxh31 + dyh12*dyh31;
JtJ[6][2] += dxh13*dxh31 + dyh13*dyh31;
JtJ[6][3] += dxh21*dxh31 + dyh21*dyh31;
JtJ[6][4] += dxh22*dxh31 + dyh22*dyh31;
JtJ[6][5] += dxh23*dxh31 + dyh23*dyh31;
JtJ[6][6] += dxh31*dxh31 + dyh31*dyh31;
JtJ[7][0] += dxh11*dxh32 + dyh11*dyh32;
JtJ[7][1] += dxh12*dxh32 + dyh12*dyh32;
JtJ[7][2] += dxh13*dxh32 + dyh13*dyh32;
JtJ[7][3] += dxh21*dxh32 + dyh21*dyh32;
JtJ[7][4] += dxh22*dxh32 + dyh22*dyh32;
JtJ[7][5] += dxh23*dxh32 + dyh23*dyh32;
JtJ[7][6] += dxh31*dxh32 + dyh31*dyh32;
JtJ[7][7] += dxh32*dxh32 + dyh32*dyh32;
}
*Sp = S;
}
/**
* Cholesky decomposition on 8x8 real positive-definite matrix defined by its
* lower-triangular half. Outputs L, the lower triangular part of the
* decomposition.
*
* A and L can overlap fully (in-place) or not at all, but may not partially
* overlap.
*
* Source: http://en.wikipedia.org/wiki/Cholesky_decomposition#
* The_Cholesky.E2.80.93Banachiewicz_and_Cholesky.E2.80.93Crout_algorithms
*/
static inline void sacChol8x8(const float (*A)[8],
float (*L)[8]){
const register int N = 8;
int i, j, k;
double x;
for(i=0;i<N;i++){/* Row */
/* Pre-diagonal elements */
for(j=0;j<i;j++){
x = A[i][j]; /* Aij */
for(k=0;k<j;k++){
x -= (double)L[i][k] * L[j][k];/* - Sum_{k=0..j-1} Lik*Ljk */
}
L[i][j] = x / L[j][j]; /* Lij = ... / Ljj */
}
/* Diagonal element */
{j = i;
x = A[j][j]; /* Ajj */
for(k=0;k<j;k++){
x -= (double)L[j][k] * L[j][k];/* - Sum_{k=0..j-1} Ljk^2 */
}
L[j][j] = sqrt(x); /* Ljj = sqrt( ... ) */
}
}
}
/**
* Invert lower-triangular 8x8 matrix L into lower-triangular matrix M.
*
* L and M can overlap fully (in-place) or not at all, but may not partially
* overlap.
*
* Uses formulation from
* http://www.cs.berkeley.edu/~knight/knight_math221_poster.pdf
* , adjusted for the fact that A^T^-1 = A^-1^T. Thus:
*
* U11 U12 U11^-1 -U11^-1*U12*U22^-1
* ->
* 0 U22 0 U22^-1
*
* Becomes
*
* L11 0 L11^-1 0
* ->
* L21 L22 -L22^-1*L21*L11^-1 L22^-1
*
* Since
*
* ( -L11^T^-1*L21^T*L22^T^-1 )^T = -L22^T^-1^T*L21^T^T*L11^T^-1^T
* = -L22^T^T^-1*L21^T^T*L11^T^T^-1
* = -L22^-1*L21*L11^-1
*/
static inline void sacTRInv8x8(const float (*L)[8],
float (*M)[8]){
float s[2][2], t[2][2];
float u[4][4], v[4][4];
/*
L00 0 0 0 0 0 0 0
L10 L11 0 0 0 0 0 0
L20 L21 L22 0 0 0 0 0
L30 L31 L32 L33 0 0 0 0
L40 L41 L42 L43 L44 0 0 0
L50 L51 L52 L53 L54 L55 0 0
L60 L61 L62 L63 L64 L65 L66 0
L70 L71 L72 L73 L74 L75 L76 L77
*/
/* Invert 4*2 1x1 matrices; Starts recursion. */
M[0][0] = 1.0f/L[0][0];
M[1][1] = 1.0f/L[1][1];
M[2][2] = 1.0f/L[2][2];
M[3][3] = 1.0f/L[3][3];
M[4][4] = 1.0f/L[4][4];
M[5][5] = 1.0f/L[5][5];
M[6][6] = 1.0f/L[6][6];
M[7][7] = 1.0f/L[7][7];
/*
M00 0 0 0 0 0 0 0
L10 M11 0 0 0 0 0 0
L20 L21 M22 0 0 0 0 0
L30 L31 L32 M33 0 0 0 0
L40 L41 L42 L43 M44 0 0 0
L50 L51 L52 L53 L54 M55 0 0
L60 L61 L62 L63 L64 L65 M66 0
L70 L71 L72 L73 L74 L75 L76 M77
*/
/* 4*2 Matrix products of 1x1 matrices */
M[1][0] = -M[1][1]*L[1][0]*M[0][0];
M[3][2] = -M[3][3]*L[3][2]*M[2][2];
M[5][4] = -M[5][5]*L[5][4]*M[4][4];
M[7][6] = -M[7][7]*L[7][6]*M[6][6];
/*
M00 0 0 0 0 0 0 0
M10 M11 0 0 0 0 0 0
L20 L21 M22 0 0 0 0 0
L30 L31 M32 M33 0 0 0 0
L40 L41 L42 L43 M44 0 0 0
L50 L51 L52 L53 M54 M55 0 0
L60 L61 L62 L63 L64 L65 M66 0
L70 L71 L72 L73 L74 L75 M76 M77
*/
/* 2*2 Matrix products of 2x2 matrices */
/*
(M22 0 ) (L20 L21) (M00 0 )
- (M32 M33) x (L30 L31) x (M10 M11)
*/
s[0][0] = M[2][2]*L[2][0];
s[0][1] = M[2][2]*L[2][1];
s[1][0] = M[3][2]*L[2][0]+M[3][3]*L[3][0];
s[1][1] = M[3][2]*L[2][1]+M[3][3]*L[3][1];
t[0][0] = s[0][0]*M[0][0]+s[0][1]*M[1][0];
t[0][1] = s[0][1]*M[1][1];
t[1][0] = s[1][0]*M[0][0]+s[1][1]*M[1][0];
t[1][1] = s[1][1]*M[1][1];
M[2][0] = -t[0][0];
M[2][1] = -t[0][1];
M[3][0] = -t[1][0];
M[3][1] = -t[1][1];
/*
(M66 0 ) (L64 L65) (M44 0 )
- (L76 M77) x (L74 L75) x (M54 M55)
*/
s[0][0] = M[6][6]*L[6][4];
s[0][1] = M[6][6]*L[6][5];
s[1][0] = M[7][6]*L[6][4]+M[7][7]*L[7][4];
s[1][1] = M[7][6]*L[6][5]+M[7][7]*L[7][5];
t[0][0] = s[0][0]*M[4][4]+s[0][1]*M[5][4];
t[0][1] = s[0][1]*M[5][5];
t[1][0] = s[1][0]*M[4][4]+s[1][1]*M[5][4];
t[1][1] = s[1][1]*M[5][5];
M[6][4] = -t[0][0];
M[6][5] = -t[0][1];
M[7][4] = -t[1][0];
M[7][5] = -t[1][1];
/*
M00 0 0 0 0 0 0 0
M10 M11 0 0 0 0 0 0
M20 M21 M22 0 0 0 0 0
M30 M31 M32 M33 0 0 0 0
L40 L41 L42 L43 M44 0 0 0
L50 L51 L52 L53 M54 M55 0 0
L60 L61 L62 L63 M64 M65 M66 0
L70 L71 L72 L73 M74 M75 M76 M77
*/
/* 1*2 Matrix products of 4x4 matrices */
/*
(M44 0 0 0 ) (L40 L41 L42 L43) (M00 0 0 0 )
(M54 M55 0 0 ) (L50 L51 L52 L53) (M10 M11 0 0 )
(M64 M65 M66 0 ) (L60 L61 L62 L63) (M20 M21 M22 0 )
- (M74 M75 M76 M77) x (L70 L71 L72 L73) x (M30 M31 M32 M33)
*/
u[0][0] = M[4][4]*L[4][0];
u[0][1] = M[4][4]*L[4][1];
u[0][2] = M[4][4]*L[4][2];
u[0][3] = M[4][4]*L[4][3];
u[1][0] = M[5][4]*L[4][0]+M[5][5]*L[5][0];
u[1][1] = M[5][4]*L[4][1]+M[5][5]*L[5][1];
u[1][2] = M[5][4]*L[4][2]+M[5][5]*L[5][2];
u[1][3] = M[5][4]*L[4][3]+M[5][5]*L[5][3];
u[2][0] = M[6][4]*L[4][0]+M[6][5]*L[5][0]+M[6][6]*L[6][0];
u[2][1] = M[6][4]*L[4][1]+M[6][5]*L[5][1]+M[6][6]*L[6][1];
u[2][2] = M[6][4]*L[4][2]+M[6][5]*L[5][2]+M[6][6]*L[6][2];
u[2][3] = M[6][4]*L[4][3]+M[6][5]*L[5][3]+M[6][6]*L[6][3];
u[3][0] = M[7][4]*L[4][0]+M[7][5]*L[5][0]+M[7][6]*L[6][0]+M[7][7]*L[7][0];
u[3][1] = M[7][4]*L[4][1]+M[7][5]*L[5][1]+M[7][6]*L[6][1]+M[7][7]*L[7][1];
u[3][2] = M[7][4]*L[4][2]+M[7][5]*L[5][2]+M[7][6]*L[6][2]+M[7][7]*L[7][2];
u[3][3] = M[7][4]*L[4][3]+M[7][5]*L[5][3]+M[7][6]*L[6][3]+M[7][7]*L[7][3];
v[0][0] = u[0][0]*M[0][0]+u[0][1]*M[1][0]+u[0][2]*M[2][0]+u[0][3]*M[3][0];
v[0][1] = u[0][1]*M[1][1]+u[0][2]*M[2][1]+u[0][3]*M[3][1];
v[0][2] = u[0][2]*M[2][2]+u[0][3]*M[3][2];
v[0][3] = u[0][3]*M[3][3];
v[1][0] = u[1][0]*M[0][0]+u[1][1]*M[1][0]+u[1][2]*M[2][0]+u[1][3]*M[3][0];
v[1][1] = u[1][1]*M[1][1]+u[1][2]*M[2][1]+u[1][3]*M[3][1];
v[1][2] = u[1][2]*M[2][2]+u[1][3]*M[3][2];
v[1][3] = u[1][3]*M[3][3];
v[2][0] = u[2][0]*M[0][0]+u[2][1]*M[1][0]+u[2][2]*M[2][0]+u[2][3]*M[3][0];
v[2][1] = u[2][1]*M[1][1]+u[2][2]*M[2][1]+u[2][3]*M[3][1];
v[2][2] = u[2][2]*M[2][2]+u[2][3]*M[3][2];
v[2][3] = u[2][3]*M[3][3];
v[3][0] = u[3][0]*M[0][0]+u[3][1]*M[1][0]+u[3][2]*M[2][0]+u[3][3]*M[3][0];
v[3][1] = u[3][1]*M[1][1]+u[3][2]*M[2][1]+u[3][3]*M[3][1];
v[3][2] = u[3][2]*M[2][2]+u[3][3]*M[3][2];
v[3][3] = u[3][3]*M[3][3];
M[4][0] = -v[0][0];
M[4][1] = -v[0][1];
M[4][2] = -v[0][2];
M[4][3] = -v[0][3];
M[5][0] = -v[1][0];
M[5][1] = -v[1][1];
M[5][2] = -v[1][2];
M[5][3] = -v[1][3];
M[6][0] = -v[2][0];
M[6][1] = -v[2][1];
M[6][2] = -v[2][2];
M[6][3] = -v[2][3];
M[7][0] = -v[3][0];
M[7][1] = -v[3][1];
M[7][2] = -v[3][2];
M[7][3] = -v[3][3];
/*
M00 0 0 0 0 0 0 0
M10 M11 0 0 0 0 0 0
M20 M21 M22 0 0 0 0 0
M30 M31 M32 M33 0 0 0 0
M40 M41 M42 M43 M44 0 0 0
M50 M51 M52 M53 M54 M55 0 0
M60 M61 M62 M63 M64 M65 M66 0
M70 M71 M72 M73 M74 M75 M76 M77
*/
}
/**
* Solves dH = inv(JtJ) Jte. The argument lower-triangular matrix is the
* inverse of L as produced by the Cholesky decomposition LL^T of the matrix
* JtJ; Thus the operation performed here is a left-multiplication of a vector
* by two triangular matrices. The math is below:
*
* JtJ = LL^T
* Linv = L^-1
* (JtJ)^-1 = (LL^T)^-1
* = (L^T^-1)(Linv)
* = (Linv^T)(Linv)
* dH = ((JtJ)^-1) (Jte)
* = (Linv^T)(Linv) (Jte)
*
* where J is nx8, Jt is 8xn, JtJ is 8x8 PD, e is nx1, Jte is 8x1, L is lower
* triangular 8x8 and dH is 8x1.
