switched back to FitEllipse algorithm by Dr. Daniel Weiss; improved its accuracy in some cases. It fixes #1638
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Vadim Pisarevsky
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7901879e48
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4eda1662aa
@ -771,202 +771,6 @@ cvContourArea( const void *array, CvSlice slice, int oriented )
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}
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/* for now this function works bad with singular cases
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You can see in the code, that when some troubles with
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matrices or some variables occur -
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box filled with zero values is returned.
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However in general function works fine.
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*/
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static void
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icvFitEllipse_F( CvSeq* points, CvBox2D* box )
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{
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cv::Ptr<CvMat> D;
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double S[36], C[36], T[36];
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int i, j;
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double eigenvalues[6], eigenvectors[36];
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double a, b, c, d, e, f;
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double x0, y0, idet, scale, offx = 0, offy = 0;
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int n = points->total;
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CvSeqReader reader;
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int is_float = CV_SEQ_ELTYPE(points) == CV_32FC2;
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CvMat matS = cvMat(6,6,CV_64F,S), matC = cvMat(6,6,CV_64F,C), matT = cvMat(6,6,CV_64F,T);
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CvMat _EIGVECS = cvMat(6,6,CV_64F,eigenvectors), _EIGVALS = cvMat(6,1,CV_64F,eigenvalues);
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/* create matrix D of input points */
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D = cvCreateMat( n, 6, CV_64F );
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cvStartReadSeq( points, &reader );
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/* shift all points to zero */
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for( i = 0; i < n; i++ )
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{
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if( !is_float )
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{
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offx += ((CvPoint*)reader.ptr)->x;
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offy += ((CvPoint*)reader.ptr)->y;
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}
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else
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{
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offx += ((CvPoint2D32f*)reader.ptr)->x;
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offy += ((CvPoint2D32f*)reader.ptr)->y;
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}
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CV_NEXT_SEQ_ELEM( points->elem_size, reader );
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}
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offx /= n;
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offy /= n;
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// fill matrix rows as (x*x, x*y, y*y, x, y, 1 )
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for( i = 0; i < n; i++ )
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{
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double x, y;
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double* Dptr = D->data.db + i*6;
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if( !is_float )
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{
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x = ((CvPoint*)reader.ptr)->x - offx;
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y = ((CvPoint*)reader.ptr)->y - offy;
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}
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else
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{
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x = ((CvPoint2D32f*)reader.ptr)->x - offx;
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y = ((CvPoint2D32f*)reader.ptr)->y - offy;
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}
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CV_NEXT_SEQ_ELEM( points->elem_size, reader );
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Dptr[0] = x * x;
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Dptr[1] = x * y;
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Dptr[2] = y * y;
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Dptr[3] = x;
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Dptr[4] = y;
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Dptr[5] = 1.;
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}
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// S = D^t*D
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cvMulTransposed( D, &matS, 1 );
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cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
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for( i = 0; i < 6; i++ )
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{
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double a = eigenvalues[i];
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a = a < DBL_EPSILON ? 0 : 1./sqrt(sqrt(a));
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for( j = 0; j < 6; j++ )
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eigenvectors[i*6 + j] *= a;
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}
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// C = Q^-1 = transp(INVEIGV) * INVEIGV
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cvMulTransposed( &_EIGVECS, &matC, 1 );
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cvZero( &matS );
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S[2] = 2.;
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S[7] = -1.;
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S[12] = 2.;
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// S = Q^-1*S*Q^-1
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cvMatMul( &matC, &matS, &matT );
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cvMatMul( &matT, &matC, &matS );
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// and find its eigenvalues and vectors too
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//cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
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cvEigenVV( &matS, &_EIGVECS, &_EIGVALS, 0 );
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for( i = 0; i < 3; i++ )
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if( eigenvalues[i] > 0 )
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break;
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if( i >= 3 /*eigenvalues[0] < DBL_EPSILON*/ )
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{
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box->center.x = box->center.y =
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box->size.width = box->size.height =
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box->angle = 0.f;
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return;
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}
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// now find truthful eigenvector
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_EIGVECS = cvMat( 6, 1, CV_64F, eigenvectors + 6*i );
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matT = cvMat( 6, 1, CV_64F, T );
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// Q^-1*eigenvecs[0]
