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/*
* Implementation of the paper Shape Matching and Object Recognition Using Shape Contexts
* Belongie et al., 2002 by Juan Manuel Perez for GSoC 2013.
*/
#include "precomp.hpp"
//#include "opencv2/highgui.hpp"
/*
* ShapeContextDescriptor class
*/
class SCD
{
public:
//! the full constructor taking all the necessary parameters
explicit SCD(int _nAngularBins=12, int _nRadialBins=5,
double _innerRadius=0.1, double _outerRadius=1, bool _rotationInvariant=false)
{
setAngularBins(_nAngularBins);
setRadialBins(_nRadialBins);
setInnerRadius(_innerRadius);
setOuterRadius(_outerRadius);
setRotationInvariant(_rotationInvariant);
}
void extractSCD(cv::Mat& contour, cv::Mat& descriptors,
const std::vector<int>& queryInliers=std::vector<int>(),
const float _meanDistance=-1)
{
cv::Mat contourMat = contour;
cv::Mat disMatrix = cv::Mat::zeros(contourMat.cols, contourMat.cols, CV_32F);
cv::Mat angleMatrix = cv::Mat::zeros(contourMat.cols, contourMat.cols, CV_32F);
std::vector<double> logspaces, angspaces;
logarithmicSpaces(logspaces);
angularSpaces(angspaces);
buildNormalizedDistanceMatrix(contourMat, disMatrix, queryInliers, _meanDistance);
buildAngleMatrix(contourMat, angleMatrix);
// Now, build the descriptor matrix (each row is a point) //
descriptors = cv::Mat::zeros(contourMat.cols, descriptorSize(), CV_32F);
for (int ptidx=0; ptidx<contourMat.cols; ptidx++)
{
for (int cmp=0; cmp<contourMat.cols; cmp++)
{
if (ptidx==cmp) continue;
if ((int)queryInliers.size()>0)
{
if (queryInliers[ptidx]==0 || queryInliers[cmp]==0) continue; //avoid outliers
}
int angidx=-1, radidx=-1;
for (int i=0; i<nRadialBins; i++)
{
if (disMatrix.at<float>(ptidx, cmp)<logspaces[i])
{
radidx=i;
break;
}
}
for (int i=0; i<nAngularBins; i++)
{
if (angleMatrix.at<float>(ptidx, cmp)<angspaces[i])
{
angidx=i;
break;
}
}
if (angidx!=-1 && radidx!=-1)
{
int idx = angidx+radidx*nAngularBins;
descriptors.at<float>(ptidx, idx)++;
}
}
}
}
int descriptorSize() {return nAngularBins*nRadialBins;}
void setAngularBins(int angularBins) { nAngularBins=angularBins; }
void setRadialBins(int radialBins) { nRadialBins=radialBins; }
void setInnerRadius(double _innerRadius) { innerRadius=_innerRadius; }
void setOuterRadius(double _outerRadius) { outerRadius=_outerRadius; }
void setRotationInvariant(bool _rotationInvariant) { rotationInvariant=_rotationInvariant; }
int getAngularBins() const { return nAngularBins; }
int getRadialBins() const { return nRadialBins; }
double getInnerRadius() const { return innerRadius; }
double getOuterRadius() const { return outerRadius; }
bool getRotationInvariant() const { return rotationInvariant; }
float getMeanDistance() const { return meanDistance; }
private:
int nAngularBins;
int nRadialBins;
double innerRadius;
double outerRadius;
bool rotationInvariant;
float meanDistance;
protected:
void logarithmicSpaces(std::vector<double>& vecSpaces) const
{
double logmin=log10(innerRadius);
double logmax=log10(outerRadius);
double delta=(logmax-logmin)/(nRadialBins-1);
double accdelta=0;
for (int i=0; i<nRadialBins; i++)
{
double val = std::pow(10,logmin+accdelta);
vecSpaces.push_back(val);
accdelta += delta;
}
}
void angularSpaces(std::vector<double>& vecSpaces) const
{
double delta=2*CV_PI/nAngularBins;
double val=0;
for (int i=0; i<nAngularBins; i++)
{
val += delta;
vecSpaces.push_back(val);
}
}
void buildNormalizedDistanceMatrix(cv::Mat& contour,