*/
static inline void sacTRISolve8x8(const float (*L)[8],
const float* Jte,
float* dH){
float t[8];
t[0] = L[0][0]*Jte[0];
t[1] = L[1][0]*Jte[0]+L[1][1]*Jte[1];
t[2] = L[2][0]*Jte[0]+L[2][1]*Jte[1]+L[2][2]*Jte[2];
t[3] = L[3][0]*Jte[0]+L[3][1]*Jte[1]+L[3][2]*Jte[2]+L[3][3]*Jte[3];
t[4] = L[4][0]*Jte[0]+L[4][1]*Jte[1]+L[4][2]*Jte[2]+L[4][3]*Jte[3]+L[4][4]*Jte[4];
t[5] = L[5][0]*Jte[0]+L[5][1]*Jte[1]+L[5][2]*Jte[2]+L[5][3]*Jte[3]+L[5][4]*Jte[4]+L[5][5]*Jte[5];
t[6] = L[6][0]*Jte[0]+L[6][1]*Jte[1]+L[6][2]*Jte[2]+L[6][3]*Jte[3]+L[6][4]*Jte[4]+L[6][5]*Jte[5]+L[6][6]*Jte[6];
t[7] = L[7][0]*Jte[0]+L[7][1]*Jte[1]+L[7][2]*Jte[2]+L[7][3]*Jte[3]+L[7][4]*Jte[4]+L[7][5]*Jte[5]+L[7][6]*Jte[6]+L[7][7]*Jte[7];
dH[0] = L[0][0]*t[0]+L[1][0]*t[1]+L[2][0]*t[2]+L[3][0]*t[3]+L[4][0]*t[4]+L[5][0]*t[5]+L[6][0]*t[6]+L[7][0]*t[7];
dH[1] = L[1][1]*t[1]+L[2][1]*t[2]+L[3][1]*t[3]+L[4][1]*t[4]+L[5][1]*t[5]+L[6][1]*t[6]+L[7][1]*t[7];
dH[2] = L[2][2]*t[2]+L[3][2]*t[3]+L[4][2]*t[4]+L[5][2]*t[5]+L[6][2]*t[6]+L[7][2]*t[7];
dH[3] = L[3][3]*t[3]+L[4][3]*t[4]+L[5][3]*t[5]+L[6][3]*t[6]+L[7][3]*t[7];
dH[4] = L[4][4]*t[4]+L[5][4]*t[5]+L[6][4]*t[6]+L[7][4]*t[7];
dH[5] = L[5][5]*t[5]+L[6][5]*t[6]+L[7][5]*t[7];
dH[6] = L[6][6]*t[6]+L[7][6]*t[7];
dH[7] = L[7][7]*t[7];
}
/**
* Multiply the diagonal elements of the 8x8 matrix A by 1+lambda and store to
* B.
*
* A and B may overlap exactly or not at all; Partial overlap is forbidden.
*/
static inline void sacScaleDiag8x8(const float (*A)[8],
float lambda,
float (*B)[8]){
float lambdap1 = lambda + 1.0f;
int i;
if(A != B){
memcpy((void*)B, (void*)A, 8*8*sizeof(float));
}
for(i=0;i<8;i++){
B[i][i] *= lambdap1;
}
}
/**
* Subtract dH from H.
*/
static inline void sacSub8x1(float* Hout, const float* H, const float* dH){
Hout[0] = H[0] - dH[0];
Hout[1] = H[1] - dH[1];
Hout[2] = H[2] - dH[2];
Hout[3] = H[3] - dH[3];
Hout[4] = H[4] - dH[4];
Hout[5] = H[5] - dH[5];
Hout[6] = H[6] - dH[6];
Hout[7] = H[7] - dH[7];
}
#ifdef __cplusplus
}
#endif
modules/calib3d/src/rhorefc.h 0 → 100644
View file @ 68e59d61
/*
IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
By downloading, copying, installing or using the software you agree to this license.
If you do not agree to this license, do not download, install,
copy or use the software.
BSD 3-Clause License
Copyright (C) 2014, Olexa Bilaniuk, Hamid Bazargani & Robert Laganiere, all rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistribution's of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistribution's in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* The name of the copyright holders may not be used to endorse or promote products
derived from this software without specific prior written permission.
This software is provided by the copyright holders and contributors "as is" and
any express or implied warranties, including, but not limited to, the implied
warranties of merchantability and fitness for a particular purpose are disclaimed.
In no event shall the Intel Corporation or contributors be liable for any direct,
indirect, incidental, special, exemplary, or consequential damages
(including, but not limited to, procurement of substitute goods or services;
loss of use, data, or profits; or business interruption) however caused
and on any theory of liability, whether in contract, strict liability,
or tort (including negligence or otherwise) arising in any way out of
the use of this software, even if advised of the possibility of such damage.
*/
/**
* Bilaniuk, Olexa, Hamid Bazargani, and Robert Laganiere. "Fast Target
* Recognition on Mobile Devices: Revisiting Gaussian Elimination for the
* Estimation of Planar Homographies." In Computer Vision and Pattern
* Recognition Workshops (CVPRW), 2014 IEEE Conference on, pp. 119-125.
* IEEE, 2014.
*/
/* Include Guards */
#ifndef __RHOREFC_H__
#define __RHOREFC_H__
/* Includes */
/* Defines */
#ifdef __cplusplus
/* C++ does not have the restrict keyword. */
#ifdef restrict
#undef restrict
#endif
#define restrict
#else
/* C99 and over has the restrict keyword. */
#if !defined(__STDC_VERSION__) || __STDC_VERSION__ < 199901L
#define restrict
#endif
#endif
/* Flags */
#ifndef RHO_FLAG_NONE
#define RHO_FLAG_NONE (0U<<0)
#endif
#ifndef RHO_FLAG_ENABLE_NR
#define RHO_FLAG_ENABLE_NR (1U<<0)
#endif
#ifndef RHO_FLAG_ENABLE_REFINEMENT
#define RHO_FLAG_ENABLE_REFINEMENT (1U<<1)
#endif
#ifndef RHO_FLAG_ENABLE_FINAL_REFINEMENT
#define RHO_FLAG_ENABLE_FINAL_REFINEMENT (1U<<2)
#endif
/* Data structures */
/**
* Homography Estimation context.
*/
typedef struct{
/**
* Virtual Arguments.
*
* Exactly the same as at function call, except:
* - minInl is enforced to be >= 4.
*/
struct{
const float* restrict src;
const float* restrict dst;
char* restrict inl;
unsigned N;
float maxD;
unsigned maxI;
unsigned rConvg;
double cfd;
unsigned minInl;
double beta;
unsigned flags;
const float* guessH;
float* finalH;
} arg;
/* PROSAC Control */
struct{
unsigned i; /* Iteration Number */
unsigned phNum; /* Phase Number */
unsigned phEndI; /* Phase End Iteration */
double phEndFpI; /* Phase floating-point End Iteration */
unsigned phMax; /* Termination phase number */
unsigned phNumInl; /* Number of inliers for termination phase */
unsigned numModels; /* Number of models tested */
unsigned* restrict smpl; /* Sample of match indexes */
} ctrl;
/* Current model being tested */
struct{
float* restrict pkdPts; /* Packed points */
float* restrict H; /* Homography */
char* restrict inl; /* Mask of inliers */
unsigned numInl; /* Number of inliers */
} curr;
/* Best model (so far) */
struct{
float* restrict H; /* Homography */
char* restrict inl; /* Mask of inliers */
unsigned numInl; /* Number of inliers */
} best;
/* Non-randomness criterion */
struct{
unsigned* restrict tbl; /* Non-Randomness: Table */
unsigned size; /* Non-Randomness: Size */
double beta; /* Non-Randomness: Beta */
} nr;
/* SPRT Evaluator */
struct{
double t_M; /* t_M */
double m_S; /* m_S */
double epsilon; /* Epsilon */
double delta; /* delta */
double A; /* SPRT Threshold */
unsigned Ntested; /* Number of points tested */
unsigned Ntestedtotal; /* Number of points tested in total */
int good; /* Good/bad flag */
double lambdaAccept; /* Accept multiplier */
double lambdaReject; /* Reject multiplier */
} eval;
/* Levenberg-Marquardt Refinement */
struct{
float* ws; /* Levenberg-Marqhard Workspace */
float (* restrict JtJ)[8]; /* JtJ matrix */
float (* restrict tmp1)[8]; /* Temporary 1 */
float (* restrict tmp2)[8]; /* Temporary 2 */
float* restrict Jte; /* Jte vector */
} lm;
} RHO_HEST_REFC;
/* Extern C */
#ifdef __cplusplus
namespace cv{
/* extern "C" { */
#endif
/* Functions */
/**
* Initialize the estimator context, by allocating the aligned buffers
* internally needed.
*
* @param [in/out] p The uninitialized estimator context to initialize.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoRefCInit(RHO_HEST_REFC* p);
/**
* Ensure that the estimator context's internal table for non-randomness
* criterion is at least of the given size, and uses the given beta. The table
* should be larger than the maximum number of matches fed into the estimator.
*
* A value of N of 0 requests deallocation of the table.
*
* @param [in] p The initialized estimator context
* @param [in] N If 0, deallocate internal table. If > 0, ensure that the
* internal table is of at least this size, reallocating if
* necessary.
* @param [in] beta The beta-factor to use within the table.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoRefCEnsureCapacity(RHO_HEST_REFC* p, unsigned N, double beta);
/**
* Finalize the estimator context, by freeing the aligned buffers used
* internally.
*
* @param [in] p The initialized estimator context to finalize.
*/
void rhoRefCFini(RHO_HEST_REFC* p);
/**
* Estimates the homography using the given context, matches and parameters to
* PROSAC.
*
* The given context must have been initialized.
*
* The matches are provided as two arrays of N single-precision, floating-point
* (x,y) points. Points with corresponding offsets in the two arrays constitute
* a match. The homography estimation attempts to find the 3x3 matrix H which
* best maps the homogeneous-coordinate points in the source array to their
* corresponding homogeneous-coordinate points in the destination array.
*
* Note: At least 4 matches must be provided (N >= 4).
* Note: A point in either array takes up 2 floats. The first of two stores
* the x-coordinate and the second of the two stores the y-coordinate.
* Thus, the arrays resemble this in memory:
*
* src = [x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, ...]
* Matches: | | | | |
* dst = [x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, ...]
* Note: The matches are expected to be provided sorted by quality, or at
* least not be worse-than-random in ordering.
*
* A pointer to the base of an array of N bytes can be provided. It serves as
* an output mask to indicate whether the corresponding match is an inlier to
* the returned homography, if any. A zero indicates an outlier; A non-zero
* value indicates an inlier.
*
* The PROSAC estimator requires a few parameters of its own. These are:
*
* - The maximum distance that a source point projected onto the destination
* plane can be from its putative match and still be considered an
* inlier. Must be non-negative.
