/*M/////////////////////////////////////////////////////////////////////////////////////// // // 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. // // // Intel License Agreement // For Open Source Computer Vision Library // // Copyright (C) 2000, Intel Corporation, all rights reserved. // Third party copyrights are property of their respective owners. // // 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 Intel Corporation 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. // //M*/ #include "precomp.hpp" #include "_vm.h" #include #define Sgn(x) ( (x)<0 ? -1:1 ) /* Sgn(0) = 1 ! */ /*===========================================================================*/ CvStatus icvLMedS( int *points1, int *points2, int numPoints, CvMatrix3 * fundamentalMatrix ) { int sample, j, amount_samples, done; int amount_solutions; int ml7[21], mr7[21]; double F_try[9 * 3]; double F[9]; double Mj, Mj_new; int i, num; int *ml; int *mr; int *new_ml; int *new_mr; int new_num; CvStatus error; error = CV_NO_ERR; if( fundamentalMatrix == 0 ) return CV_BADFACTOR_ERR; num = numPoints; if( num < 6 ) { return CV_BADFACTOR_ERR; } /* if */ ml = (int *) cvAlloc( sizeof( int ) * num * 3 ); mr = (int *) cvAlloc( sizeof( int ) * num * 3 ); for( i = 0; i < num; i++ ) { ml[i * 3] = points1[i * 2]; ml[i * 3 + 1] = points1[i * 2 + 1]; ml[i * 3 + 2] = 1; mr[i * 3] = points2[i * 2]; mr[i * 3 + 1] = points2[i * 2 + 1]; mr[i * 3 + 2] = 1; } /* for */ if( num > 7 ) { Mj = -1; amount_samples = 1000; /* ------- Must be changed ! --------- */ for( sample = 0; sample < amount_samples; sample++ ) { icvChoose7( ml, mr, num, ml7, mr7 ); icvPoint7( ml7, mr7, F_try, &amount_solutions ); for( i = 0; i < amount_solutions / 9; i++ ) { Mj_new = icvMedian( ml, mr, num, F_try + i * 9 ); if( Mj_new >= 0 && (Mj == -1 || Mj_new < Mj) ) { for( j = 0; j < 9; j++ ) { F[j] = F_try[i * 9 + j]; } /* for */ Mj = Mj_new; } /* if */ } /* for */ } /* for */ if( Mj == -1 ) return CV_BADFACTOR_ERR; done = icvBoltingPoints( ml, mr, num, F, Mj, &new_ml, &new_mr, &new_num ); if( done == -1 ) { cvFree( &mr ); cvFree( &ml ); return CV_OUTOFMEM_ERR; } /* if */ if( done > 7 ) error = icvPoints8( new_ml, new_mr, new_num, F ); cvFree( &new_mr ); cvFree( &new_ml ); } else { error = icvPoint7( ml, mr, F, &i ); } /* if */ if( error == CV_NO_ERR ) error = icvRank2Constraint( F ); for( i = 0; i < 3; i++ ) for( j = 0; j < 3; j++ ) fundamentalMatrix->m[i][j] = (float) F[i * 3 + j]; return error; } /* icvLMedS */ /*===========================================================================*/ /*===========================================================================*/ #if defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ == 8) # pragma GCC diagnostic push # pragma GCC diagnostic ignored "-Warray-bounds" #endif void icvChoose7( int *ml, int *mr, int num, int *ml7, int *mr7 ) { int indexes[7], i, j; if( !ml || !mr || num < 7 || !ml7 || !mr7 ) return; for( i = 0; i < 7; i++ ) { indexes[i] = (int) ((double) rand() / RAND_MAX * num); for( j = 0; j < i; j++ ) { if( indexes[i] == indexes[j] ) i--; } /* for */ } /* for */ for( i = 0; i < 21; i++ ) { ml7[i] = ml[3 * indexes[i / 3] + i % 3]; mr7[i] = mr[3 * indexes[i / 3] + i % 3]; } /* for */ } /* cs_Choose7 */ /*===========================================================================*/ /*===========================================================================*/ CvStatus icvCubic( double a2, double a1, double a0, double *squares ) { double p, q, D, c1, c2, b1, b2, ro1, ro2, fi1, fi2, tt; double x[6][3]; int i, j, t; if( !squares ) return CV_BADFACTOR_ERR; p = a1 - a2 * a2 / 3; q = (9 * a1 * a2 - 27 * a0 - 2 * a2 * a2 * a2) / 27; D = q * q / 4 + p * p * p / 27; if( D < 0 ) { c1 = q / 2; c2 = c1; b1 = sqrt( -D ); b2 = -b1; ro1 = sqrt( c1 * c1 - D ); ro2 = ro1; fi1 = atan2( b1, c1 ); fi2 = -fi1; } else { c1 = q / 2 + sqrt( D ); c2 = q / 2 - sqrt( D ); b1 = 0; b2 = 0; ro1 = fabs( c1 ); ro2 = fabs( c2 ); fi1 = CV_PI * (1 - SIGN( c1 )) / 2; fi2 = CV_PI * (1 - SIGN( c2 )) / 2; } /* if */ for( i = 0; i < 6; i++ ) { x[i][0] = -a2 / 3; x[i][1] = 0; x[i][2] = 0; squares[i] = x[i][i % 2]; } /* for */ if( !REAL_ZERO( ro1 )) { tt = SIGN( ro1 ) * pow( fabs( ro1 ), 0.333333333333 ); c1 = tt - p / (3. * tt); c2 = tt + p / (3. * tt); } /* if */ if( !REAL_ZERO( ro2 )) { tt = SIGN( ro2 ) * pow( fabs( ro2 ), 0.333333333333 ); b1 = tt - p / (3. * tt); b2 = tt + p / (3. * tt); } /* if */ for( i = 0; i < 6; i++ ) { if( i < 3 ) { if( !REAL_ZERO( ro1 )) { x[i][0] = cos( fi1 / 3. + 2 * CV_PI * (i % 3) / 3. ) * c1 - a2 / 3; x[i][1] = sin( fi1 / 3. + 2 * CV_PI * (i % 3) / 3. ) * c2; } else { x[i][2] = 1; } /* if */ } else { if( !REAL_ZERO( ro2 )) { x[i][0] = cos( fi2 / 3. + 2 * CV_PI * (i % 3) / 3. ) * b1 - a2 / 3; x[i][1] = sin( fi2 / 3. + 2 * CV_PI * (i % 3) / 3. ) * b2; } else { x[i][2] = 1; } /* if */ } /* if */ } /* for */ t = 0; for( i = 0; i < 6; i++ ) { if( !x[i][2] ) { squares[t++] = x[i][0]; squares[t++] = x[i][1]; x[i][2] = 1; for( j = i + 1; j < 6; j++ ) { if( !x[j][2] && REAL_ZERO( x[i][0] - x[j][0] ) && REAL_ZERO( x[i][1] - x[j][1] )) { x[j][2] = 1; break; } /* if */ } /* for */ } /* if */ } /* for */ return CV_NO_ERR; } /* icvCubic */ #if defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ == 8) # pragma GCC diagnostic pop #endif /*======================================================================================*/ double icvDet( double *M ) { double value; if( !M ) return 0; value = M[0] * M[4] * M[8] + M[2] * M[3] * M[7] + M[1] * M[5] * M[6] - M[2] * M[4] * M[6] - M[0] * M[5] * M[7] - M[1] * M[3] * M[8]; return value; } /* icvDet */ /*===============================================================================*/ double icvMinor( double *M, int x, int y ) { int row1, row2, col1, col2; double value; if( !M || x < 0 || x > 2 || y < 0 || y > 2 ) return 0; row1 = (y == 0 ? 1 : 0); row2 = (y == 2 ? 1 : 2); col1 = (x == 0 ? 1 : 0); col2 = (x == 2 ? 1 : 2); value = M[row1 * 3 + col1] * M[row2 * 3 + col2] - M[row2 * 3 + col1] * M[row1 * 3 + col2]; value *= 1 - (x + y) % 2 * 2; return value; } /* icvMinor */ /*======================================================================================*/ CvStatus icvGetCoef( double *f1, double *f2, double *a2, double *a1, double *a0 ) { double G[9], a3; int i; if( !f1 || !f2 || !a0 || !a1 || !a2 ) return CV_BADFACTOR_ERR; for( i = 0; i < 9; i++ ) { G[i] = f1[i] - f2[i]; } /* for */ a3 = icvDet( G ); if( REAL_ZERO( a3 )) return CV_BADFACTOR_ERR; *a2 = 0; *a1 = 0; *a0 = icvDet( f2 ); for( i = 0; i < 9; i++ ) { *a2 += f2[i] * icvMinor( G, (int) (i % 3), (int) (i / 3) ); *a1 += G[i] * icvMinor( f2, (int) (i % 3), (int) (i / 3) ); } /* for */ *a0 /= a3; *a1 /= a3; *a2 /= a3; return CV_NO_ERR; } /* icvGetCoef */ /*===========================================================================*/ double icvMedian( int *ml, int *mr, int num, double *F ) { double l1, l2, l3, d1, d2, value; double *deviation; int i, i3; if( !ml || !mr || !F ) return -1; deviation = (double *) cvAlloc( (num) * sizeof( double )); if( !deviation ) return -1; for( i = 0, i3 = 0; i < num; i++, i3 += 3 ) { l1 = F[0] * mr[i3] + F[1] * mr[i3 + 1] + F[2]; l2 = F[3] * mr[i3] + F[4] * mr[i3 + 1] + F[5]; l3 = F[6] * mr[i3] + F[7] * mr[i3 + 1] + F[8]; d1 = (l1 * ml[i3] + l2 * ml[i3 + 1] + l3) / sqrt( l1 * l1 + l2 * l2 ); l1 = F[0] * ml[i3] + F[3] * ml[i3 + 1] + F[6]; l2 = F[1] * ml[i3] + F[4] * ml[i3 + 1] + F[7]; l3 = F[2] * ml[i3] + F[5] * ml[i3 + 1] + F[8]; d2 = (l1 * mr[i3] + l2 * mr[i3 + 1] + l3) / sqrt( l1 * l1 + l2 * l2 ); deviation[i] = (double) (d1 * d1 + d2 * d2); } /* for */ if( icvSort( deviation, num ) != CV_NO_ERR ) { cvFree( &deviation ); return -1; } /* if */ value = deviation[num / 2]; cvFree( &deviation ); return value; } /* cs_Median */ /*===========================================================================*/ CvStatus icvSort( double *array, int length ) { int i, j, index; double swapd; if( !array || length < 1 ) return CV_BADFACTOR_ERR; for( i = 0; i < length - 1; i++ ) { index = i; for( j = i + 1; j < length; j++ ) { if( array[j] < array[index] ) index = j; } /* for */ if( index - i ) { swapd = array[i]; array[i] = array[index]; array[index] = swapd; } /* if */ } /* for */ return CV_NO_ERR; } /* cs_Sort */ /*===========================================================================*/ int icvBoltingPoints( int *ml, int *mr, int num, double *F, double Mj, int **new_ml, int **new_mr, int *new_num ) { double l1, l2, l3, d1, d2, sigma; int i, j, length; int *index; if( !ml || !mr || num < 1 || !F || Mj < 0 ) return -1; index = (int *) cvAlloc( (num) * sizeof( int )); if( !index ) return -1; length = 0; sigma = (double) (2.5 * 1.4826 * (1 + 5. / (num - 7)) * sqrt( Mj )); for( i = 0; i < num * 3; i += 3 ) { l1 = F[0] * mr[i] + F[1] * mr[i + 1] + F[2]; l2 = F[3] * mr[i] + F[4] * mr[i + 1] + F[5]; l3 = F[6] * mr[i] + F[7] * mr[i + 1] + F[8]; d1 = (l1 * ml[i] + l2 * ml[i + 1] + l3) / sqrt( l1 * l1 + l2 * l2 ); l1 = F[0] * ml[i] + F[3] * ml[i + 1] + F[6]; l2 = F[1] * ml[i] + F[4] * ml[i + 1] + F[7]; l3 = F[2] * ml[i] + F[5] * ml[i + 1] + F[8]; d2 = (l1 * mr[i] + l2 * mr[i + 1] + l3) / sqrt( l1 * l1 + l2 * l2 ); if( d1 * d1 + d2 * d2 <= sigma * sigma ) { index[i / 3] = 1; length++; } else { index[i / 3] = 0; } /* if */ } /* for */ *new_num = length; *new_ml = (int *) cvAlloc( (length * 3) * sizeof( int )); if( !new_ml ) { cvFree( &index ); return -1; } /* if */ *new_mr = (int *) cvAlloc( (length * 3) * sizeof( int )); if( !new_mr ) { cvFree( &new_ml ); cvFree( &index ); return -1; } /* if */ j = 0; for( i = 0; i < num * 3; ) { if( index[i / 