cv::Mat& disMatrix, const std::vector<int> &queryInliers,
const float _meanDistance=-1)
{
cv::Mat contourMat = contour;
cv::Mat mask(disMatrix.rows, disMatrix.cols, CV_8U);
for (int i=0; i<contourMat.cols; i++)
{
for (int j=0; j<contourMat.cols; j++)
{
disMatrix.at<float>(i,j) = (float)norm( cv::Mat(contourMat.at<cv::Point2f>(0,i)-contourMat.at<cv::Point2f>(0,j)), cv::NORM_L2 );
if (_meanDistance<0)
{
if (queryInliers.size()>0)
{
mask.at<char>(i,j)=char(queryInliers[j] & queryInliers[i]);
}
else
{
mask.at<char>(i,j)=1;
}
}
}
}
if (_meanDistance<0)
{
meanDistance=(float)mean(disMatrix, mask)[0];
}
else
{
meanDistance=_meanDistance;
}
disMatrix/=meanDistance+FLT_EPSILON;
}
void buildAngleMatrix(cv::Mat& contour,
cv::Mat& angleMatrix) const
{
cv::Mat contourMat = contour;
// if descriptor is rotationInvariant compute massCenter //
cv::Point2f massCenter(0,0);
if (rotationInvariant)
{
for (int i=0; i<contourMat.cols; i++)
{
massCenter+=contourMat.at<cv::Point2f>(0,i);
}
massCenter.x=massCenter.x/(float)contourMat.cols;
massCenter.y=massCenter.y/(float)contourMat.cols;
}
for (int i=0; i<contourMat.cols; i++)
{
for (int j=0; j<contourMat.cols; j++)
{
if (i==j)
{
angleMatrix.at<float>(i,j)=0.0;
}
else
{
cv::Point2f dif = contourMat.at<cv::Point2f>(0,i) - contourMat.at<cv::Point2f>(0,j);
angleMatrix.at<float>(i,j) = std::atan2(dif.y, dif.x);
if (rotationInvariant)
{
cv::Point2f refPt = contourMat.at<cv::Point2f>(0,i) - massCenter;
float refAngle = atan2(refPt.y, refPt.x);
angleMatrix.at<float>(i,j) -= refAngle;
}
angleMatrix.at<float>(i,j) = float(fmod(double(angleMatrix.at<float>(i,j)+(double)FLT_EPSILON),2*CV_PI)+CV_PI);
//angleMatrix.at<float>(i,j) = 1+floor( angleMatrix.at<float>(i,j)*nAngularBins/(2*CV_PI) );
}
}
}
}
};
/*
* Matcher
*/
class SCDMatcher
{
public:
// the full constructor
SCDMatcher()
{
}
// the matcher function using Hungarian method
void matchDescriptors(cv::Mat& descriptors1, cv::Mat& descriptors2, std::vector<cv::DMatch>& matches, cv::Ptr<cv::HistogramCostExtractor>& comparer,
std::vector<int>& inliers1, std::vector<int> &inliers2)
{
matches.clear();
// Build the cost Matrix between descriptors //
cv::Mat costMat;
buildCostMatrix(descriptors1, descriptors2, costMat, comparer);
// Solve the matching problem using the hungarian method //
hungarian(costMat, matches, inliers1, inliers2, descriptors1.rows, descriptors2.rows);
}
// matching cost
float getMatchingCost() const {return minMatchCost;}
private:
float minMatchCost;
float betaAdditional;
protected:
void buildCostMatrix(const cv::Mat& descriptors1, const cv::Mat& descriptors2,
cv::Mat& costMatrix, cv::Ptr<cv::HistogramCostExtractor>& comparer) const
{
comparer->buildCostMatrix(descriptors1, descriptors2, costMatrix);
}
void hungarian(cv::Mat& costMatrix, std::vector<cv::DMatch>& outMatches, std::vector<int> &inliers1,
std::vector<int> &inliers2, int sizeScd1=0, int sizeScd2=0)
{
std::vector<int> free(costMatrix.rows, 0), collist(costMatrix.rows, 0);
std::vector<int> matches(costMatrix.rows, 0), colsol(costMatrix.rows), rowsol(costMatrix.rows);
std::vector<float> d(costMatrix.rows), pred(costMatrix.rows), v(costMatrix.rows);
const float LOWV=1e-10;
bool unassignedfound;
int i=0, imin=0, numfree=0, prvnumfree=0, f=0, i0=0, k=0, freerow=0;
int j=0, j1=0, j2=0, endofpath=0, last=0, low=0, up=0;
float min=0, h=0, umin=0, usubmin=0, v2=0;
// COLUMN REDUCTION //
for (j = costMatrix.rows-1; j >= 0; j--)
{
// find minimum cost over rows.
