Merge pull request #1248 from vkocheganov:chi_square_alt

modules/imgproc/doc/histograms.rst

@@ -173,6 +173,8 @@ Compares two histograms.
 
             * **CV_COMP_CHISQR**     Chi-Square
 
+            * **CV_COMP_CHISQR_ALT**     Alternative Chi-Square
+
             * **CV_COMP_INTERSECT**     Intersection
 
             * **CV_COMP_BHATTACHARYYA**     Bhattacharyya distance
@@ -202,6 +204,14 @@ The functions ``compareHist`` compare two dense or two sparse histograms using t
 
         d(H_1,H_2) =  \sum _I  \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)}
 
+* Alternative Chi-Square (``method=CV_COMP_CHISQR_ALT``)
+
+    .. math::
+
+        d(H_1,H_2) =  2 * \sum _I  \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)+H_2(I)}
+
+    This alternative formula is regularly used for texture comparison. See e.g. [Puzicha1997]_.
+
 * Intersection (``method=CV_COMP_INTERSECT``)
 
     .. math::
@@ -493,3 +503,4 @@ The function clears histogram bins that are below the specified threshold.
 
 
 .. [RubnerSept98] Y. Rubner. C. Tomasi, L.J. Guibas. *The Earth Mover’s Distance as a Metric for Image Retrieval*. Technical Report STAN-CS-TN-98-86, Department of Computer Science, Stanford University, September 1998.
+.. [Puzicha1997] Puzicha, J., Hofmann, T., and Buhmann, J. *Non-parametric similarity measures for unsupervised texture segmentation and image retrieval.* In Proc. IEEE Conf. Computer Vision and Pattern Recognition, San Juan, Puerto Rico, pp. 267-272, 1997.

modules/imgproc/include/opencv2/imgproc/types_c.h

@@ -508,7 +508,8 @@ enum
     CV_COMP_CHISQR        =1,
     CV_COMP_INTERSECT     =2,
     CV_COMP_BHATTACHARYYA =3,
-    CV_COMP_HELLINGER     =CV_COMP_BHATTACHARYYA
+    CV_COMP_HELLINGER     =CV_COMP_BHATTACHARYYA,
+    CV_COMP_CHISQR_ALT    =4
 };
 
 /* Mask size for distance transform */

modules/imgproc/src/histogram.cpp

@@ -1990,12 +1990,12 @@ double cv::compareHist( InputArray _H1, InputArray _H2, int method )
         const float* h2 = (const float*)it.planes[1].data;
         len = it.planes[0].rows*it.planes[0].cols*H1.channels();
 
-        if( method == CV_COMP_CHISQR )
+        if( (method == CV_COMP_CHISQR) || (method == CV_COMP_CHISQR_ALT))
         {
             for( j = 0; j < len; j++ )
             {
                 double a = h1[j] - h2[j];
-                double b = h1[j];
+                double b = (method == CV_COMP_CHISQR) ? h1[j] : h1[j] + h2[j];
                 if( fabs(b) > DBL_EPSILON )
                     result += a*a/b;
             }
@@ -2034,7 +2034,9 @@ double cv::compareHist( InputArray _H1, InputArray _H2, int method )
             CV_Error( CV_StsBadArg, "Unknown comparison method" );
     }
 
-    if( method == CV_COMP_CORREL )
+    if( method == CV_COMP_CHISQR_ALT )
+        result *= 2;
+    else if( method == CV_COMP_CORREL )
     {
         size_t total = H1.total();
         double scale = 1./total;
@@ -2063,13 +2065,13 @@ double cv::compareHist( const SparseMat& H1, const SparseMat& H2, int method )
         CV_Assert( H1.size(i) == H2.size(i) );
 
     const SparseMat *PH1 = &H1, *PH2 = &H2;
-    if( PH1->nzcount() > PH2->nzcount() && method != CV_COMP_CHISQR )
+    if( PH1->nzcount() > PH2->nzcount() && method != CV_COMP_CHISQR && method != CV_COMP_CHISQR_ALT)
         std::swap(PH1, PH2);
 
     SparseMatConstIterator it = PH1->begin();
     int N1 = (int)PH1->nzcount(), N2 = (int)PH2->nzcount();
 
-    if( method == CV_COMP_CHISQR )
+    if( (method == CV_COMP_CHISQR) || (method == CV_COMP_CHISQR_ALT) )
     {
         for( i = 0; i < N1; i++, ++it )
         {
@@ -2077,7 +2079,7 @@ double cv::compareHist( const SparseMat& H1, const SparseMat& H2, int method )
             const SparseMat::Node* node = it.node();
             float v2 = PH2->value<float>(node->idx, (size_t*)&node->hashval);
             double a = v1 - v2;
-            double b = v1;
+            double b = (method == CV_COMP_CHISQR) ? v1 : v1 + v2;
             if( fabs(b) > DBL_EPSILON )
                 result += a*a/b;
         }
@@ -2146,6 +2148,9 @@ double cv::compareHist( const SparseMat& H1, const SparseMat& H2, int method )
     else
         CV_Error( CV_StsBadArg, "Unknown comparison method" );
 
