/*M///////////////////////////////////////////////////////////////////////////////////////
//
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//
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// 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.
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// derived from this software without specific prior written permission.
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// (including, but not limited to, procurement of substitute goods or services;
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//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 */