min = costMatrix.at<float>(0,j);
imin = 0;
for (i = 1; i < costMatrix.rows; i++)
if (costMatrix.at<float>(i,j) < min)
{
min = costMatrix.at<float>(i,j);
imin = i;
}
v[j] = min;
if (++matches[imin] == 1)
{
rowsol[imin] = j;
colsol[j] = imin;
}
else
{
colsol[j]=-1;
}
}
// REDUCTION TRANSFER //
for (i=0; i<costMatrix.rows; i++)
{
if (matches[i] == 0)
{
free[numfree++] = i;
}
else
{
if (matches[i] == 1)
{
j1=rowsol[i];
min=std::numeric_limits<float>::max();
for (j=0; j<costMatrix.rows; j++)
{
if (j!=j1)
{
if (costMatrix.at<float>(i,j)-v[j] < min)
{
min=costMatrix.at<float>(i,j)-v[j];
}
}
}
v[j1] = v[j1]-min;
}
}
}
// AUGMENTING ROW REDUCTION //
int loopcnt = 0;
do
{
loopcnt++;
k=0;
prvnumfree=numfree;
numfree=0;
while (k < prvnumfree)
{
i=free[k];
k++;
umin = costMatrix.at<float>(i,0)-v[0];
j1=0;
usubmin = std::numeric_limits<float>::max();
for (j=1; j<costMatrix.rows; j++)
{
h = costMatrix.at<float>(i,j)-v[j];
if (h < usubmin)
{
if (h >= umin)
{
usubmin = h;
j2 = j;
}
else
{
usubmin = umin;
umin = h;
j2 = j1;
j1 = j;
}
}
}
i0 = colsol[j1];
if (fabs(umin-usubmin) > LOWV) //if( umin < usubmin )
{
v[j1] = v[j1] - (usubmin - umin);
}
else // minimum and subminimum equal.
{
if (i0 >= 0) // minimum column j1 is assigned.
{
j1 = j2;
i0 = colsol[j2];
}
}
// (re-)assign i to j1, possibly de-assigning an i0.
rowsol[i]=j1;
colsol[j1]=i;
if (i0 >= 0)
{
//if( umin < usubmin )
if (fabs(umin-usubmin) > LOWV)
{
free[--k] = i0;
}
else
{
free[numfree++] = i0;
}
}
}
}while (loopcnt<2); // repeat once.
// AUGMENT SOLUTION for each free row //
for (f = 0; f<numfree; f++)
{
freerow = free[f]; // start row of augmenting path.
// Dijkstra shortest path algorithm.
// runs until unassigned column added to shortest path tree.
for (j = 0; j < costMatrix.rows; j++)
{
d[j] = costMatrix.at<float>(freerow,j) - v[j];
pred[j] = float(freerow);
collist[j] = j; // init column list.
}
low=0; // columns in 0..low-1 are ready, now none.
up=0; // columns in low..up-1 are to be scanned for current minimum, now none.
unassignedfound = false;
do
{
if (up == low)
{
last=low-1;
min = d[collist[up++]];
for (k = up; k < costMatrix.rows; k++)
{
j = collist[k];
h = d[j];
if (h <= min)
{
if (h < min) // new minimum.