3] ) { (*new_ml)[j] = ml[i]; (*new_mr)[j++] = mr[i++]; (*new_ml)[j] = ml[i]; (*new_mr)[j++] = mr[i++]; (*new_ml)[j] = ml[i]; (*new_mr)[j++] = mr[i++]; } else i += 3; } /* for */ cvFree( &index ); return length; } /* cs_BoltingPoints */ /*===========================================================================*/ CvStatus icvPoints8( int *ml, int *mr, int num, double *F ) { double *U; double l1, l2, w, old_norm = -1, new_norm = -2, summ; int i3, i9, j, num3, its = 0, a, t; if( !ml || !mr || num < 8 || !F ) return CV_BADFACTOR_ERR; U = (double *) cvAlloc( (num * 9) * sizeof( double )); if( !U ) return CV_OUTOFMEM_ERR; num3 = num * 3; while( !REAL_ZERO( new_norm - old_norm )) { if( its++ > 1e+2 ) { cvFree( &U ); return CV_BADFACTOR_ERR; } /* if */ old_norm = new_norm; for( i3 = 0, i9 = 0; i3 < num3; i3 += 3, i9 += 9 ) { l1 = F[0] * mr[i3] + F[1] * mr[i3 + 1] + F[2]; l2 = F[3] * mr[i3] + F[4] * mr[i3 + 1] + F[5]; if( REAL_ZERO( l1 ) && REAL_ZERO( l2 )) { cvFree( &U ); return CV_BADFACTOR_ERR; } /* if */ w = 1 / (l1 * l1 + l2 * l2); l1 = F[0] * ml[i3] + F[3] * ml[i3 + 1] + F[6]; l2 = F[1] * ml[i3] + F[4] * ml[i3 + 1] + F[7]; if( REAL_ZERO( l1 ) && REAL_ZERO( l2 )) { cvFree( &U ); return CV_BADFACTOR_ERR; } /* if */ w += 1 / (l1 * l1 + l2 * l2); w = sqrt( w ); for( j = 0; j < 9; j++ ) { U[i9 + j] = w * (double) ml[i3 + j / 3] * (double) mr[i3 + j % 3]; } /* for */ } /* for */ new_norm = 0; for( a = 0; a < num; a++ ) { /* row */ summ = 0; for( t = 0; t < 9; t++ ) { summ += U[a * 9 + t] * F[t]; } /* for */ new_norm += summ * summ; } /* for */ new_norm = sqrt( new_norm ); icvAnalyticPoints8( U, num, F ); } /* while */ cvFree( &U ); return CV_NO_ERR; } /* cs_Points8 */ /*===========================================================================*/ double icvAnalyticPoints8( double *A, int num, double *F ) { double *U; double V[8 * 8]; double W[8]; double *f; double solution[9]; double temp1[8 * 8]; double *temp2; double *A_short; double norm, summ, best_norm; int num8 = num * 8, num9 = num * 9; int i, j, j8, j9, value, a, a8, a9, a_num, b, b8, t; /* --------- Initialization data ------------------ */ if( !A || num < 8 || !F ) return -1; best_norm = -1; U = (double *) cvAlloc( (num8) * sizeof( double )); if( !U ) return -1; f = (double *) cvAlloc( (num) * sizeof( double )); if( !f ) { cvFree( &U ); return -1; } /* if */ temp2 = (double *) cvAlloc( (num8) * sizeof( double )); if( !temp2 ) { cvFree( &f ); cvFree( &U ); return -1; } /* if */ A_short = (double *) cvAlloc( (num8) * sizeof( double )); if( !A_short ) { cvFree( &temp2 ); cvFree( &f ); cvFree( &U ); return -1; } /* if */ for( i = 0; i < 8; i++ ) { for( j8 = 0, j9 = 0; j9 < num9; j8 += 8, j9 += 9 ) { A_short[j8 + i] = A[j9 + i + 1]; } /* for */ } /* for */ for( i = 0; i < 9; i++ ) { for( j = 0, j8 = 0, j9 = 0; j < num; j++, j8 += 8, j9 += 9 ) { f[j] = -A[j9 + i]; if( i ) A_short[j8 + i - 1] = A[j9 + i - 1]; } /* for */ value = icvSingularValueDecomposition( num, 8, A_short, W, 1, U, 1, V ); if( !value ) { /* ----------- computing the solution ----------- */ /* ----------- W = W(-1) ----------- */ for( j = 0; j < 8; j++ ) { if( !REAL_ZERO( W[j] )) W[j] = 1 / W[j]; } /* for */ /* ----------- temp1 = V * W(-1) ----------- */ for( a8 = 0; a8 < 64; a8 += 8 ) { /* row */ for( b = 0; b < 8; b++ ) { /* column */ temp1[a8 + b] = V[a8 + b] * W[b]; } /* for */ } /* for */ /* ----------- temp2 = V * W(-1) * U(T) ----------- */ for( a8 = 0, a_num = 0; a8 < 64; a8 += 8, a_num += num ) { /* row */ for( b = 0, b8 = 0; b < num; b++, b8 += 8 ) { /* column */ temp2[a_num + b] = 0; for( t = 0; t < 8; t++ ) { temp2[a_num + b] += temp1[a8 + t] * U[b8 + t]; } /* for */ } /* for */ } /* for */ /* ----------- solution = V * W(-1) * U(T) * f ----------- */ for( a = 0, a_num = 0; a < 8; a++, a_num += num ) { /* row */ for( b = 0; b < num; b++ ) { /* column */ solution[a] = 0; for( t = 0; t < num && W[a]; t++ ) { solution[a] += temp2[a_num + t] * f[t]; } /* for */ } /* for */ } /* for */ for( a = 8; a > 0; a-- ) { if( a == i ) break; solution[a] = solution[a - 1]; } /* for */ solution[a] = 1; norm = 0; for( a9 = 0; a9 < num9; a9 += 9 ) { /* row */ summ = 0; for( t = 0; t < 9; t++ ) { summ += A[a9 + t] * solution[t]; } /* for */ norm += summ * summ; } /* for */ norm = sqrt( norm ); if( best_norm == -1 || norm < best_norm ) { for( j = 0; j < 9; j++ ) F[j] = solution[j]; best_norm = norm; } /* if */ } /* if */ } /* for */ cvFree( &A_short ); cvFree( &temp2 ); cvFree( &f ); cvFree( &U ); return best_norm; } /* cs_AnalyticPoints8 */ /*===========================================================================*/ CvStatus icvRank2Constraint( double *F ) { double U[9], V[9], W[3]; double aW[3]; int i, i3, j, j3, t; if( F == 0 ) return CV_BADFACTOR_ERR; if( icvSingularValueDecomposition( 3, 3, F, W, 1, U, 1, V )) return CV_BADFACTOR_ERR; aW[0] = fabs(W[0]); aW[1] = fabs(W[1]); aW[2] = fabs(W[2]); if( aW[0] < aW[1] ) { if( aW[0] < aW[2] ) { if( REAL_ZERO( W[0] )) return CV_NO_ERR; else W[0] = 0; } else { if( REAL_ZERO( W[2] )) return CV_NO_ERR; else W[2] = 0; } /* if */ } else { if( aW[1] < aW[2] ) { if( REAL_ZERO( W[1] )) return CV_NO_ERR; else W[1] = 0; } else { if( REAL_ZERO( W[2] )) return CV_NO_ERR; else W[2] = 0; } /* if */ } /* if */ for( i = 0; i < 3; i++ ) { for( j3 = 0; j3 < 9; j3 += 3 ) { U[j3 + i] *= W[i]; } /* for */ } /* for */ for( i = 0, i3 = 0; i < 3; i++, i3 += 3 ) { for( j = 0, j3 = 0; j < 3; j++, j3 += 3 ) { F[i3 + j] = 0; for( t = 0; t < 3; t++ ) { F[i3 + j] += U[i3 + t] * V[j3 + t]; } /* for */ } /* for */ } /* for */ return CV_NO_ERR; } /* cs_Rank2Constraint */ /*===========================================================================*/ int icvSingularValueDecomposition( int M, int N, double *A, double *W, int get_U, double *U, int get_V, double *V ) { int i = 0, j, k, l = 0, i1, k1, l1 = 0; int iterations, error = 0, jN, iN, kN, lN = 0; double *rv1; double c, f, g, h, s, x, y, z, scale, anorm; double af, ag, ah, t; int MN = M * N; int NN = N * N; /* max_iterations - maximum number QR-iterations cc - reduces requirements to number stitch (cc>1) */ int max_iterations = 100; double cc = 100; if( M < N ) return N; rv1 = (double *) cvAlloc( N * sizeof( double )); if( rv1 == 0 ) return N; for( iN = 0; iN < MN; iN += N ) { for( j = 0; j < N; j++ ) U[iN + j] = A[iN + j]; } /* for */ /* Adduction to bidiagonal type (transformations of reflection). Bidiagonal matrix is located in W (diagonal elements) and in rv1 (upperdiagonal elements) */ g = 0; scale = 0; anorm = 0; for( i = 0, iN = 0; i < N; i++, iN += N ) { l = i + 1; lN = iN + N; rv1[i] = scale * g; /* Multiplyings on the left */ g = 0; s = 0; scale = 0; for( kN = iN; kN < MN; kN += N ) scale += fabs( U[kN + i] ); if( !REAL_ZERO( scale )) { for( kN = iN; kN < MN; kN += N ) { U[kN + i] /= scale; s += U[kN + i] * U[kN + i]; } /* for */ f = U[iN + i]; g = -sqrt( s ) * Sgn( f ); h = f * g - s; U[iN + i] = f - g; for( j = l; j < N; j++ ) { s = 0; for( kN = iN; kN < MN; kN += N ) { s += U[kN + i] * U[kN + j]; } /* for */ f = s / h; for( kN = iN; kN < MN; kN += N ) { U[kN + j] += f * U[kN + i]; } /* for */ } /* for */ for( kN = iN; kN < MN; kN += N ) U[kN + i] *= scale; } /* if */ W[i] = scale * g; /* Multiplyings on the right */ g = 0; s = 0; scale = 0; for( k = l; k < N; k++ ) scale += fabs( U[iN + k] ); if( !REAL_ZERO( scale )) { for( k = l; k < N; k++ ) { U[iN + k] /= scale; s += (U[iN + k]) * (U[iN + k]); } /* for */ f = U[iN + l]; g = -sqrt( s ) * Sgn( f ); h = f * g - s; U[i * N + l] = f - g; for( k = l; k < N; k++ ) rv1[k] = U[iN + k] / h; for( jN = lN; jN < MN; jN += N ) { s = 0; for( k = l; k < N; k++ ) s += U[jN + k] * U[iN + k]; for( k = l; k < N; k++ ) U[jN + k] += s * rv1[k]; } /* for */ for( k = l; k < N; k++ ) U[iN + k] *= scale; } /* if */ t = fabs( W[i] ); t += fabs( rv1[i] ); anorm = MAX( anorm, t ); } /* for */ anorm *= cc; /* accumulation of right transformations, if needed */ if( get_V ) { for( i = N - 1, iN = NN - N; i >= 0; i--, iN -= N ) { if( i < N - 1 ) { /* pass-by small g */ if( !REAL_ZERO( g )) { for( j = l, jN = lN; j < N; j++, jN += N ) V[jN + i] = U[iN + j] / U[iN + l] / g; for( j = l; j < N; j++ ) { s = 0; for( k = l, kN = lN; k < N; k++, kN += N ) s += U[iN + k] * V[kN + j]; for( kN = lN; kN < NN; kN += N ) V[kN + j] += s * V[kN + i]; } /* for */ } /* if */ for( j = l, jN = lN; j < N; j++, jN += N ) { V[iN + j] = 0; V[jN + i] = 0; } /* for */ } /* if */ V[iN + i] = 1; g = rv1[i]; l = i; lN = iN; } /* for */ } /* if */ /* accumulation of left transformations, if needed */ if( get_U ) { for( i = N - 1, iN = NN - N; i >= 0; i--, iN -= N ) { l = i + 1; lN = iN + N; g = W[i]; for( j = l; j < N; j++ ) U[iN + j] = 0; /* pass-by small g */ if( !REAL_ZERO( g )) { for( j = l; j < N; j++ ) { s = 0; for( kN = lN; kN < MN; kN += N ) s += U[kN + i] * U[kN + j]; f = s / U[iN + i] / g; for( kN = iN; kN < MN; kN += N ) U[kN + j] += f * U[kN + i]; } /* for */ for( jN = iN; jN < MN; jN += N ) U[jN + i] /= g; } else { for( jN = iN; jN < MN; jN += N ) U[jN + i] = 0; } /* if */ U[iN + i] += 1; } /* for */ } /* if */ /* Iterations QR-algorithm for bidiagonal matrices W[i] - is the main diagonal rv1[i] - is the top diagonal, rv1[0]=0. */ for( k = N - 1; k >= 0; k-- ) { k1 = k - 1; iterations = 0; for( ;; ) { /* Cycle: checking a possibility of fission matrix */ for( l = k; l >= 0; l-- ) { l1 = l - 1; if( REAL_ZERO( rv1[l] ) || REAL_ZERO( W[l1] )) break; } /* for */ if( !REAL_ZERO( rv1[l] )) { /* W[l1] = 0, matrix possible to fission by clearing out rv1[l] */ c = 0; s = 1; for( i = l; i <= k; i++ ) { f = s * rv1[i]; rv1[i] = c * rv1[i]; /* Rotations are done before the end of the block, or when element in the line is finagle. */ if( REAL_ZERO( f )) break; g = W[i]; /* Scaling prevents finagling H ( F!