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cvMatMul( &matC, &_EIGVECS, &matT );
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// extract vector components
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a = T[0]; b = T[1]; c = T[2]; d = T[3]; e = T[4]; f = T[5];
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///////////////// extract ellipse axes from above values ////////////////
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/*
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1) find center of ellipse
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it satisfy equation
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| a b/2 | * | x0 | + | d/2 | = |0 |
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| b/2 c | | y0 | | e/2 | |0 |
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*/
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idet = a * c - b * b * 0.25;
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idet = idet > DBL_EPSILON ? 1./idet : 0;
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// we must normalize (a b c d e f ) to fit (4ac-b^2=1)
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scale = sqrt( 0.25 * idet );
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if( scale < DBL_EPSILON )
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{
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box->center.x = (float)offx;
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box->center.y = (float)offy;
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box->size.width = box->size.height = box->angle = 0.f;
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return;
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}
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a *= scale;
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b *= scale;
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c *= scale;
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d *= scale;
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e *= scale;
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f *= scale;
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x0 = (-d * c + e * b * 0.5) * 2.;
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y0 = (-a * e + d * b * 0.5) * 2.;
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// recover center
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box->center.x = (float)(x0 + offx);
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box->center.y = (float)(y0 + offy);
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// offset ellipse to (x0,y0)
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// new f == F(x0,y0)
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f += a * x0 * x0 + b * x0 * y0 + c * y0 * y0 + d * x0 + e * y0;
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if( fabs(f) < DBL_EPSILON )
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{
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box->size.width = box->size.height = box->angle = 0.f;
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return;
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}
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scale = -1. / f;
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// normalize to f = 1
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a *= scale;
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b *= scale;
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c *= scale;
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// extract axis of ellipse
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// one more eigenvalue operation
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S[0] = a;
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S[1] = S[2] = b * 0.5;
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S[3] = c;
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matS = cvMat( 2, 2, CV_64F, S );
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_EIGVECS = cvMat( 2, 2, CV_64F, eigenvectors );
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_EIGVALS = cvMat( 1, 2, CV_64F, eigenvalues );
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cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
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// exteract axis length from eigenvectors
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box->size.width = (float)(2./sqrt(eigenvalues[0]));
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box->size.height = (float)(2./sqrt(eigenvalues[1]));
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// calc angle
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box->angle = (float)(180 - atan2(eigenvectors[2], eigenvectors[3])*180/CV_PI);
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}
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CV_IMPL CvBox2D
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cvFitEllipse2( const CvArr* array )
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{
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@ -993,12 +797,11 @@ cvFitEllipse2( const CvArr* array )
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n = ptseq->total;
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if( n < 5 )
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CV_Error( CV_StsBadSize, "Number of points should be >= 5" );
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#if 1
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icvFitEllipse_F( ptseq, &box );
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#else
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/*
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* New fitellipse algorithm, contributed by Dr. Daniel Weiss
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*/
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CvPoint2D32f c = {0,0};
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double gfp[5], rp[5], t;
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CvMat A, b, x;
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const double min_eps = 1e-6;
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@ -1015,6 +818,23 @@ cvFitEllipse2( const CvArr* array )
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cvStartReadSeq( ptseq, &reader );
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is_float = CV_SEQ_ELTYPE(ptseq) == CV_32FC2;
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for( i = 0; i < n; i++ )
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{
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CvPoint2D32f p;
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if( is_float )
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p = *(CvPoint2D32f*)(reader.ptr);
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else
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{
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p.x = (float)((int*)reader.ptr)[0];
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p.y = (float)((int*)reader.ptr)[1];
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}
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CV_NEXT_SEQ_ELEM( sizeof(p), reader );
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c.x += p.x;
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c.y += p.y;
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}
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c.x /= n;
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c.y /= n;
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for( i = 0; i < n; i++ )
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{
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@ -1027,6 +847,8 @@ cvFitEllipse2( const CvArr* array )
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p.y = (float)((int*)reader.ptr)[1];
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}
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CV_NEXT_SEQ_ELEM( sizeof(p), reader );
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p.x -= c.x;
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p.y -= c.y;
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bd[i] = 10000.0; // 1.0?