{
up = low; // restart list at index low.
min = h;
}
collist[k] = collist[up];
collist[up++] = j;
}
}
for (k=low; k<up; k++)
{
if (colsol[collist[k]] < 0)
{
endofpath = collist[k];
unassignedfound = true;
break;
}
}
}
if (!unassignedfound)
{
// update 'distances' between freerow and all unscanned columns, via next scanned column.
j1 = collist[low];
low++;
i = colsol[j1];
h = costMatrix.at<float>(i,j1)-v[j1]-min;
for (k = up; k < costMatrix.rows; k++)
{
j = collist[k];
v2 = costMatrix.at<float>(i,j) - v[j] - h;
if (v2 < d[j])
{
pred[j] = float(i);
if (v2 == min)
{
if (colsol[j] < 0)
{
// if unassigned, shortest augmenting path is complete.
endofpath = j;
unassignedfound = true;
break;
}
else
{
collist[k] = collist[up];
collist[up++] = j;
}
}
d[j] = v2;
}
}
}
}while (!unassignedfound);
// update column prices.
for (k = 0; k <= last; k++)
{
j1 = collist[k];
v[j1] = v[j1] + d[j1] - min;
}
// reset row and column assignments along the alternating path.
do
{
i = int(pred[endofpath]);
colsol[endofpath] = i;
j1 = endofpath;
endofpath = rowsol[i];
rowsol[i] = j1;
}while (i != freerow);
}
// calculate symmetric shape context cost
cv::Mat trueCostMatrix(costMatrix, cv::Rect(0,0,sizeScd1, sizeScd2));
float leftcost = 0;
for (int nrow=0; nrow<trueCostMatrix.rows; nrow++)
{
double minval;
minMaxIdx(trueCostMatrix.row(nrow), &minval);
leftcost+=float(minval);
}
leftcost /= trueCostMatrix.rows;
float rightcost = 0;
for (int ncol=0; ncol<trueCostMatrix.cols; ncol++)
{
double minval;
minMaxIdx(trueCostMatrix.col(ncol), &minval);
rightcost+=float(minval);
}
rightcost /= trueCostMatrix.cols;
minMatchCost = std::max(leftcost,rightcost);
// Save in a DMatch vector
for (i=0;i<costMatrix.cols;i++)
{
cv::DMatch singleMatch(colsol[i],i,costMatrix.at<float>(colsol[i],i));//queryIdx,trainIdx,distance
outMatches.push_back(singleMatch);
}
// Update inliers
inliers1.reserve(sizeScd1);
for (size_t kc = 0; kc<inliers1.size(); kc++)
{
if (rowsol[kc]<sizeScd1) // if a real match
inliers1[kc]=1;
else
inliers1[kc]=0;
}
inliers2.reserve(sizeScd2);
for (size_t kc = 0; kc<inliers2.size(); kc++)
{
if (colsol[kc]<sizeScd2) // if a real match
inliers2[kc]=1;
else
inliers2[kc]=0;
}
}
};
/*
*
*/
namespace cv
{
class ShapeContextDistanceExtractorImpl : public ShapeContextDistanceExtractor
{
public:
/* Constructors */
ShapeContextDistanceExtractorImpl(int _nAngularBins, int _nRadialBins, float _innerRadius, float _outerRadius, int _iterations,
const Ptr<HistogramCostExtractor> &_comparer, const Ptr<ShapeTransformer> &_transformer)
{
nAngularBins=_nAngularBins;
nRadialBins=_nRadialBins;
innerRadius=_innerRadius;
outerRadius=_outerRadius;
rotationInvariant=false;
comparer=_comparer;
iterations=_iterations;
transformer=_transformer;
bendingEnergyWeight=0.3;
imageAppearanceWeight=0.0;
shapeContextWeight=1.0;
sigma=10;
name_ = "ShapeDistanceExtractor.SCD";
}
/* Destructor */
~ShapeContextDistanceExtractorImpl()
{
}
virtual AlgorithmInfo* info() const { return 0; }
//! the main operator
virtual float computeDistance(InputArray contour1, InputArray contour2);
//! Setters/Getters
virtual void setAngularBins(int _nAngularBins){CV_Assert(_nAngularBins>0); nAngularBins=_nAngularBins;}
virtual int getAngularBins() const {return nAngularBins;}
virtual void setRadialBins(int _nRadialBins){CV_Assert(_nRadialBins>0); nRadialBins=_nRadialBins;}
virtual int getRadialBins() const {return nRadialBins;}
virtual void setInnerRadius(float _innerRadius) {CV_Assert(_innerRadius>0); innerRadius=_innerRadius;}