=0!) */ af = fabs( f ); ag = fabs( g ); if( af < ag ) h = ag * sqrt( 1 + (f / g) * (f / g) ); else h = af * sqrt( 1 + (f / g) * (f / g) ); W[i] = h; c = g / h; s = -f / h; if( get_U ) { for( jN = 0; jN < MN; jN += N ) { y = U[jN + l1]; z = U[jN + i]; U[jN + l1] = y * c + z * s; U[jN + i] = -y * s + z * c; } /* for */ } /* if */ } /* for */ } /* if */ /* Output in this place of program means, that rv1[L] = 0, matrix fissioned Iterations of the process of the persecution will be executed always for the bottom block ( from l before k ), with increase l possible. */ z = W[k]; if( l == k ) break; /* Completion iterations: lower block became trivial ( rv1[K]=0) */ if( iterations++ == max_iterations ) return k; /* Shift is computed on the lowest order 2 minor. */ x = W[l]; y = W[k1]; g = rv1[k1]; h = rv1[k]; /* consequent fission prevents forming a machine zero */ f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2 * h) / y; /* prevented overflow */ if( fabs( f ) > 1 ) { g = fabs( f ); g *= sqrt( 1 + (1 / f) * (1 / f) ); } else g = sqrt( f * f + 1 ); f = ((x - z) * (x + z) + h * (y / (f + fabs( g ) * Sgn( f )) - h)) / x; c = 1; s = 1; for( i1 = l; i1 <= k1; i1++ ) { i = i1 + 1; g = rv1[i]; y = W[i]; h = s * g; g *= c; /* Scaling at calculation Z prevents its clearing, however if F and H both are zero - pass-by of fission on Z. */ af = fabs( f ); ah = fabs( h ); if( af < ah ) z = ah * sqrt( 1 + (f / h) * (f / h) ); else { z = 0; if( !REAL_ZERO( af )) z = af * sqrt( 1 + (h / f) * (h / f) ); } /* if */ rv1[i1] = z; /* if Z=0, the rotation is free. */ if( !REAL_ZERO( z )) { c = f / z; s = h / z; } /* if */ f = x * c + g * s; g = -x * s + g * c; h = y * s; y *= c; if( get_V ) { for( jN = 0; jN < NN; jN += N ) { x = V[jN + i1]; z = V[jN + i]; V[jN + i1] = x * c + z * s; V[jN + i] = -x * s + z * c; } /* for */ } /* if */ af = fabs( f ); ah = fabs( h ); if( af < ah ) z = ah * sqrt( 1 + (f / h) * (f / h) ); else { z = 0; if( !REAL_ZERO( af )) z = af * sqrt( 1 + (h / f) * (h / f) ); } /* if */ W[i1] = z; if( !REAL_ZERO( z )) { c = f / z; s = h / z; } /* if */ f = c * g + s * y; x = -s * g + c * y; if( get_U ) { for( jN = 0; jN < MN; jN += N ) { y = U[jN + i1]; z = U[jN + i]; U[jN + i1] = y * c + z * s; U[jN + i] = -y * s + z * c; } /* for */ } /* if */ } /* for */ rv1[l] = 0; rv1[k] = f; W[k] = x; } /* for */ if( z < 0 ) { W[k] = -z; if( get_V ) { for( jN = 0; jN < NN; jN += N ) V[jN + k] *= -1; } /* if */ } /* if */ } /* for */ cvFree( &rv1 ); return error; } /* vm_SingularValueDecomposition */ /*========================================================================*/ /* Obsolete functions. Just for ViewMorping */ /*=====================================================================================*/ int icvGaussMxN( double *A, double *B, int M, int N, double **solutions ) { int *variables; int row, swapi, i, i_best = 0, j, j_best = 0, t; double swapd, ratio, bigest; if( !A || !B || !M || !N ) return -1; variables = (int *) cvAlloc( (size_t) N * sizeof( int )); if( variables == 0 ) return -1; for( i = 0; i < N; i++ ) { variables[i] = i; } /* for */ /* ----- Direct way ----- */ for( row = 0; row < M; row++ ) { bigest = 0; for( j = row; j < M; j++ ) { /* search