+    if( method == CV_COMP_CHISQR_ALT )
+        result *= 2;
+
     return result;
 }
 
@@ -2485,13 +2490,13 @@ cvCompareHist( const CvHistogram* hist1,
     CvSparseMatIterator iterator;
     CvSparseNode *node1, *node2;
 
-    if( mat1->heap->active_count > mat2->heap->active_count && method != CV_COMP_CHISQR )
+    if( mat1->heap->active_count > mat2->heap->active_count && method != CV_COMP_CHISQR && method != CV_COMP_CHISQR_ALT)
     {
         CvSparseMat* t;
         CV_SWAP( mat1, mat2, t );
     }
 
-    if( method == CV_COMP_CHISQR )
+    if( (method == CV_COMP_CHISQR) || (method == CV_COMP_CHISQR_ALT) )
     {
         for( node1 = cvInitSparseMatIterator( mat1, &iterator );
              node1 != 0; node1 = cvGetNextSparseNode( &iterator ))
@@ -2500,7 +2505,7 @@ cvCompareHist( const CvHistogram* hist1,
             uchar* node2_data = cvPtrND( mat2, CV_NODE_IDX(mat1,node1), 0, 0, &node1->hashval );
             double v2 = node2_data ? *(float*)node2_data : 0.f;
             double a = v1 - v2;
-            double b = v1;
+            double b = (method == CV_COMP_CHISQR) ? v1 : v1 + v2;
             if( fabs(b) > DBL_EPSILON )
                 result += a*a/b;
         }
@@ -2590,6 +2595,9 @@ cvCompareHist( const CvHistogram* hist1,
     else
         CV_Error( CV_StsBadArg, "Unknown comparison method" );
 
+    if( method == CV_COMP_CHISQR_ALT )
+        result *= 2;
+
     return result;
 }
 

modules/imgproc/test/test_histograms.cpp

@@ -948,7 +948,7 @@ int CV_ThreshHistTest::validate_test_results( int /*test_case_idx*/ )
 class CV_CompareHistTest : public CV_BaseHistTest
 {
 public:
-    enum { MAX_METHOD = 4 };
+    enum { MAX_METHOD = 5 };
 
     CV_CompareHistTest();
 protected:
@@ -1014,6 +1014,8 @@ int CV_CompareHistTest::validate_test_results( int /*test_case_idx*/ )
             result0[CV_COMP_INTERSECT] += MIN(v0,v1);
             if( fabs(v0) > DBL_EPSILON )
                 result0[CV_COMP_CHISQR] += (v0 - v1)*(v0 - v1)/v0;
+            if( fabs(v0 + v1) > DBL_EPSILON )
+                result0[CV_COMP_CHISQR_ALT] += (v0 - v1)*(v0 - v1)/(v0 + v1);
             s0 += v0;
             s1 += v1;
             sq0 += v0*v0;
@@ -1039,6 +1041,8 @@ int CV_CompareHistTest::validate_test_results( int /*test_case_idx*/ )
             result0[CV_COMP_INTERSECT] += MIN(v0,v1);
             if( fabs(v0) > DBL_EPSILON )
                 result0[CV_COMP_CHISQR] += (v0 - v1)*(v0 - v1)/v0;
+            if( fabs(v0 + v1) > DBL_EPSILON )
+                result0[CV_COMP_CHISQR_ALT] += (v0 - v1)*(v0 - v1)/(v0 + v1);
             s0 += v0;
             sq0 += v0*v0;
             result0[CV_COMP_BHATTACHARYYA] += sqrt(v0*v1);
@@ -1053,6 +1057,8 @@ int CV_CompareHistTest::validate_test_results( int /*test_case_idx*/ )
         }
     }
 
+    result0[CV_COMP_CHISQR_ALT] *= 2;
+
     t = (sq0 - s0*s0/total_size)*(sq1 - s1*s1/total_size);
     result0[CV_COMP_CORREL] = fabs(t) > DBL_EPSILON ?
         (result0[CV_COMP_CORREL] - s0*s1/total_size)/sqrt(t) : 1;
@@ -1067,6 +1073,7 @@ int CV_CompareHistTest::validate_test_results( int /*test_case_idx*/ )
         double v = result[i], v0 = result0[i];
         const char* method_name =
             i == CV_COMP_CHISQR ? "Chi-Square" :
+            i == CV_COMP_CHISQR_ALT ? "Alternative Chi-Square" :
             i == CV_COMP_CORREL ? "Correlation" :
             i == CV_COMP_INTERSECT ? "Intersection" :
             i == CV_COMP_BHATTACHARYYA ? "Bhattacharyya" : "Unknown";