virtual float getInnerRadius() const {return innerRadius;}
virtual void setOuterRadius(float _outerRadius) {CV_Assert(_outerRadius>0); outerRadius=_outerRadius;}
virtual float getOuterRadius() const {return outerRadius;}
virtual void setRotationInvariant(bool _rotationInvariant) {rotationInvariant=_rotationInvariant;}
virtual bool getRotationInvariant() const {return rotationInvariant;}
virtual void setCostExtractor(Ptr<HistogramCostExtractor> _comparer) { comparer = _comparer; }
virtual Ptr<HistogramCostExtractor> getCostExtractor() const { return comparer; }
virtual void setShapeContextWeight(float _shapeContextWeight) {shapeContextWeight=_shapeContextWeight;}
virtual float getShapeContextWeight() const {return shapeContextWeight;}
virtual void setImageAppearanceWeight(float _imageAppearanceWeight) {imageAppearanceWeight=_imageAppearanceWeight;}
virtual float getImageAppearanceWeight() const {return imageAppearanceWeight;}
virtual void setBendingEnergyWeight(float _bendingEnergyWeight) {bendingEnergyWeight=_bendingEnergyWeight;}
virtual float getBendingEnergyWeight() const {return bendingEnergyWeight;}
virtual void setStdDev(float _sigma) {sigma=_sigma;}
virtual float getStdDev() const {return sigma;}
virtual void setImages(InputArray _image1, InputArray _image2)
{
Mat image1_=_image1.getMat(), image2_=_image2.getMat();
CV_Assert((image1_.depth()==0) & (image2_.depth()==0));
image1=image1_;
image2=image2_;
}
virtual void getImages(OutputArray _image1, OutputArray _image2) const
{
CV_Assert((!image1.empty()) & (!image2.empty()));
_image1.create(image1.size(), image1.type());
_image2.create(image2.size(), image2.type());
_image1.getMat()=image1;
_image2.getMat()=image2;
}
virtual void setIterations(int _iterations) {CV_Assert(_iterations>0); iterations=_iterations;}
virtual int getIterations() const {return iterations;}
virtual void setTransformAlgorithm(Ptr<ShapeTransformer> _transformer) {transformer=_transformer;}
virtual Ptr<ShapeTransformer> getTransformAlgorithm() const {return transformer;}
//! write/read
virtual void write(FileStorage& fs) const
{
fs << "name" << name_
<< "nRads" << nRadialBins
<< "nAngs" << nAngularBins
<< "iters" << iterations
<< "img_1" << image1
<< "img_2" << image2
<< "beWei" << bendingEnergyWeight
<< "scWei" << shapeContextWeight
<< "iaWei" << imageAppearanceWeight
<< "costF" << costFlag
<< "rotIn" << rotationInvariant
<< "sigma" << sigma;
}
virtual void read(const FileNode& fn)
{
CV_Assert( (String)fn["name"] == name_ );
nRadialBins = (int)fn["nRads"];
nAngularBins = (int)fn["nAngs"];
iterations = (int)fn["iters"];
bendingEnergyWeight = (float)fn["beWei"];
shapeContextWeight = (float)fn["scWei"];
imageAppearanceWeight = (float)fn["iaWei"];
costFlag = (int)fn["costF"];
sigma = (float)fn["sigma"];
}
private:
int nAngularBins;
int nRadialBins;
float innerRadius;
float outerRadius;
bool rotationInvariant;
int costFlag;
int iterations;
Ptr<ShapeTransformer> transformer;
Ptr<HistogramCostExtractor> comparer;
Mat image1;
Mat image2;
float bendingEnergyWeight;
float imageAppearanceWeight;
float shapeContextWeight;
float sigma;
protected:
String name_;
};
float ShapeContextDistanceExtractorImpl::computeDistance(InputArray contour1, InputArray contour2)
{
// Checking //
Mat sset1=contour1.getMat(), sset2=contour2.getMat(), set1, set2;
if (set1.type() != CV_32F)
sset1.convertTo(set1, CV_32F);
else
sset1.copyTo(set1);