* A sane default is 3.0.
* - The maximum number of PROSAC iterations. This corresponds to the
* largest number of samples that will be drawn and tested.
* A sane default is 2000.
* - The RANSAC convergence parameter. This corresponds to the number of
* iterations after which PROSAC will start sampling like RANSAC.
* A sane default is 2000.
* - The confidence threshold. This corresponds to the probability of
* finding a correct solution. Must be bounded by [0, 1].
* A sane default is 0.995.
* - The minimum number of inliers acceptable. Only a solution with at
* least this many inliers will be returned. The minimum is 4.
* A sane default is 10% of N.
* - The beta-parameter for the non-randomness termination criterion.
* Ignored if non-randomness criterion disabled, otherwise must be
* bounded by (0, 1).
* A sane default is 0.35.
* - Optional flags to control the estimation. Available flags are:
* HEST_FLAG_NONE:
* No special processing.
* HEST_FLAG_ENABLE_NR:
* Enable non-randomness criterion. If set, the beta parameter
* must also be set.
* HEST_FLAG_ENABLE_REFINEMENT:
* Enable refinement of each new best model, as they are found.
* HEST_FLAG_ENABLE_FINAL_REFINEMENT:
* Enable one final refinement of the best model found before
* returning it.
*
* The PROSAC estimator optionally accepts an extrinsic initial guess of H.
*
* The PROSAC estimator outputs a final estimate of H provided it was able to
* find one with a minimum of supporting inliers. If it was not, it outputs
* the all-zero matrix.
*
* The extrinsic guess at and final estimate of H are both in the same form:
* A 3x3 single-precision floating-point matrix with step 3. Thus, it is a
* 9-element array of floats, with the elements as follows:
*
* [ H00, H01, H02,
* H10, H11, H12,
* H20, H21, 1.0 ]
*
* Notice that the homography is normalized to H22 = 1.0.
*
* The function returns the number of inliers if it was able to find a
* homography with at least the minimum required support, and 0 if it was not.
*
*
* @param [in/out] p The context to use for homography estimation. Must
* be already initialized. Cannot be NULL.
* @param [in] src The pointer to the source points of the matches.
* Must be aligned to 4 bytes. Cannot be NULL.
* @param [in] dst The pointer to the destination points of the matches.
* Must be aligned to 4 bytes. Cannot be NULL.
* @param [out] inl The pointer to the output mask of inlier matches.
* Must be aligned to 4 bytes. May be NULL.
* @param [in] N The number of matches. Minimum 4.
* @param [in] maxD The maximum distance. Minimum 0.
* @param [in] maxI The maximum number of PROSAC iterations.
* @param [in] rConvg The RANSAC convergence parameter.
* @param [in] cfd The required confidence in the solution.
* @param [in] minInl The minimum required number of inliers. Minimum 4.
* @param [in] beta The beta-parameter for the non-randomness criterion.
* @param [in] flags A union of flags to fine-tune the estimation.
* @param [in] guessH An extrinsic guess at the solution H, or NULL if
* none provided.
* @param [out] finalH The final estimation of H, or the zero matrix if
* the minimum number of inliers was not met.
* Cannot be NULL.
* @return The number of inliers if the minimum number of
* inliers for acceptance was reached; 0 otherwise.
*/
unsigned rhoRefC(RHO_HEST_REFC* restrict p, /* Homography estimation context. */
const float* restrict src, /* Source points */
const float* restrict dst, /* Destination points */
char* restrict inl, /* Inlier mask */
unsigned N, /* = src.length = dst.length = inl.length */
float maxD, /* 3.0 */
unsigned maxI, /* 2000 */
unsigned rConvg, /* 2000 */
double cfd, /* 0.995 */
unsigned minInl, /* 4 */
double beta, /* 0.35 */
unsigned flags, /* 0 */
const float* guessH, /* Extrinsic guess, NULL if none provided */
float* finalH); /* Final result. */
/* Extern C */
#ifdef __cplusplus
/* } *//* End extern "C" */
}
#endif
#endif
modules/calib3d/src/rhosse2.cpp 0 → 100644
View file @ 68e59d61
/*
IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
By downloading, copying, installing or using the software you agree to this license.
If you do not agree to this license, do not download, install,
copy or use the software.
BSD 3-Clause License
Copyright (C) 2014, Olexa Bilaniuk, Hamid Bazargani & Robert Laganiere, all rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistribution's of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistribution's in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* The name of the copyright holders may not be used to endorse or promote products
derived from this software without specific prior written permission.
This software is provided by the copyright holders and contributors "as is" and
any express or implied warranties, including, but not limited to, the implied
warranties of merchantability and fitness for a particular purpose are disclaimed.
In no event shall the Intel Corporation or contributors be liable for any direct,
indirect, incidental, special, exemplary, or consequential damages
(including, but not limited to, procurement of substitute goods or services;
loss of use, data, or profits; or business interruption) however caused
and on any theory of liability, whether in contract, strict liability,
or tort (including negligence or otherwise) arising in any way out of
the use of this software, even if advised of the possibility of such damage.
*/
/**
* Bilaniuk, Olexa, Hamid Bazargani, and Robert Laganiere. "Fast Target
* Recognition on Mobile Devices: Revisiting Gaussian Elimination for the
* Estimation of Planar Homographies." In Computer Vision and Pattern
* Recognition Workshops (CVPRW), 2014 IEEE Conference on, pp. 119-125.
* IEEE, 2014.
*/
/* Includes */
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <stddef.h>
#include <limits.h>
#include <math.h>
#include <emmintrin.h>
#include "rhosse2.h"
/* Defines */
#define MEM_ALIGN 32
#define HSIZE (3*4*sizeof(float))
#define MIN_DELTA_CHNG 0.1
#define REL_CHNG(a, b) (fabs((a) - (b))/(a))
#define CHNG_SIGNIFICANT(a, b) (REL_CHNG(a, b) > MIN_DELTA_CHNG)
#define CHI_STAT 2.706
#define CHI_SQ 1.645
namespace cv{
/* Data Structures */
/* Prototypes */
static inline void* almalloc(size_t nBytes);
static inline void alfree(void* ptr);
static inline int sacInitRun(RHO_HEST_SSE2* restrict p,
const float* restrict src,
const float* restrict dst,
char* restrict inl,
unsigned N,
float maxD,
unsigned maxI,
unsigned rConvg,
double cfd,
unsigned minInl,
double beta,
unsigned flags,
const float* guessH,
float* finalH);
static inline void sacFiniRun(RHO_HEST_SSE2* p);
static inline int sacIsNREnabled(RHO_HEST_SSE2* p);
static inline int sacIsRefineEnabled(RHO_HEST_SSE2* p);
static inline int sacIsFinalRefineEnabled(RHO_HEST_SSE2* p);
static inline int sacPhaseEndReached(RHO_HEST_SSE2* p);
static inline void sacGoToNextPhase(RHO_HEST_SSE2* p);
static inline void sacGetPROSACSample(RHO_HEST_SSE2* p);
static inline int sacIsSampleDegenerate(RHO_HEST_SSE2* p);
static inline void sacGenerateModel(RHO_HEST_SSE2* p);
static inline int sacIsModelDegenerate(RHO_HEST_SSE2* p);
static inline void sacEvaluateModelSPRT(RHO_HEST_SSE2* p);
static inline void sacUpdateSPRT(RHO_HEST_SSE2* p);
static inline void sacDesignSPRTTest(RHO_HEST_SSE2* p);
static inline int sacIsBestModel(RHO_HEST_SSE2* p);
static inline int sacIsBestModelGoodEnough(RHO_HEST_SSE2* p);
static inline void sacSaveBestModel(RHO_HEST_SSE2* p);
static inline void sacInitNonRand(double beta,
unsigned start,
unsigned N,
unsigned* nonRandMinInl);
static inline void sacNStarOptimize(RHO_HEST_SSE2* p);
static inline void sacUpdateBounds(RHO_HEST_SSE2* p);
static inline void sacOutputModel(RHO_HEST_SSE2* p);
static inline double sacInitPEndFpI(const unsigned ransacConvg,
const unsigned n,
const unsigned m);
static inline void sacRndSmpl(unsigned sampleSize,
unsigned* currentSample,
unsigned dataSetSize);
static inline double sacRandom(void);
static inline unsigned sacCalcIterBound(double confidence,
double inlierRate,
unsigned sampleSize,
unsigned maxIterBound);
static inline void hFuncRefC(float* packedPoints, float* H);
/* Functions */
/**
* Initialize the estimator context, by allocating the aligned buffers
* internally needed.
*
* @param [in/out] p The uninitialized estimator context to initialize.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoSSE2Init(RHO_HEST_SSE2* p){
p->smpl = (unsigned*)almalloc(4*sizeof(*p->smpl));
p->H = (float*) almalloc(HSIZE);
p->bestH = (float*) almalloc(HSIZE);
p->pkdPts = (float*) almalloc(4*2*2*sizeof(*p->pkdPts));
p->nrTBL = NULL;
p->nrSize = 0;
p->nrBeta = 0.0;
int ret = p->smpl &&
p->H &&
p->bestH &&
p->pkdPts;
if(!ret){
rhoSSE2Fini(p);
}
return ret;
}
/**
* Ensure that the estimator context's internal table for non-randomness
* criterion is at least of the given size, and uses the given beta. The table
* should be larger than the maximum number of matches fed into the estimator.
*
* A value of N of 0 requests deallocation of the table.
*
* @param [in] p The initialized estimator context
* @param [in] N If 0, deallocate internal table. If > 0, ensure that the
* internal table is of at least this size, reallocating if
* necessary.
* @param [in] beta The beta-factor to use within the table.
* @return 1 if successful; 0 if an error occured.
*/
int rhoSSE2EnsureCapacity(RHO_HEST_SSE2* p, unsigned N, double beta){
unsigned* tmp;
if(N == 0){
/* Deallocate table */
alfree(p->nrTBL);
p->nrTBL = NULL;
p->nrSize = 0;
}else{
/* Ensure table at least as big as N and made for correct beta. */
if(p->nrTBL && p->nrBeta == beta && p->nrSize >= N){
/* Table already correctly set up */
}else{
if(p->nrSize < N){
/* Reallocate table because it is too small. */
tmp = (unsigned*)almalloc(N*sizeof(unsigned));
if(!tmp){
return 0;
}
/* Must recalculate in whole or part. */
if(p->nrBeta != beta){
/* Beta changed; recalculate in whole. */
sacInitNonRand(beta, 0, N, tmp);
alfree(p->nrTBL);
}else{
/* Beta did not change; Copy over any work already done. */
memcpy(tmp, p->nrTBL, p->nrSize*sizeof(unsigned));
sacInitNonRand(beta, p->nrSize, N, tmp);
alfree(p->nrTBL);
}
p->nrTBL = tmp;
p->nrSize = N;
p->nrBeta = beta;
}else{
/* Might recalculate in whole, or not at all. */
if(p->nrBeta != beta){
/* Beta changed; recalculate in whole. */
sacInitNonRand(beta, 0, p->nrSize, p->nrTBL);
p->nrBeta = beta;
}else{
/* Beta did not change; Table was already big enough. Do nothing. */
/* Besides, this is unreachable. */
}
}
}
}
return 1;
}
/**
* Finalize the estimator context, by freeing the aligned buffers used
* internally.
*
* @param [in] p The initialized estimator context to finalize.
*/
void rhoSSE2Fini(RHO_HEST_SSE2* p){
alfree(p->smpl);
alfree(p->H);
alfree(p->bestH);
alfree(p->pkdPts);
alfree(p->nrTBL);
}
/**
* Estimates the homography using the given context, matches and parameters to
* PROSAC.
*
* @param [in/out] p The context to use for homography estimation. Must
* be already initialized. Cannot be NULL.
* @param [in] src The pointer to the source points of the matches.
* Must be aligned to 16 bytes. Cannot be NULL.
