--- /dev/null
+/*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 "_cvaux.h"
+#include "_cvvm.h"
+#include <stdlib.h>
+
+#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 */
+
+/*===========================================================================*/
+/*===========================================================================*/
+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 */
+
+/*======================================================================================*/
+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 matrixes
+ 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)<M */
+
+ for( j = row; j < M; j++ )
+ {
+ if( !REAL_ZERO( B[j] ))
+ {
+
+ cvFree( &variables );
+ return -1; /* if system is antithetic */
+ } /* if */
+ } /* for */
+
+ M = row; /* decreasing size of the task */
+ } /* if */
+
+ /* ----- Reverse way ----- */
+
+ if( M < N )
+ { /* if solution are not exclusive */
+
+ *solutions = (double *) cvAlloc( ((N - M + 1) * N) * sizeof( double ));
+
+ if( *solutions == 0 )
+ {
+ cvFree( &variables );
+ return -1;
+ }
+
+
+ for( t = M; t <= N; t++ )
+ {
+ for( j = M; j < N; j++ )
+ {
+
+ (*solutions)[(t - M) * N + variables[j]] = (double) (t == j);
+ } /* for */
+
+ for( i = M - 1; i >= 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 */
+
+/*=====================================================================================*/
+/*
+static CvStatus
+icvGetCoof( 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];
+ }
+
+ 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) );
+ }
+
+ *a0 /= a3;
+ *a1 /= a3;
+ *a2 /= a3;
+
+ return CV_NO_ERR;
+
+}*/ /* icvGetCoof */
+
+
+
+/*======================================================================================*/
+
+/*F///////////////////////////////////////////////////////////////////////////////////////
+// Name: icvLMedS7
+// Purpose:
+//
+//
+// Context:
+// Parameters:
+//
+//
+//
+//
+//
+//
+//
+// Returns:
+// CV_NO_ERR if all Ok or error code
+// Notes:
+//F*/
+
+CvStatus
+icvLMedS7( int *points1, int *points2, CvMatrix3 * matrix )
+{ /* Incorrect realization */
+ CvStatus error = CV_NO_ERR;
+
+/* int amount; */
+ matrix = matrix;
+ points1 = points1;
+ points2 = points2;
+
+/* error = cs_Point7( points1, points2, matrix ); */
+/* error = icvPoint7 ( points1, points2, matrix,&amount ); */
+ return error;
+
+} /* icvLMedS7 */
+
+
+/*======================================================================================*/
+/*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;
+ 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 */
+
projects / opencv / blobdiff