non null element */ for( i = row; i < N; i++ ) { double a = fabs( A[j * N + i] ), b = fabs( bigest ); if( a > b ) { bigest = A[j * N + i]; i_best = i; j_best = j; } /* if */ } /* for */ } /* for */ if( REAL_ZERO( bigest )) break; /* if all shank elements are null */ if( j_best - row ) { for( t = 0; t < N; t++ ) { /* swap a rows */ swapd = A[row * N + t]; A[row * N + t] = A[j_best * N + t]; A[j_best * N + t] = swapd; } /* for */ swapd = B[row]; B[row] = B[j_best]; B[j_best] = swapd; } /* if */ if( i_best - row ) { for( t = 0; t < M; t++ ) { /* swap a columns */ swapd = A[t * N + i_best]; A[t * N + i_best] = A[t * N + row]; A[t * N + row] = swapd; } /* for */ swapi = variables[row]; variables[row] = variables[i_best]; variables[i_best] = swapi; } /* if */ for( i = row + 1; i < M; i++ ) { /* recounting A and B */ ratio = -A[i * N + row] / A[row * N + row]; B[i] += B[row] * ratio; for( j = N - 1; j >= row; j-- ) { A[i * N + j] += A[row * N + j] * ratio; } /* for */ } /* for */ } /* for */ if( row < M ) { /* if rank(A)= 0; i-- ) { /* finding component of solution */ if( t < N ) { (*solutions)[(t - M) * N + variables[i]] = 0; } else { (*solutions)[(t - M) * N + variables[i]] = B[i] / A[i * N + i]; } /* if */ for( j = i + 1; j < N; j++ ) { (*solutions)[(t - M) * N + variables[i]] -= (*solutions)[(t - M) * N + variables[j]] * A[i * N + j] / A[i * N + i]; } /* for */ } /* for */ } /* for */ cvFree( &variables ); return N - M; } /* if */ *solutions = (double *) cvAlloc( (N) * sizeof( double )); if( solutions == 0 ) return -1; for( i = N - 1; i >= 0; i-- ) { /* finding exclusive solution */ (*solutions)[variables[i]] = B[i] / A[i * N + i]; for( j = i + 1; j < N; j++ ) { (*solutions)[variables[i]] -= (*solutions)[variables[j]] * A[i * N + j] / A[i * N + i]; } /* for */ } /* for */ cvFree( &variables ); return 0; } /* icvGaussMxN */ /*======================================================================================*/ /*F/////////////////////////////////////////////////////////////////////////////////////// // Name: icvPoint7 // Purpose: // // // Context: // Parameters: // // // // // // // // Returns: // CV_NO_ERR if all Ok or error code // Notes: //F*/ CvStatus icvPoint7( int *ml, int *mr, double *F, int *amount ) { double A[63], B[7]; double *solutions = 0; double a2, a1, a0; double squares[6]; int i, j; /* int amount; */ /* float* F; */ CvStatus error = CV_BADFACTOR_ERR; /* F = (float*)matrix->m; */ if( !ml || !mr || !F ) return CV_BADFACTOR_ERR; for( i = 0; i < 7; i++ ) { for( j = 0; j < 9; j++ ) { A[i * 9 + j] = (double) ml[i * 3 + j / 3] * (double) mr[i * 3 + j % 3]; } /* for */ B[i] = 0; } /* for */ *amount = 0; if( icvGaussMxN( A, B, 7, 9, &solutions ) == 2 ) { if( icvGetCoef( solutions, solutions + 9, &a2, &a1, &a0 ) == CV_NO_ERR ) { icvCubic( a2, a1, a0, squares ); for( i = 0; i < 1; i++ ) { if( REAL_ZERO( squares[i * 2 + 1] )) { for( j = 0; j < 9; j++ ) { F[*amount + j] = (float) (squares[i] * solutions[j] + (1 - squares[i]) * solutions[j + 9]); } /* for */ *amount += 9; error = CV_NO_ERR; } /* if */ } /* for */ cvFree( &solutions ); return error; } else { cvFree( &solutions ); } /* if */ } else { cvFree( &solutions ); } /* if */ return error; } /* icvPoint7 */