* @param [in] dst The pointer to the destination points of the matches.
* Must be aligned to 16 bytes. Cannot be NULL.
* @param [out] bestInl The pointer to the output mask of inlier matches.
* Must be aligned to 16 bytes. May be NULL.
* @param [in] N The number of matches.
* @param [in] maxD The maximum distance.
* @param [in] maxI The maximum number of PROSAC iterations.
* @param [in] rConvg The RANSAC convergence parameter.
* @param [in] cfd The required confidence in the solution.
* @param [in] minInl The minimum required number of inliers.
* @param [in] beta The beta-parameter for the non-randomness criterion.
* @param [in] flags A union of flags to control the estimation.
* @param [in] guessH An extrinsic guess at the solution H, or NULL if
* none provided.
* @param [out] finalH The final estimation of H, or the zero matrix if
* the minimum number of inliers was not met.
* Cannot be NULL.
* @return The number of inliers if the minimum number of
* inliers for acceptance was reached; 0 otherwise.
*/
unsigned rhoSSE2(RHO_HEST_SSE2* restrict p, /* Homography estimation context. */
const float* restrict src, /* Source points */
const float* restrict dst, /* Destination points */
char* restrict bestInl, /* Inlier mask */
unsigned N, /* = src.length = dst.length = inl.length */
float maxD, /* 3.0 */
unsigned maxI, /* 2000 */
unsigned rConvg, /* 2000 */
double cfd, /* 0.995 */
unsigned minInl, /* 4 */
double beta, /* 0.35 */
unsigned flags, /* 0 */
const float* guessH, /* Extrinsic guess, NULL if none provided */
float* finalH){ /* Final result. */
/**
* Setup
*/
if(!sacInitRun(p, src, dst, bestInl, N, maxD, maxI, rConvg, cfd, minInl, beta, flags, guessH, finalH)){
sacFiniRun(p);
return 0;
}
/**
* PROSAC Loop
*/
for(p->i=0; p->i < p->maxI; p->i++){
if(sacPhaseEndReached(p)){
sacGoToNextPhase(p);
}
sacGetPROSACSample(p);
if(sacIsSampleDegenerate(p)){
continue;
}
sacGenerateModel(p);
if(sacIsModelDegenerate(p)){
continue;
}
sacEvaluateModelSPRT(p);
sacUpdateSPRT(p);
if(sacIsBestModel(p)){
if(sacIsRefineEnabled(p)){
/* sacRefine(p) */
}
sacSaveBestModel(p);
sacUpdateBounds(p);
if(sacIsNREnabled(p)){
sacNStarOptimize(p);
}
}
}
/**
* Teardown
*/
if(sacIsFinalRefineEnabled(p)){
/* sacRefineFinal(p) */
}
sacOutputModel(p);
sacFiniRun(p);
return sacIsBestModelGoodEnough(p) ? p->bestNumInl : 0;
}
/**
* Allocate memory aligned to a boundary of MEMALIGN.
*/
static inline void* almalloc(size_t nBytes){
if(nBytes){
unsigned char* ptr = (unsigned char*)malloc(MEM_ALIGN + nBytes);
if(ptr){
unsigned char* adj = (unsigned char*)(((intptr_t)(ptr+MEM_ALIGN))&((intptr_t)(-MEM_ALIGN)));
ptrdiff_t diff = adj - ptr;
adj[-1] = diff - 1;
return adj;
}
}
return NULL;
}
/**
* Free aligned memory
*/
static inline void alfree(void* ptr){
if(ptr){
unsigned char* cptr = (unsigned char*)ptr;
free(cptr - (ptrdiff_t)cptr[-1] - 1);
}
}
/**
* Initialize SAC for a run.
*
* Passed all the arguments of hest.
*/
static inline int sacInitRun(RHO_HEST_SSE2* restrict p,
const float* restrict src,
const float* restrict dst,
char* restrict bestInl,
unsigned N,
float maxD,
unsigned maxI,
unsigned rConvg,
double cfd,
unsigned minInl,
double beta,
unsigned flags,
const float* guessH,
float* finalH){
p->src = src;
p->dst = dst;
p->allocBestInl = !bestInl;
p->bestInl = bestInl ? bestInl : (char*)almalloc(N);
p->inl = (char*)almalloc(N);
p->N = N;
p->maxD = maxD;
p->maxI = maxI;
p->rConvg = rConvg;
p->cfd = cfd;
p->minInl = minInl < 4 ? 4 : minInl;
p->beta = beta;
p->flags = flags;
p->guessH = guessH;
p->finalH = finalH;
if(p->guessH){
memcpy(p->H, p->guessH, HSIZE);
}
memset(p->bestH, 0, HSIZE);
memset(p->finalH, 0, HSIZE);
if(!p->inl || !p->bestInl){/* Malloc failure */
return 0;
}
if(sacIsNREnabled(p) && !rhoSSE2EnsureCapacity(p, N, beta)){
return 0;
}
p->phNum = 4;
p->phEndI = 1;
p->phEndFpI = sacInitPEndFpI(p->rConvg, p->N, 4);
p->phMax = p->N;
p->phNumInl = 0;
p->bestNumInl = 0;
p->numInl = 0;
p->numModels = 0;
p->Ntested = 0;
p->Ntestedtotal = 0;
p->good = 1;
p->t_M = 25;
p->m_S = 1;
p->epsilon = 0.1;
p->delta = 0.01;
sacDesignSPRTTest(p);
return 1;
}
/**
* Finalize SAC run.
*
* @param p
*/
static inline void sacFiniRun(RHO_HEST_SSE2* p){
if(p->allocBestInl){
alfree(p->bestInl);
}
alfree(p->inl);
}
/**
* Check whether non-randomness criterion is enabled.
*
* @param p
* @return Zero if disabled; non-zero if not.
*/
static inline int sacIsNREnabled(RHO_HEST_SSE2* p){
return p->flags & RHO_FLAG_ENABLE_NR;
}
/**
* Check whether best-model-so-far refinement is enabled.
*
* @param p
* @return Zero if disabled; non-zero if not.
*/
static inline int sacIsRefineEnabled(RHO_HEST_SSE2* p){
return p->flags & RHO_FLAG_ENABLE_REFINEMENT;
}
/**
* Check whether final-model refinement is enabled.
*
* @param p
* @return Zero if disabled; non-zero if not.
*/
static inline int sacIsFinalRefineEnabled(RHO_HEST_SSE2* p){
return p->flags & RHO_FLAG_ENABLE_FINAL_REFINEMENT;
}
/**
* @brief sacPhaseEndReached
* @param p
* @return
*/
static inline int sacPhaseEndReached(RHO_HEST_SSE2* p){
return p->i >= p->phEndI && p->phNum < p->phMax;
}
/**
* @brief sacGoToNextPhase
* @param p
*/
static inline void sacGoToNextPhase(RHO_HEST_SSE2* p){
double next;
unsigned m = 4;
p->phNum++;
next = (p->phEndFpI * p->phNum)/(p->phNum - m);
p->phEndI += ceil(next - p->phEndFpI);
p->phEndFpI = next;
}
/**
* @brief sacGetPROSACSample
* @param p
*/
static inline void sacGetPROSACSample(RHO_HEST_SSE2* p){
if(p->i > p->phEndI){
sacRndSmpl(4, p->smpl, p->phNum);/* Used to be phMax */
}else{
sacRndSmpl(3, p->smpl, p->phNum-1);
p->smpl[3] = p->phNum-1;
}
}
/**
* @brief sacIsSampleDegenerate
* @param p
* @return
*/
static inline int sacIsSampleDegenerate(RHO_HEST_SSE2* p){
unsigned i0 = p->smpl[0], i1 = p->smpl[1], i2 = p->smpl[2], i3 = p->smpl[3];
/**
* Pack the matches selected by the SAC algorithm.
* Must be packed points[0:7] = {srcx0, srcy0, srcx1, srcy1, srcx2, srcy2, srcx3, srcy3}
* points[8:15] = {dstx0, dsty0, dstx1, dsty1, dstx2, dsty2, dstx3, dsty3}
* Gather 4 points into the vector
*/
__m128 src10 = _mm_castpd_ps(_mm_load_sd((const double*)&p->src[2*i0]));
src10 = _mm_loadh_pi(src10, (__m64*)&p->src[2*i1]);
__m128 src32 = _mm_castpd_ps(_mm_load_sd((const double*)&p->src[2*i2]));
src32 = _mm_loadh_pi(src32, (__m64*)&p->src[2*i3]);
__m128 dst10 = _mm_castpd_ps(_mm_load_sd((const double*)&p->dst[2*i0]));
dst10 = _mm_loadh_pi(dst10, (__m64*)&p->dst[2*i1]);
__m128 dst32 = _mm_castpd_ps(_mm_load_sd((const double*)&p->dst[2*i2]));
dst32 = _mm_loadh_pi(dst32, (__m64*)&p->dst[2*i3]);
/**
* If the matches' source points have common x and y coordinates, abort.