if (set2.type() != CV_32F)
sset2.convertTo(set2, CV_32F);
else
sset1.copyTo(set2);
CV_Assert((set1.channels()==2) & (set1.cols>0));
CV_Assert((set2.channels()==2) & (set2.cols>0));
if (imageAppearanceWeight!=0)
{
CV_Assert((!image1.empty()) & (!image2.empty()));
}
// Initializing Extractor, Descriptor structures and Matcher //
SCD set1SCE(nAngularBins, nRadialBins, innerRadius, outerRadius, false);
Mat set1SCD;
SCD set2SCE(nAngularBins, nRadialBins, innerRadius, outerRadius, false);
Mat set2SCD;
SCDMatcher matcher;
std::vector<DMatch> matches;
// Distance components (The output is a linear combination of these 3) //
float sDistance=0, bEnergy=0, iAppearance=0;
float beta;
// Initializing some variables //
std::vector<int> inliers1, inliers2;
bool isTPS=false;
if ( dynamic_cast<ThinPlateSplineShapeTransformer*>(&*transformer) )
isTPS=true;
Mat warpedImage;
for (int ii=0; ii<iterations; ii++)
{
// Extract SCD descriptor in the set1 //
set1SCE.extractSCD(set1, set1SCD, inliers1);
// Extract SCD descriptor of the set2 (TARGET) //
set2SCE.extractSCD(set2, set2SCD, inliers2, set1SCE.getMeanDistance());
// regularization parameter with annealing rate annRate //
beta=std::pow(set1SCE.getMeanDistance(),2);
// match //
matcher.matchDescriptors(set1SCD, set2SCD, matches, comparer, inliers1, inliers2);
// apply TPS transform //
if ( isTPS )
dynamic_cast<ThinPlateSplineShapeTransformer*>(&*transformer)->setRegularizationParameter(beta);
transformer->estimateTransformation(set1, set2, matches);
bEnergy += transformer->applyTransformation(set1, set1);
// Image appearance //
if (imageAppearanceWeight!=0)
{
// Have to accumulate the transformation along all the iterations
if (ii==0)
{
if ( isTPS )
{
image2.copyTo(warpedImage);
}
else
{
image1.copyTo(warpedImage);
}
}
transformer->warpImage(warpedImage, warpedImage);
}
}
Mat gaussWindow, diffIm;
if (imageAppearanceWeight!=0)
{
// compute appearance cost
if ( isTPS )
{
resize(warpedImage, warpedImage, image1.size());
Mat temp=(warpedImage-image1);
multiply(temp, temp, diffIm);
}
else
{
resize(warpedImage, warpedImage, image2.size());
Mat temp=(warpedImage-image2);
multiply(temp, temp, diffIm);
}
gaussWindow = Mat::zeros(warpedImage.rows, warpedImage.cols, CV_32F);
for (int pt=0; pt<sset1.cols; pt++)
{
for (int ii=0; ii<diffIm.rows; ii++)
{
for (int jj=0; jj<diffIm.cols; jj++)
{
float xx = sset1.at<Point2f>(0,pt).x;
float yy = sset1.at<Point2f>(0,pt).y;
float val = float(std::exp( -float( (xx-jj)*(xx-jj) + (yy-ii)*(yy-ii) )/(2*sigma*sigma) ) / (sigma*sigma*2*CV_PI));
gaussWindow.at<float>(ii,jj) += val;
}
}
}
Mat appIm(diffIm.rows, diffIm.cols, CV_32F);
for (int ii=0; ii<diffIm.rows; ii++)
{
for (int jj=0; jj<diffIm.cols; jj++)
{
float elema=float( diffIm.at<uchar>(ii,jj) )/255;
float elemb=gaussWindow.at<float>(ii,jj);
appIm.at<float>(ii,jj) = elema*elemb;
}
}
iAppearance = float(cv::sum(appIm)[0]/sset1.cols);
}
sDistance = matcher.getMatchingCost();
return (sDistance*shapeContextWeight+bEnergy*bendingEnergyWeight+iAppearance*imageAppearanceWeight);
}
Ptr <ShapeContextDistanceExtractor> createShapeContextDistanceExtractor(int nAngularBins, int nRadialBins, float innerRadius, float outerRadius, int iterations,
const Ptr<HistogramCostExtractor> &comparer, const Ptr<ShapeTransformer> &transformer)
{
return Ptr <ShapeContextDistanceExtractor> ( new ShapeContextDistanceExtractorImpl(nAngularBins, nRadialBins, innerRadius,
outerRadius, iterations, comparer, transformer) );
}
} // cv