+++ /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