*/
/**
* Check:
* packedPoints[0].x == packedPoints[2].x
* packedPoints[0].y == packedPoints[2].y
* packedPoints[1].x == packedPoints[3].x
* packedPoints[1].y == packedPoints[3].y
*/
__m128 chkEq0 = _mm_cmpeq_ps(src10, src32);
/**
* Check:
* packedPoints[1].x == packedPoints[2].x
* packedPoints[1].y == packedPoints[2].y
* packedPoints[0].x == packedPoints[3].x
* packedPoints[0].y == packedPoints[3].y
*/
__m128 chkEq1 = _mm_cmpeq_ps(_mm_shuffle_ps(src10, src10, _MM_SHUFFLE(1, 0, 3, 2)), src32);
/**
* Check:
* packedPoints[0].x == packedPoints[1].x
* packedPoints[0].y == packedPoints[1].y
* packedPoints[2].x == packedPoints[3].x
* packedPoints[2].y == packedPoints[3].y
*/
__m128 chkEq2 = _mm_cmpeq_ps(_mm_shuffle_ps(src10, src32, _MM_SHUFFLE(1, 0, 1, 0)),
_mm_shuffle_ps(src10, src32, _MM_SHUFFLE(3, 2, 3, 2)));
/* Verify */
if(_mm_movemask_ps(_mm_or_ps(chkEq0, _mm_or_ps(chkEq1, chkEq2)))){
return 1;
}
/* If the matches do not satisfy the strong geometric constraint, abort. */
/**
* p6420x = (p6.x, p4.x, p2.x, p0.x)
* p6420y = (p6.y, p4.y, p2.y, p0.y)
* p7531x = (p7.x, p5.x, p3.x, p1.x)
* p7531y = (p7.y, p5.y, p3.y, p1.y)
* crosssd0 = p6420y - p7531y = (cross2d0, cross0d0, cross2s0, cross0s0)
* crosssd1 = p7531x - p6420x = (cross2d1, cross0d1, cross2s1, cross0s1)
* crosssd2 = p6420x * p7531y - p6420y * p7531x = (cross2d2, cross0d2, cross2s2, cross0s2)
*
* shufcrosssd0 = (cross0d0, cross2d0, cross0s0, cross2s0)
* shufcrosssd1 = (cross0d1, cross2d1, cross0s1, cross2s1)
* shufcrosssd2 = (cross0d2, cross2d2, cross0s2, cross2s2)
*
* dotsd0 = shufcrosssd0 * p6420x +
* shufcrosssd1 * p6420y +
* shufcrosssd2
* = (dotd0, dotd2, dots0, dots2)
* dotsd1 = shufcrosssd0 * p7531x +
* shufcrosssd1 * p7531y +
* shufcrosssd2
* = (dotd1, dotd3, dots1, dots3)
*
* dots = shufps(dotsd0, dotsd1, _MM_SHUFFLE(1, 0, 1, 0))
* dotd = shufps(dotsd0, dotsd1, _MM_SHUFFLE(3, 2, 3, 2))
* movmaskps(dots ^ dotd)
*/
__m128 p3210x = _mm_shuffle_ps(src10, src32, _MM_SHUFFLE(2, 0, 2, 0));
__m128 p3210y = _mm_shuffle_ps(src10, src32, _MM_SHUFFLE(3, 1, 3, 1));
__m128 p7654x = _mm_shuffle_ps(dst10, dst32, _MM_SHUFFLE(2, 0, 2, 0));
__m128 p7654y = _mm_shuffle_ps(dst10, dst32, _MM_SHUFFLE(3, 1, 3, 1));
__m128 p6420x = _mm_shuffle_ps(p3210x, p7654x, _MM_SHUFFLE(2, 0, 2, 0));
__m128 p6420y = _mm_shuffle_ps(p3210y, p7654y, _MM_SHUFFLE(2, 0, 2, 0));
__m128 p7531x = _mm_shuffle_ps(p3210x, p7654x, _MM_SHUFFLE(3, 1, 3, 1));
__m128 p7531y = _mm_shuffle_ps(p3210y, p7654y, _MM_SHUFFLE(3, 1, 3, 1));
__m128 crosssd0 = _mm_sub_ps(p6420y, p7531y);
__m128 crosssd1 = _mm_sub_ps(p7531x, p6420x);
__m128 crosssd2 = _mm_sub_ps(_mm_mul_ps(p6420x, p7531y), _mm_mul_ps(p6420y, p7531x));
__m128 shufcrosssd0 = _mm_shuffle_ps(crosssd0, crosssd0, _MM_SHUFFLE(2, 3, 0, 1));
__m128 shufcrosssd1 = _mm_shuffle_ps(crosssd1, crosssd1, _MM_SHUFFLE(2, 3, 0, 1));
__m128 shufcrosssd2 = _mm_shuffle_ps(crosssd2, crosssd2, _MM_SHUFFLE(2, 3, 0, 1));
__m128 dotsd0 = _mm_add_ps(_mm_add_ps(_mm_mul_ps(shufcrosssd0, p6420x),
_mm_mul_ps(shufcrosssd1, p6420y)),
shufcrosssd2);
__m128 dotsd1 = _mm_add_ps(_mm_add_ps(_mm_mul_ps(shufcrosssd0, p7531x),
_mm_mul_ps(shufcrosssd1, p7531y)),
shufcrosssd2);
__m128 dots = _mm_shuffle_ps(dotsd0, dotsd1, _MM_SHUFFLE(0, 1, 0, 1));
__m128 dotd = _mm_shuffle_ps(dotsd0, dotsd1, _MM_SHUFFLE(2, 3, 2, 3));
/* if(_mm_movemask_ps(_mm_cmpge_ps(_mm_setzero_ps(), _mm_mul_ps(dots, dotd)))){ */
if(_mm_movemask_epi8(_mm_cmplt_epi32(_mm_xor_si128(_mm_cvtps_epi32(dots), _mm_cvtps_epi32(dotd)), _mm_setzero_si128()))){
return 1;
}
/* Otherwise, proceed with evaluation */
_mm_store_ps(&p->pkdPts[0], src10);
_mm_store_ps(&p->pkdPts[4], src32);
_mm_store_ps(&p->pkdPts[8], dst10);
_mm_store_ps(&p->pkdPts[12], dst32);
return 0;
}
/**
* Compute homography of matches in p->pkdPts with hFuncRefC and store in p->H.
*
* @param p
*/
static inline void sacGenerateModel(RHO_HEST_SSE2* p){
hFuncRefC(p->pkdPts, p->H);
}
/**
* @brief sacIsModelDegenerate
* @param p
* @return
*/
static inline int sacIsModelDegenerate(RHO_HEST_SSE2* p){
int degenerate;
float* H = p->H;
float f=H[0]+H[1]+H[2]+H[4]+H[5]+H[6]+H[8]+H[9];
/* degenerate = isnan(f); */
degenerate = f!=f;/* Only NaN is not equal to itself. */
/* degenerate = 0; */
if(degenerate){return degenerate;}
#if 0
/**
* Convexity test
*
* x' = Hx for i=1..4 must be convex.
*
* [ x' ] [ H00 H01 H02 ] [ x ]
* [ y' ] = [ H10 H11 H12 ] [ y ], where:
* [ z' ] [ H20 H21 H22 ] [ 1 ]
*
* p0 = (0, 0)
* p1 = (0, 1)
* p2 = (1, 1)
* p3 = (1, 0)
*/
float pt[4][2];
float pz[4][1];
pt[0][0] = H[2];
pt[0][1] = H[6];
pz[0][0] = H[10];
pt[1][0] = H[1]+H[2];
pt[1][1] = H[5]+H[6];
pz[1][0] = H[9]+H[10];
pt[2][0] = H[0]+H[1]+H[2];
pt[2][1] = H[4]+H[5]+H[6];
pz[2][0] = H[8]+H[9]+H[10];
pt[3][0] = H[0]+H[2];
pt[3][1] = H[4]+H[6];
pz[3][0] = H[8]+H[10];
pt[0][0] /= pz[0][0];
pt[0][1] /= pz[0][0];
pt[1][0] /= pz[1][0];
pt[1][1] /= pz[1][0];
pt[2][0] /= pz[2][0];
pt[2][1] /= pz[2][0];
pt[3][0] /= pz[3][0];
pt[3][1] /= pz[3][0];
/**
* Crossproduct:
*
* (x, y, z) = (ay bz - az by,
* az bx - ax bz,
* ax by - ay bx)
*/
__m128 src10 = _mm_load_ps(&pt[0][0]);
__m128 src32 = _mm_load_ps(&pt[2][0]);
__m128 p3210x = _mm_shuffle_ps(src10, src32, _MM_SHUFFLE(2, 0, 2, 0));
__m128 p3210y = _mm_shuffle_ps(src10, src32, _MM_SHUFFLE(3, 1, 3, 1));
__m128 p2103x = _mm_shuffle_ps(p3210x, p3210x, _MM_SHUFFLE(2, 1, 0, 3));
__m128 p2103y = _mm_shuffle_ps(p3210y, p3210y, _MM_SHUFFLE(2, 1, 0, 3));
__m128 vax = _mm_sub_ps(p3210x, p2103x);
__m128 vay = _mm_sub_ps(p3210y, p2103y);
__m128 vbx = _mm_shuffle_ps(vax, vax, _MM_SHUFFLE(2, 1, 0, 3));
__m128 vby = _mm_shuffle_ps(vay, vay, _MM_SHUFFLE(2, 1, 0, 3));
__m128 cross = _mm_sub_ps(_mm_mul_ps(vax, vby), _mm_mul_ps(vay, vbx));
degenerate = _mm_movemask_ps(cross);
degenerate = degenerate != 0x0;
#endif
return degenerate;
}
/**
* @brief sacEvaluateModelSPRT
* @param p
*/
static inline void sacEvaluateModelSPRT(RHO_HEST_SSE2* p){
unsigned i = 0;
unsigned isInlier;
double lambda = 1.0;
float distSq = p->maxD*p->maxD;
const float* src = p->src;
const float* dst = p->dst;
char* inl = p->inl;
float* H = p->H;
p->numModels++;
p->numInl = 0;
p->Ntested = 0;
p->good = 1;
/* VECTOR */
const __m128 distSqV=_mm_set1_ps(distSq);
const __m128 H00=_mm_set1_ps(H[0]);
const __m128 H01=_mm_set1_ps(H[1]);
const __m128 H02=_mm_set1_ps(H[2]);
const __m128 H10=_mm_set1_ps(H[4]);
const __m128 H11=_mm_set1_ps(H[5]);
const __m128 H12=_mm_set1_ps(H[6]);
const __m128 H20=_mm_set1_ps(H[8]);
const __m128 H21=_mm_set1_ps(H[9]);
const __m128 H22=_mm_set1_ps(H[10]);
for(;i<(p->N-3) && p->good;i+=4){
/* Backproject */
__m128 x, y, X, Y, inter0, inter1, inter2, inter3;
inter0 = _mm_loadu_ps(src+2*i);
inter1 = _mm_loadu_ps(src+2*i+4);
inter2 = _mm_loadu_ps(dst+2*i);
inter3 = _mm_loadu_ps(dst+2*i+4);
x = _mm_shuffle_ps(inter0, inter1, _MM_SHUFFLE(2, 0, 2, 0));
y = _mm_shuffle_ps(inter0, inter1, _MM_SHUFFLE(3, 1, 3, 1));
X = _mm_shuffle_ps(inter2, inter3, _MM_SHUFFLE(2, 0, 2, 0));
Y = _mm_shuffle_ps(inter2, inter3, _MM_SHUFFLE(3, 1, 3, 1));
__m128 reprojX = _mm_add_ps(_mm_add_ps(_mm_mul_ps(H00, x), _mm_mul_ps(H01, y)), H02);
__m128 reprojY = _mm_add_ps(_mm_add_ps(_mm_mul_ps(H10, x), _mm_mul_ps(H11, y)), H12);
__m128 reprojZ = _mm_add_ps(_mm_add_ps(_mm_mul_ps(H20, x), _mm_mul_ps(H21, y)), H22);
__m128 recipZ = _mm_rcp_ps(reprojZ);
reprojX = _mm_mul_ps(reprojX, recipZ);
reprojY = _mm_mul_ps(reprojY, recipZ);
/* reprojX = _mm_div_ps(reprojX, reprojZ); */
/* reprojY = _mm_div_ps(reprojY, reprojZ); */
reprojX = _mm_sub_ps(reprojX, X);
reprojY = _mm_sub_ps(reprojY, Y);
reprojX = _mm_mul_ps(reprojX, reprojX);
reprojY = _mm_mul_ps(reprojY, reprojY);
__m128 reprojDistV = _mm_add_ps(reprojX, reprojY);
__m128 cmp = _mm_cmple_ps(reprojDistV, distSqV);
int msk = _mm_movemask_ps(cmp);
/* ... */
/* 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15*/
static const unsigned bitCnt[16] = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4};
p->numInl += bitCnt[msk];
static const char byteMsk[16][4] = {{0,0,0,0},{1,0,0,0},{0,1,0,0},{1,1,0,0},
{0,0,1,0},{1,0,1,0},{0,1,1,0},{1,1,1,0},
{0,0,0,1},{1,0,0,1},{0,1,0,1},{1,1,0,1},
{0,0,1,1},{1,0,1,1},{0,1,1,1},{1,1,1,1}};
memcpy(inl, byteMsk[msk], 4);
inl+=4;
/* SPRT */
lambda *= p->lambdaTBL[msk];
p->good = lambda <= p->A;
/* If !p->good, the threshold A was exceeded, so we're rejecting */
}
/* SCALAR */
for(;i<p->N && p->good;i++){
/* Backproject */
float x=src[i*2],y=src[i*2+1];
float X=dst[i*2],Y=dst[i*2+1];
float reprojX=H[0]*x+H[1]*y+H[2]; /* ( X_1 ) ( H_11 H_12 H_13 ) (x_1) */
float reprojY=H[4]*x+H[5]*y+H[6]; /* ( X_2 ) = ( H_21 H_22 H_23 ) (x_2) */
float reprojZ=H[8]*x+H[9]*y+H[10];/* ( X_3 ) ( H_31 H_32 H_33=1.0 ) (x_3 = 1.0) */
/* reproj is in homogeneous coordinates. To bring back to "regular" coordinates, divide by Z. */
reprojX/=reprojZ;
reprojY/=reprojZ;
/* Compute distance */
reprojX-=X;
reprojY-=Y;
reprojX*=reprojX;
reprojY*=reprojY;
float reprojDist = reprojX+reprojY;
/* ... */
isInlier = reprojDist <= distSq;
p->numInl += isInlier;
*inl++ = isInlier;
/* SPRT */
lambda *= isInlier ? p->lambdaAccept : p->lambdaReject;
p->good = lambda <= p->A;
/* If !p->good, the threshold A was exceeded, so we're rejecting */
}
p->Ntested = i;
p->Ntestedtotal += i;
}
/**
* Update either the delta or epsilon SPRT parameters, depending on the events
* that transpired in the previous evaluation.