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Ad[i*5] = -(double)p.x * p.x; // A - C signs inverted as proposed by APP
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@ -1065,6 +887,8 @@ cvFitEllipse2( const CvArr* array )
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p.y = (float)((int*)reader.ptr)[1];
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}
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CV_NEXT_SEQ_ELEM( sizeof(p), reader );
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p.x -= c.x;
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p.y -= c.y;
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bd[i] = 1.0;
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Ad[i * 3] = (p.x - rp[0]) * (p.x - rp[0]);
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Ad[i * 3 + 1] = (p.y - rp[1]) * (p.y - rp[1]);
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@ -1086,8 +910,8 @@ cvFitEllipse2( const CvArr* array )
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if( rp[3] > min_eps )
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rp[3] = sqrt(2.0 / rp[3]);
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box.center.x = (float)rp[0];
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box.center.y = (float)rp[1];
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box.center.x = (float)rp[0] + c.x;
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box.center.y = (float)rp[1] + c.y;
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box.size.width = (float)(rp[2]*2);
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box.size.height = (float)(rp[3]*2);
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if( box.size.width > box.size.height )
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@ -1100,7 +924,6 @@ cvFitEllipse2( const CvArr* array )
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box.angle += 360;
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if( box.angle > 360 )
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box.angle -= 360;
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#endif
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return box;
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}
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@ -1134,6 +1134,8 @@ int CV_FitEllipseTest::validate_test_results( int test_case_idx )
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_exit_:
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#if 0
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if( code < 0 )
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{
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cvNamedWindow( "test", 0 );
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IplImage* img = cvCreateImage( cvSize(cvRound(low_high_range*4),
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cvRound(low_high_range*4)), 8, 3 );
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@ -1154,6 +1156,7 @@ _exit_:
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cvShowImage( "test", img );
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cvReleaseImage( &img );
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cvWaitKey(0);
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}
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#endif
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if( code < 0 )
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@ -1164,6 +1167,36 @@ _exit_:
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}
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class CV_FitEllipseSmallTest : public cvtest::BaseTest
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{
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public:
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CV_FitEllipseSmallTest() {}
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~CV_FitEllipseSmallTest() {}
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protected:
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void run(int)
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{
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Size sz(50, 50);
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vector<vector<Point> > c;
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c.push_back(vector<Point>());
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int scale = 1;
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Point ofs = Point(0,0);//sz.width/2, sz.height/2) - Point(4,4)*scale;
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c[0].push_back(Point(2, 0)*scale+ofs);
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c[0].push_back(Point(0, 2)*scale+ofs);
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c[0].push_back(Point(0, 6)*scale+ofs);
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c[0].push_back(Point(2, 8)*scale+ofs);
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c[0].push_back(Point(6, 8)*scale+ofs);
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c[0].push_back(Point(8, 6)*scale+ofs);
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c[0].push_back(Point(8, 2)*scale+ofs);
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c[0].push_back(Point(6, 0)*scale+ofs);
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RotatedRect e = fitEllipse(c[0]);
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CV_Assert( fabs(e.center.x - 4) <= 1. &&
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fabs(e.center.y - 4) <= 1. &&
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fabs(e.size.width - 9) <= 1. &&
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fabs(e.size.height - 9) <= 1. );
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}
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};
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/****************************************************************************************\
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* FitLine Test *
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\****************************************************************************************/
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@ -1664,6 +1697,7 @@ TEST(Imgproc_FitEllipse, accuracy) { CV_FitEllipseTest test; test.safe_run(); }
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TEST(Imgproc_FitLine, accuracy) { CV_FitLineTest test; test.safe_run(); }
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TEST(Imgproc_ContourMoments, accuracy) { CV_ContourMomentsTest test; test.safe_run(); }
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TEST(Imgproc_ContourPerimeterSlice, accuracy) { CV_PerimeterAreaSliceTest test; test.safe_run(); }
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TEST(Imgproc_FitEllipse, small) { CV_FitEllipseSmallTest test; test.safe_run(); }
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/* End of file. */
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