*
* If a "good" model that is also the best was encountered, update epsilon,
* since
*/
static inline void sacUpdateSPRT(RHO_HEST_SSE2* p){
if(p->good){
if(sacIsBestModel(p)){
p->epsilon = (double)p->numInl/p->N;
sacDesignSPRTTest(p);
}
}else{
double newDelta = (double)p->numInl/p->Ntested;
if(newDelta > 0 && CHNG_SIGNIFICANT(p->delta, newDelta)){
p->delta = newDelta;
sacDesignSPRTTest(p);
}
}
}
/**
* Numerically compute threshold A from the estimated delta, epsilon, t_M and
* m_S values.
*
* Epsilon: Denotes the probability that a randomly chosen data point is
* consistent with a good model.
* Delta: Denotes the probability that a randomly chosen data point is
* consistent with a bad model.
* t_M: Time needed to instantiate a model hypotheses given a sample.
* (Computing model parameters from a sample takes the same time
* as verification of t_M data points)
* m_S: The number of models that are verified per sample.
*/
static inline double designSPRTTest(double delta, double epsilon, double t_M, double m_S){
double An, C, K, prevAn;
unsigned i;
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Eq (2)
*/
C = (1-delta) * log((1-delta)/(1-epsilon)) +
delta * log( delta / epsilon );
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Eq (6)
* K = K_1/K_2 + 1 = (t_M*C)/m_S + 1
*/
K = t_M*C/m_S + 1;
/**
* Randomized RANSAC with Sequential Probability Ratio Test, ICCV 2005
* Paragraph below Eq (6)
*
* A* = lim_{n -> infty} A_n, where
* A_0 = K1/K2 + 1 and
* A_{n+1} = K1/K2 + 1 + log(A_n)
* The series converges fast, typically within four iterations.
*/
An = K;
i = 0;
do{
prevAn = An;
An = K + log(An);
}while((An-prevAn > 1.5e-8) && (++i < 10));
/**
* Return A = An_stopping, with n_stopping < 10
*/
return An;
}
/**
* Design the SPRT test. Shorthand for
* A = sprt(delta, epsilon, t_M, m_S);
*
* Sets p->A, p->lambdaAccept, p->lambdaReject and p->lambdaLUT
*/
static inline void sacDesignSPRTTest(RHO_HEST_SSE2* p){
p->A = designSPRTTest(p->delta, p->epsilon, p->t_M, p->m_S);
p->lambdaReject = ((1.0 - p->delta) / (1.0 - p->epsilon));
p->lambdaAccept = (( p->delta ) / ( p->epsilon ));
double a0r4 = p->lambdaReject*p->lambdaReject*p->lambdaReject*p->lambdaReject;
double a1r3 = p->lambdaAccept*p->lambdaReject*p->lambdaReject*p->lambdaReject;
double a2r2 = p->lambdaAccept*p->lambdaAccept*p->lambdaReject*p->lambdaReject;
double a3r1 = p->lambdaAccept*p->lambdaAccept*p->lambdaAccept*p->lambdaReject;
double a4r0 = p->lambdaAccept*p->lambdaAccept*p->lambdaAccept*p->lambdaAccept;
p->lambdaTBL[ 0] = a0r4;
p->lambdaTBL[ 1] = p->lambdaTBL[ 2] = p->lambdaTBL[ 4] = p->lambdaTBL[ 8] = a1r3;
p->lambdaTBL[ 3] = p->lambdaTBL[ 5] = p->lambdaTBL[ 6] = p->lambdaTBL[ 9] = p->lambdaTBL[10] = p->lambdaTBL[12] = a2r2;
p->lambdaTBL[ 7] = p->lambdaTBL[11] = p->lambdaTBL[13] = p->lambdaTBL[14] = a3r1;
p->lambdaTBL[15] = a4r0;
}
/**
* Return whether the current model is the best model so far.
*/
static inline int sacIsBestModel(RHO_HEST_SSE2* p){
return p->numInl > p->bestNumInl;
}
/**
* Returns whether the current-best model is good enough to be an
* acceptable best model, by checking whether it meets the minimum
* number of inliers.
*/
static inline int sacIsBestModelGoodEnough(RHO_HEST_SSE2* p){
return p->bestNumInl >= p->minInl;
}
/**
*
*/
static inline void sacSaveBestModel(RHO_HEST_SSE2* p){
p->bestNumInl = p->numInl;
memcpy(p->bestH, p->H, HSIZE);
memcpy(p->bestInl, p->inl, p->N);
}
/**
*
*/
static inline void sacInitNonRand(double beta,
unsigned start,
unsigned N,
unsigned* nonRandMinInl){
unsigned m = 4;
unsigned n = m+1 > start ? m+1 : start;
double beta_beta1_sq_chi = sqrt(beta*(1.0-beta)) * CHI_SQ;
for(; n < N; n++){
double mu = n * beta;
double sigma = sqrt(n)* beta_beta1_sq_chi;
unsigned i_min = ceil(m + mu + sigma);
nonRandMinInl[n] = i_min;
}
}
/**
*
*/
static inline void sacNStarOptimize(RHO_HEST_SSE2* p){
unsigned min_sample_length = 10*2; /*(p->N * INLIERS_RATIO) */
unsigned best_n = p->N;
unsigned test_n = best_n;
unsigned bestNumInl = p->bestNumInl;
unsigned testNumInl = bestNumInl;
for(;test_n > min_sample_length && testNumInl;test_n--){
if(testNumInl*best_n > bestNumInl*test_n){
if(testNumInl < p->nrTBL[test_n]){
break;
}
best_n = test_n;
bestNumInl = testNumInl;
}
testNumInl -= !!p->bestInl[test_n-1];
}
if(bestNumInl*p->phMax > p->phNumInl*best_n){
p->phMax = best_n;
p->phNumInl = bestNumInl;
p->maxI = sacCalcIterBound(p->cfd,
(double)p->phNumInl/p->phMax,
4,
p->maxI);
}
}
/**
*
*/
static inline void sacUpdateBounds(RHO_HEST_SSE2* p){
p->maxI = sacCalcIterBound(p->cfd,
(double)p->bestNumInl/p->N,
4,
p->maxI);
}
/**
* @brief sacOutputModel
* @param p
*/
static inline void sacOutputModel(RHO_HEST_SSE2* p){
if(!sacIsBestModelGoodEnough(p)){
memset(p->bestH, 0, HSIZE);
}
if(p->finalH){
memcpy(p->finalH, p->bestH, HSIZE);
}
}
/**
* Compute the real-valued number of samples per phase, given the RANSAC convergence speed,
* data set size and sample size.
*/
static inline double sacInitPEndFpI(const unsigned ransacConvg,
const unsigned n,
const unsigned m){
double numer=1, denom=1;
unsigned i;
for(i=0;i<m;i++){
numer *= m-i;
denom *= n-i;
}
return ransacConvg*numer/denom;
}
/**
* Choose, without repetition, sampleSize integers in the range [0, numDataPoints).
*/
static inline void sacRndSmpl(unsigned sampleSize,
unsigned* currentSample,
unsigned dataSetSize){
/**
* If sampleSize is very close to dataSetSize, we use selection sampling.
* Otherwise we use the naive sampling technique wherein we select random
* indexes until sampleSize of them are distinct.
*/
if(sampleSize*2>dataSetSize){
/**
* Selection Sampling:
*
* Algorithm S (Selection sampling technique). To select n records at random from a set of N, where 0 < n ≤ N.
* S1. [Initialize.] Set t ← 0, m ← 0. (During this algorithm, m represents the number of records selected so far,
* and t is the total number of input records that we have dealt with.)
* S2. [Generate U.] Generate a random number U, uniformly distributed between zero and one.
* S3. [Test.] If (N – t)U ≥ n – m, go to step S5.
* S4. [Select.] Select the next record for the sample, and increase m and t by 1. If m < n, go to step S2;
* otherwise the sample is complete and the algorithm terminates.
* S5. [Skip.] Skip the next record (do not include it in the sample), increase t by 1, and go back to step S2.
*/
unsigned m=0,t=0;
for(m=0;m<sampleSize;t++){
double U=sacRandom();
if((dataSetSize-t)*U < (sampleSize-m)){
currentSample[m++]=t;
}
}
}else{
/**
* Naive sampling technique. Generate indexes until sampleSize of them are distinct.
*/
unsigned i, j;
for(i=0;i<sampleSize;i++){
int inList;
do{
currentSample[i]=dataSetSize*sacRandom();
inList=0;
for(j=0;j<i;j++){
if(currentSample[i] == currentSample[j]){
inList=1;
break;
}
}
}while(inList);
}
}
}
/**
* Generates a random double uniformly distributed in the range [0, 1].
*/
static inline double sacRandom(void){
#ifdef _WIN32
return ((double)rand())/RAND_MAX;
#else
return ((double)random())/INT_MAX;
#endif
}
/**
* Estimate the number of iterations required based on the requested confidence,
* proportion of inliers in the best model so far and sample size.
*
* Clamp return value at maxIterationBound.
*/
static inline unsigned sacCalcIterBound(double confidence,
double inlierRate,
unsigned sampleSize,
unsigned maxIterBound){
unsigned retVal;
/**
* Formula chosen from http://en.wikipedia.org/wiki/RANSAC#The_parameters :
*
* \[ k = \frac{\log{(1-confidence)}}{\log{(1-inlierRate**sampleSize)}} \]
*/
double atLeastOneOutlierProbability = 1.-pow(inlierRate, (double)sampleSize);
/**
* There are two special cases: When argument to log() is 0 and when it is 1.
* Each has a special meaning.
*/
if(atLeastOneOutlierProbability>=1.){
/**
* A certainty of picking at least one outlier means that we will need
* an infinite amount of iterations in order to find a correct solution.
*/
retVal = maxIterBound;
}else if(atLeastOneOutlierProbability<=0.){
/**
* The certainty of NOT picking an outlier means that only 1 iteration
* is needed to find a solution.
*/
retVal = 1;
}else{
/**
* Since 1-confidence (the probability of the model being based on at
* least one outlier in the data) is equal to
* (1-inlierRate**sampleSize)**numIterations (the probability of picking
* at least one outlier in numIterations samples), we can isolate
* numIterations (the return value) into
*/
retVal = ceil(log(1.-confidence)/log(atLeastOneOutlierProbability));
}
/**
* Clamp to maxIterationBound.
*/
return retVal <= maxIterBound ? retVal : maxIterBound;
}
/* Transposed, C */
static void hFuncRefC(float* packedPoints,/* Source (four x,y float coordinates) points followed by
destination (four x,y float coordinates) points, aligned by 32 bytes */
float* H){ /* Homography (three 16-byte aligned rows of 3 floats) */
float x0=*packedPoints++;
float y0=*packedPoints++;
float x1=*packedPoints++;
float y1=*packedPoints++;
float x2=*packedPoints++;
float y2=*packedPoints++;
float x3=*packedPoints++;
float y3=*packedPoints++;
float X0=*packedPoints++;
float Y0=*packedPoints++;
float X1=*packedPoints++;
float Y1=*packedPoints++;
float X2=*packedPoints++;
float Y2=*packedPoints++;
float X3=*packedPoints++;
float Y3=*packedPoints++;
float x0X0=x0*X0, x1X1=x1*X1, x2X2=x2*X2, x3X3=x3*X3;
float x0Y0=x0*Y0, x1Y1=x1*Y1, x2Y2=x2*Y2, x3Y3=x3*Y3;
float y0X0=y0*X0, y1X1=y1*X1, y2X2=y2*X2, y3X3=y3*X3;
float y0Y0=y0*Y0, y1Y1=y1*Y1, y2Y2=y2*Y2, y3Y3=y3*Y3;
/**
* [0] [1] Hidden Prec
* x0 y0 1 x1
* x1 y1 1 x1
* x2 y2 1 x1
* x3 y3 1 x1
*
* Eliminate ones in column 2 and 5.
* R(0)-=R(2)
* R(1)-=R(2)
* R(3)-=R(2)
*
* [0] [1] Hidden Prec
* x0-x2 y0-y2 0 x1+1
* x1-x2 y1-y2 0 x1+1
* x2 y2 1 x1
* x3-x2 y3-y2 0 x1+1
*
* Eliminate column 0 of rows 1 and 3
* R(1)=(x0-x2)*R(1)-(x1-x2)*R(0), y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
* R(3)=(x0-x2)*R(3)-(x3-x2)*R(0), y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
*
* [0] [1] Hidden Prec
* x0-x2 y0-y2 0 x1+1
* 0 y1' 0 x2+3
* x2 y2 1 x1
* 0 y3' 0 x2+3
*
* Eliminate column 1 of rows 0 and 3
* R(3)=y1'*R(3)-y3'*R(1)
* R(0)=y1'*R(0)-(y0-y2)*R(1)
*
* [0] [1] Hidden Prec
* x0' 0 0 x3+5
* 0 y1' 0 x2+3
* x2 y2 1 x1
* 0 0 0 x4+7
*
* Eliminate columns 0 and 1 of row 2
* R(0)/=x0'
* R(1)/=y1'
* R(2)-= (x2*R(0) + y2*R(1))
*
* [0] [1] Hidden Prec
* 1 0 0 x6+10
* 0 1 0 x4+6
* 0 0 1 x4+7
* 0 0 0 x4+7
*/
/**
* Eliminate ones in column 2 and 5.
* R(0)-=R(2)
* R(1)-=R(2)
* R(3)-=R(2)
*/
/*float minor[4][2] = {{x0-x2,y0-y2},
{x1-x2,y1-y2},
{x2 ,y2 },
{x3-x2,y3-y2}};*/
/*float major[8][3] = {{x2X2-x0X0,y2X2-y0X0,(X0-X2)},
{x2X2-x1X1,y2X2-y1X1,(X1-X2)},
{-x2X2 ,-y2X2 ,(X2 )},
{x2X2-x3X3,y2X2-y3X3,(X3-X2)},
{x2Y2-x0Y0,y2Y2-y0Y0,(Y0-Y2)},
{x2Y2-x1Y1,y2Y2-y1Y1,(Y1-Y2)},
{-x2Y2 ,-y2Y2 ,(Y2 )},
{x2Y2-x3Y3,y2Y2-y3Y3,(Y3-Y2)}};*/
float minor[2][4] = {{x0-x2,x1-x2,x2 ,x3-x2},
{y0-y2,y1-y2,y2 ,y3-y2}};
float major[3][8] = {{x2X2-x0X0,x2X2-x1X1,-x2X2 ,x2X2-x3X3,x2Y2-x0Y0,x2Y2-x1Y1,-x2Y2 ,x2Y2-x3Y3},
{y2X2-y0X0,y2X2-y1X1,-y2X2 ,y2X2-y3X3,y2Y2-y0Y0,y2Y2-y1Y1,-y2Y2 ,y2Y2-y3Y3},
{ (X0-X2) , (X1-X2) , (X2 ) , (X3-X2) , (Y0-Y2) , (Y1-Y2) , (Y2 ) , (Y3-Y2) }};
/**
* int i;
* for(i=0;i<8;i++) major[2][i]=-major[2][i];
* Eliminate column 0 of rows 1 and 3
* R(1)=(x0-x2)*R(1)-(x1-x2)*R(0), y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
* R(3)=(x0-x2)*R(3)-(x3-x2)*R(0), y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
*/
float scalar1=minor[0][0], scalar2=minor[0][1];
minor[1][1]=minor[1][1]*scalar1-minor[1][0]*scalar2;
major[0][1]=major[0][1]*scalar1-major[0][0]*scalar2;
major[1][1]=major[1][1]*scalar1-major[1][0]*scalar2;
major[2][1]=major[2][1]*scalar1-major[2][0]*scalar2;
major[0][5]=major[0][5]*scalar1-major[0][4]*scalar2;
major[1][5]=major[1][5]*scalar1-major[1][4]*scalar2;
major[2][5]=major[2][5]*scalar1-major[2][4]*scalar2;
scalar2=minor[0][3];
minor[1][3]=minor[1][3]*scalar1-minor[1][0]*scalar2;
major[0][3]=major[0][3]*scalar1-major[0][0]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][0]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][0]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][4]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][4]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][4]*scalar2;
/**
* Eliminate column 1 of rows 0 and 3
* R(3)=y1'*R(3)-y3'*R(1)
* R(0)=y1'*R(0)-(y0-y2)*R(1)
*/
scalar1=minor[1][1];scalar2=minor[1][3];
major[0][3]=major[0][3]*scalar1-major[0][1]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][1]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][1]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][5]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][5]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][5]*scalar2;
scalar2=minor[1][0];
minor[0][0]=minor[0][0]*scalar1-minor[0][1]*scalar2;
major[0][0]=major[0][0]*scalar1-major[0][1]*scalar2;
major[1][0]=major[1][0]*scalar1-major[1][1]*scalar2;
major[2][0]=major[2][0]*scalar1-major[2][1]*scalar2;
major[0][4]=major[0][4]*scalar1-major[0][5]*scalar2;
major[1][4]=major[1][4]*scalar1-major[1][5]*scalar2;
major[2][4]=major[2][4]*scalar1-major[2][5]*scalar2;
/**
* Eliminate columns 0 and 1 of row 2
* R(0)/=x0'
* R(1)/=y1'
* R(2)-= (x2*R(0) + y2*R(1))
*/
scalar1=minor[0][0];
major[0][0]/=scalar1;
major[1][0]/=scalar1;
major[2][0]/=scalar1;
major[0][4]/=scalar1;
major[1][4]/=scalar1;
major[2][4]/=scalar1;
scalar1=minor[1][1];
major[0][1]/=scalar1;
major[1][1]/=scalar1;
major[2][1]/=scalar1;
major[0][5]/=scalar1;
major[1][5]/=scalar1;
major[2][5]/=scalar1;
scalar1=minor[0][2];scalar2=minor[1][2];
major[0][2]-=major[0][0]*scalar1+major[0][1]*scalar2;
major[1][2]-=major[1][0]*scalar1+major[1][1]*scalar2;
major[2][2]-=major[2][0]*scalar1+major[2][1]*scalar2;
major[0][6]-=major[0][4]*scalar1+major[0][5]*scalar2;
major[1][6]-=major[1][4]*scalar1+major[1][5]*scalar2;
major[2][6]-=major[2][4]*scalar1+major[2][5]*scalar2;
/* Only major matters now. R(3) and R(7) correspond to the hollowed-out rows. */
scalar1=major[0][7];
major[1][7]/=scalar1;
major[2][7]/=scalar1;
scalar1=major[0][0];major[1][0]-=scalar1*major[1][7];major[2][0]-=scalar1*major[2][7];
scalar1=major[0][1];major[1][1]-=scalar1*major[1][7];major[2][1]-=scalar1*major[2][7];
scalar1=major[0][2];major[1][2]-=scalar1*major[1][7];major[2][2]-=scalar1*major[2][7];
scalar1=major[0][3];major[1][3]-=scalar1*major[1][7];major[2][3]-=scalar1*major[2][7];
scalar1=major[0][4];major[1][4]-=scalar1*major[1][7];major[2][4]-=scalar1*major[2][7];
scalar1=major[0][5];major[1][5]-=scalar1*major[1][7];major[2][5]-=scalar1*major[2][7];
scalar1=major[0][6];major[1][6]-=scalar1*major[1][7];major[2][6]-=scalar1*major[2][7];
/* One column left (Two in fact, but the last one is the homography) */
scalar1=major[1][3];
major[2][3]/=scalar1;
scalar1=major[1][0];major[2][0]-=scalar1*major[2][3];
scalar1=major[1][1];major[2][1]-=scalar1*major[2][3];
scalar1=major[1][2];major[2][2]-=scalar1*major[2][3];
scalar1=major[1][4];major[2][4]-=scalar1*major[2][3];
scalar1=major[1][5];major[2][5]-=scalar1*major[2][3];
scalar1=major[1][6];major[2][6]-=scalar1*major[2][3];
scalar1=major[1][7];major[2][7]-=scalar1*major[2][3];
/* Homography is done. */
H[0]=major[2][0];
H[1]=major[2][1];
H[2]=major[2][2];
H[4]=major[2][4];
H[5]=major[2][5];
H[6]=major[2][6];
H[8]=major[2][7];
H[9]=major[2][3];
H[10]=1.0;
}
} /* End namespace cv */
modules/calib3d/src/rhosse2.h 0 → 100644
View file @ 68e59d61
/*
IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
By downloading, copying, installing or using the software you agree to this license.
If you do not agree to this license, do not download, install,
copy or use the software.
BSD 3-Clause License
Copyright (C) 2014, Olexa Bilaniuk, Hamid Bazargani & Robert Laganiere, all rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistribution's of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistribution's in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* The name of the copyright holders may not be used to endorse or promote products
derived from this software without specific prior written permission.
This software is provided by the copyright holders and contributors "as is" and
any express or implied warranties, including, but not limited to, the implied
warranties of merchantability and fitness for a particular purpose are disclaimed.
In no event shall the Intel Corporation or contributors be liable for any direct,
indirect, incidental, special, exemplary, or consequential damages
(including, but not limited to, procurement of substitute goods or services;
loss of use, data, or profits; or business interruption) however caused
and on any theory of liability, whether in contract, strict liability,
or tort (including negligence or otherwise) arising in any way out of
the use of this software, even if advised of the possibility of such damage.
*/
/**
* Bilaniuk, Olexa, Hamid Bazargani, and Robert Laganiere. "Fast Target
* Recognition on Mobile Devices: Revisiting Gaussian Elimination for the
* Estimation of Planar Homographies." In Computer Vision and Pattern
* Recognition Workshops (CVPRW), 2014 IEEE Conference on, pp. 119-125.
* IEEE, 2014.
*/
/* Include Guards */
#ifndef __RHOSSE2_H__
#define __RHOSSE2_H__
/* Includes */
/* Defines */
#ifdef __cplusplus
/* C++ does not have the restrict keyword. */
#ifdef restrict
#undef restrict
#endif
#define restrict
#else
/* C99 and over has the restrict keyword. */
#if !defined(__STDC_VERSION__) || __STDC_VERSION__ < 199901L
#define restrict
#endif
#endif
/* Flags */
#ifndef RHO_FLAG_NONE
#define RHO_FLAG_NONE (0U<<0)
#endif
#ifndef RHO_FLAG_ENABLE_NR
#define RHO_FLAG_ENABLE_NR (1U<<0)
#endif
#ifndef RHO_FLAG_ENABLE_REFINEMENT
#define RHO_FLAG_ENABLE_REFINEMENT (1U<<1)
#endif
#ifndef RHO_FLAG_ENABLE_FINAL_REFINEMENT
#define RHO_FLAG_ENABLE_FINAL_REFINEMENT (1U<<2)
#endif
/* Data structures */
/**
* Homography Estimation context.
*/
typedef struct{
/* Virtual Arguments */
const float* restrict src;
const float* restrict dst;
int allocBestInl;
char* restrict bestInl;
unsigned N;
float maxD;
unsigned maxI;
unsigned rConvg;
double cfd;
unsigned minInl;
double beta;
unsigned flags;
const float* guessH;
float* finalH;
/* PROSAC */
unsigned i; /* Iteration Number */
unsigned phNum; /* Phase Number */
unsigned phEndI; /* Phase End Iteration */
double phEndFpI; /* Phase floating-point End Iteration */
unsigned phMax; /* Termination phase number */
unsigned phNumInl; /* Number of inliers for termination phase */
unsigned bestNumInl; /* Best number of inliers */
unsigned numInl; /* Current number of inliers */
unsigned numModels; /* Number of models tested */
unsigned* restrict smpl; /* Sample */
float* restrict H; /* Current homography */
float* restrict bestH; /* Best homography */
float* restrict pkdPts; /* Packed points */
char* restrict inl; /* Inliers to current model */
unsigned* restrict nrTBL; /* Non-Randomness: Table */
unsigned nrSize; /* Non-Randomness: Size */
double nrBeta; /* Non-Randomness: Beta */
/* SPRT */
double t_M; /* t_M */
double m_S; /* m_S */
double epsilon; /* Epsilon */
double delta; /* delta */
double A; /* SPRT Threshold */
unsigned Ntested; /* Number of points tested */
unsigned Ntestedtotal; /* Number of points tested in total */
int good; /* Good/bad flag */
double lambdaAccept; /* Accept multiplier */
double lambdaReject; /* Reject multiplier */
double lambdaTBL[16]; /* Multiplier LUT */
} RHO_HEST_SSE2;
/* Extern C */
#ifdef __cplusplus
namespace cv{
//extern "C" {
#endif
/* Functions */
/**
* Initialize the estimator context, by allocating the aligned buffers
* internally needed.
*
* @param [in/out] p The uninitialized estimator context to initialize.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoSSE2Init(RHO_HEST_SSE2* p);
/**
* Ensure that the estimator context's internal table for non-randomness
* criterion is at least of the given size, and uses the given beta. The table
* should be larger than the maximum number of matches fed into the estimator.
*
* A value of N of 0 requests deallocation of the table.
*
* @param [in] p The initialized estimator context
* @param [in] N If 0, deallocate internal table. If > 0, ensure that the
* internal table is of at least this size, reallocating if
* necessary.
* @param [in] beta The beta-factor to use within the table.
* @return 0 if successful; non-zero if an error occured.
*/
int rhoSSE2EnsureCapacity(RHO_HEST_SSE2* p, unsigned N, double beta);
/**
* Finalize the estimator context, by freeing the aligned buffers used
* internally.
*
* @param [in] p The initialized estimator context to finalize.
*/
void rhoSSE2Fini(RHO_HEST_SSE2* p);
/**
* Estimates the homography using the given context, matches and parameters to
* PROSAC.
*
* The given context must have been initialized.
*
* The matches are provided as two arrays of N single-precision, floating-point
* (x,y) points. Points with corresponding offsets in the two arrays constitute
* a match. The homography estimation attempts to find the 3x3 matrix H which
* best maps the homogeneous-coordinate points in the source array to their
* corresponding homogeneous-coordinate points in the destination array.
*
* Note: At least 4 matches must be provided (N >= 4).
* Note: A point in either array takes up 2 floats. The first of two stores
* the x-coordinate and the second of the two stores the y-coordinate.
* Thus, the arrays resemble this in memory:
*
* src = [x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, ...]
* Matches: | | | | |
* dst = [x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, ...]
* Note: The matches are expected to be provided sorted by quality, or at
* least not be worse-than-random in ordering.
*
* A pointer to the base of an array of N bytes can be provided. It serves as
* an output mask to indicate whether the corresponding match is an inlier to
* the returned homography, if any. A zero indicates an outlier; A non-zero
* value indicates an inlier.
*
* The PROSAC estimator requires a few parameters of its own. These are:
*
* - The maximum distance that a source point projected onto the destination
* plane can be from its putative match and still be considered an
* inlier. Must be non-negative.
* A sane default is 3.0.
* - The maximum number of PROSAC iterations. This corresponds to the
* largest number of samples that will be drawn and tested.
* A sane default is 2000.
* - The RANSAC convergence parameter. This corresponds to the number of
* iterations after which PROSAC will start sampling like RANSAC.
* A sane default is 2000.
* - The confidence threshold. This corresponds to the probability of
* finding a correct solution. Must be bounded by [0, 1].
* A sane default is 0.995.
* - The minimum number of inliers acceptable. Only a solution with at
* least this many inliers will be returned. The minimum is 4.
* A sane default is 10% of N.
* - The beta-parameter for the non-randomness termination criterion.
* Ignored if non-randomness criterion disabled, otherwise must be
* bounded by (0, 1).
* A sane default is 0.35.
* - Optional flags to control the estimation. Available flags are:
* HEST_FLAG_NONE:
* No special processing.
* HEST_FLAG_ENABLE_NR:
* Enable non-randomness criterion. If set, the beta parameter
* must also be set.
* HEST_FLAG_ENABLE_REFINEMENT:
* Enable refinement of each new best model, as they are found.
* HEST_FLAG_ENABLE_FINAL_REFINEMENT:
* Enable one final refinement of the best model found before
* returning it.
*
* The PROSAC estimator additionally accepts an extrinsic initial guess of H,
* and outputs a final estimate at H provided it was able to find one with a
* minimum of supporting inliers. If it was not, it outputs the all-zero
* matrix.
*
* The extrinsic guess at and final estimate of H are both in the same form:
* A 3x3 single-precision floating-point matrix with step 4. Thus, it is a
* 12-element array of floats, with the elements as follows:
*
* [ H00, H01, H02, <pad>,
* H10, H11, H12, <pad>,
* H20, H21, H22, <pad> ]
*
* The function returns the number of inliers if it was able to find a
* homography with at least the minimum required support, and 0 if it was not.
*
*
* @param [in/out] p The context to use for homography estimation. Must
* be already initialized. Cannot be NULL.
* @param [in] src The pointer to the source points of the matches.
* Must be aligned to 16 bytes. Cannot be NULL.
* @param [in] dst The pointer to the destination points of the matches.
* Must be aligned to 16 bytes. Cannot be NULL.
* @param [out] inl The pointer to the output mask of inlier matches.
* Must be aligned to 16 bytes. May be NULL.
* @param [in] N The number of matches.
* @param [in] maxD The maximum distance.
* @param [in] maxI The maximum number of PROSAC iterations.
* @param [in] rConvg The RANSAC convergence parameter.
* @param [in] cfd The required confidence in the solution.
* @param [in] minInl The minimum required number of inliers.
* @param [in] beta The beta-parameter for the non-randomness criterion.
* @param [in] flags A union of flags to control the estimation.
* @param [in] guessH An extrinsic guess at the solution H, or NULL if
* none provided.
* @param [out] finalH The final estimation of H, or the zero matrix if
* the minimum number of inliers was not met.
* Cannot be NULL.
* @return The number of inliers if the minimum number of
* inliers for acceptance was reached; 0 otherwise.
*/
unsigned rhoSSE2(RHO_HEST_SSE2* restrict p, /* Homography estimation context. */
const float* restrict src, /* Source points */
const float* restrict dst, /* Destination points */
char* restrict bestInl, /* Inlier mask */
unsigned N, /* = src.length = dst.length = inl.length */
float maxD, /* 3.0 */
unsigned maxI, /* 2000 */
unsigned rConvg, /* 2000 */
double cfd, /* 0.995 */
unsigned minInl, /* 4 */
double beta, /* 0.35 */
unsigned flags, /* 0 */
const float* guessH, /* Extrinsic guess, NULL if none provided */
float* finalH); /* Final result. */
/* Extern C */
#ifdef __cplusplus
//}
}
#endif
#endif
modules/calib3d/test/test_homography.cpp
View file @ 68e59d61
......@@ -62,10 +62,10 @@
#define MAX_COUNT_OF_POINTS 303
#define COUNT_NORM_TYPES 3
#define METHODS_COUNT 3
#define METHODS_COUNT 4
int NORM_TYPE[COUNT_NORM_TYPES] = {cv::NORM_L1, cv::NORM_L2, cv::NORM_INF};
int METHOD[METHODS_COUNT] = {0, cv::RANSAC, cv::LMEDS};
int METHOD[METHODS_COUNT] = {0, cv::RANSAC, cv::LMEDS, cv::RHO};
using namespace cv;
using namespace std;
......@@ -144,7 +144,7 @@ void CV_HomographyTest::print_information_1(int j, int N, int _method, const Mat
cout << "Type of srcPoints: "; if ((j>-1) && (j<2)) cout << "Mat of CV_32FC2"; else cout << "vector <Point2f>";
cout << " Type of dstPoints: "; if (j % 2 == 0) cout << "Mat of CV_32FC2"; else cout << "vector <Point2f>"; cout << endl;
cout << "Count of points: " << N << endl; cout << endl;
cout << "Method: "; if (_method == 0) cout << 0; else if (_method == 8) cout << "RANSAC"; else cout << "LMEDS"; cout << endl;
cout << "Method: "; if (_method == 0) cout << 0; else if (_method == 8) cout << "RANSAC"; else if (_method == cv::RHO) cout << "RHO"; else cout << "LMEDS"; cout << endl;
cout << "Homography matrix:" << endl; cout << endl;
cout << H << endl; cout << endl;
cout << "Number of rows: " << H.rows << " Number of cols: " << H.cols << endl; cout << endl;
......@@ -156,7 +156,7 @@ void CV_HomographyTest::print_information_2(int j, int N, int _method, const Mat
cout << "Type of srcPoints: "; if ((j>-1) && (j<2)) cout << "Mat of CV_32FC2"; else cout << "vector <Point2f>";
cout << " Type of dstPoints: "; if (j % 2 == 0) cout << "Mat of CV_32FC2"; else cout << "vector <Point2f>"; cout << endl;
cout << "Count of points: " << N << endl; cout << endl;
cout << "Method: "; if (_method == 0) cout << 0; else if (_method == 8) cout << "RANSAC"; else cout << "LMEDS"; cout << endl;
cout << "Method: "; if (_method == 0) cout << 0; else if (_method == 8) cout << "RANSAC"; else if (_method == cv::RHO) cout << "RHO"; else cout << "LMEDS"; cout << endl;
cout << "Original matrix:" << endl; cout << endl;
cout << H << endl; cout << endl;
cout << "Found matrix:" << endl; cout << endl;
......@@ -339,14 +339,15 @@ void CV_HomographyTest::run(int)
continue;
}
case cv::RHO:
case RANSAC:
{
cv::Mat mask [4]; double diff;
Mat H_res_64 [4] = { cv::findHomography(src_mat_2f, dst_mat_2f, RANSAC, reproj_threshold, mask[0]),
cv::findHomography(src_mat_2f, dst_vec, RANSAC, reproj_threshold, mask[1]),
cv::findHomography(src_vec, dst_mat_2f, RANSAC, reproj_threshold, mask[2]),
cv::findHomography(src_vec, dst_vec, RANSAC, reproj_threshold, mask[3]) };
Mat H_res_64 [4] = { cv::findHomography(src_mat_2f, dst_mat_2f, method, reproj_threshold, mask[0]),
cv::findHomography(src_mat_2f, dst_vec, method, reproj_threshold, mask[1]),
cv::findHomography(src_vec, dst_mat_2f, method, reproj_threshold, mask[2]),
cv::findHomography(src_vec, dst_vec, method, reproj_threshold, mask[3]) };
for (int j = 0; j < 4; ++j)
{
......@@ -466,14 +467,15 @@ void CV_HomographyTest::run(int)
continue;
}
case cv::RHO:
case RANSAC:
{
cv::Mat mask_res [4];
Mat H_res_64 [4] = { cv::findHomography(src_mat_2f, dst_mat_2f, RANSAC, reproj_threshold, mask_res[0]),
cv::findHomography(src_mat_2f, dst_vec, RANSAC, reproj_threshold, mask_res[1]),
cv::findHomography(src_vec, dst_mat_2f, RANSAC, reproj_threshold, mask_res[2]),
cv::findHomography(src_vec, dst_vec, RANSAC, reproj_threshold, mask_res[3]) };
Mat H_res_64 [4] = { cv::findHomography(src_mat_2f, dst_mat_2f, method, reproj_threshold, mask_res[0]),
cv::findHomography(src_mat_2f, dst_vec, method, reproj_threshold, mask_res[1]),
cv::findHomography(src_vec, dst_mat_2f, method, reproj_threshold, mask_res[2]),
cv::findHomography(src_vec, dst_vec, method, reproj_threshold, mask_res[3]) };
for (int j = 0; j < 4; ++j)
{
......
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