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#include "_cv.h"
template<typename T> int icvCompressPoints( T* ptr, const uchar* mask, int mstep, int count )
{
int i, j;
for( i = j = 0; i < count; i++ )
if( mask[i*mstep] )
{
if( i > j )
ptr[j] = ptr[i];
j++;
}
return j;
}
class CvModelEstimator2
{
public:
CvModelEstimator2(int _modelPoints, CvSize _modelSize, int _maxBasicSolutions);
virtual ~CvModelEstimator2();
virtual int runKernel( const CvMat* m1, const CvMat* m2, CvMat* model )=0;
virtual bool runLMeDS( const CvMat* m1, const CvMat* m2, CvMat* model,
CvMat* mask, double confidence=0.99, int maxIters=1000 );
virtual bool runRANSAC( const CvMat* m1, const CvMat* m2, CvMat* model,
CvMat* mask, double threshold,
double confidence=0.99, int maxIters=1000 );
virtual bool refine( const CvMat*, const CvMat*, CvMat*, int ) { return true; }
virtual void setSeed( int64 seed );
protected:
virtual void computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error ) = 0;
virtual int findInliers( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error,
CvMat* mask, double threshold );
virtual bool getSubset( const CvMat* m1, const CvMat* m2,
CvMat* ms1, CvMat* ms2, int maxAttempts=1000 );
virtual bool checkSubset( const CvMat* ms1, int count );
CvRNG rng;
int modelPoints;
CvSize modelSize;
int maxBasicSolutions;
bool checkPartialSubsets;
};
CvModelEstimator2::CvModelEstimator2(int _modelPoints, CvSize _modelSize, int _maxBasicSolutions)
{
modelPoints = _modelPoints;
modelSize = _modelSize;
maxBasicSolutions = _maxBasicSolutions;
checkPartialSubsets = true;
rng = cvRNG(-1);
}
CvModelEstimator2::~CvModelEstimator2()
{
}
void CvModelEstimator2::setSeed( int64 seed )
{
rng = cvRNG(seed);
}
int CvModelEstimator2::findInliers( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* _err,
CvMat* _mask, double threshold )
{
int i, count = _err->rows*_err->cols, goodCount = 0;
const float* err = _err->data.fl;
uchar* mask = _mask->data.ptr;
computeReprojError( m1, m2, model, _err );
threshold *= threshold;
for( i = 0; i < count; i++ )
goodCount += mask[i] = err[i] <= threshold;
return goodCount;
}
CV_IMPL int
cvRANSACUpdateNumIters( double p, double ep,
int model_points, int max_iters )
{
int result = 0;
CV_FUNCNAME( "cvRANSACUpdateNumIters" );
__BEGIN__;
double num, denom;
if( model_points <= 0 )
CV_ERROR( CV_StsOutOfRange, "the number of model points should be positive" );
p = MAX(p, 0.);
p = MIN(p, 1.);
ep = MAX(ep, 0.);
ep = MIN(ep, 1.);
// avoid inf's & nan's
num = MAX(1. - p, DBL_MIN);
denom = 1. - pow(1. - ep,model_points);
if( denom < DBL_MIN )
EXIT;
num = log(num);
denom = log(denom);
result = denom >= 0 || -num >= max_iters*(-denom) ?
max_iters : cvRound(num/denom);
__END__;
return result;
}
bool CvModelEstimator2::runRANSAC( const CvMat* m1, const CvMat* m2, CvMat* model,
CvMat* mask, double reprojThreshold,
double confidence, int maxIters )
{
bool result = false;
CvMat* mask0 = mask, *tmask = 0, *t;
CvMat* models = 0, *err = 0;
CvMat *ms1 = 0, *ms2 = 0;
CV_FUNCNAME( "CvModelEstimator2::estimateRansac" );
__BEGIN__;
int iter, niters = maxIters;
int count = m1->rows*m1->cols, maxGoodCount = 0;
CV_ASSERT( CV_ARE_SIZES_EQ(m1, m2) && CV_ARE_SIZES_EQ(m1, mask) );
if( count < modelPoints )
EXIT;
models = cvCreateMat( modelSize.height*maxBasicSolutions, modelSize.width, CV_64FC1 );
err = cvCreateMat( 1, count, CV_32FC1 );
tmask = cvCreateMat( 1, count, CV_8UC1 );
if( count > modelPoints )
{
ms1 = cvCreateMat( 1, modelPoints, m1->type );
ms2 = cvCreateMat( 1, modelPoints, m2->type );
}
else
{
niters = 1;
ms1 = (CvMat*)m1;
ms2 = (CvMat*)m2;
}
for( iter = 0; iter < niters; iter++ )
{
int i, goodCount, nmodels;
if( count > modelPoints )
{
bool found = getSubset( m1, m2, ms1, ms2, modelPoints );
if( !found )
{
if( iter == 0 )
EXIT;
break;
}
}
nmodels = runKernel( ms1, ms2, models );
if( nmodels <= 0 )
continue;
for( i = 0; i < nmodels; i++ )
{
CvMat model_i;
cvGetRows( models, &model_i, i*modelSize.height, (i+1)*modelSize.height );
goodCount = findInliers( m1, m2, &model_i, err, tmask, reprojThreshold );
if( goodCount > MAX(maxGoodCount, modelPoints-1) )
{
CV_SWAP( tmask, mask, t );
cvCopy( &model_i, model );
maxGoodCount = goodCount;
niters = cvRANSACUpdateNumIters( confidence,
(double)(count - goodCount)/count, modelPoints, niters );
}
}
}
if( maxGoodCount > 0 )
{
if( mask != mask0 )
{
CV_SWAP( tmask, mask, t );
cvCopy( tmask, mask );
}
result = true;
}
__END__;
if( ms1 != m1 )
cvReleaseMat( &ms1 );
if( ms2 != m2 )
cvReleaseMat( &ms2 );
cvReleaseMat( &models );
cvReleaseMat( &err );
cvReleaseMat( &tmask );
return result;
}
static CV_IMPLEMENT_QSORT( icvSortDistances, int, CV_LT )
bool CvModelEstimator2::runLMeDS( const CvMat* m1, const CvMat* m2, CvMat* model,
CvMat* mask, double confidence, int maxIters )
{
const double outlierRatio = 0.45;
bool result = false;
CvMat* models = 0;
CvMat *ms1 = 0, *ms2 = 0;
CvMat* err = 0;
CV_FUNCNAME( "CvModelEstimator2::estimateLMeDS" );
__BEGIN__;
int iter, niters = maxIters;
int count = m1->rows*m1->cols;
double minMedian = DBL_MAX, sigma;
CV_ASSERT( CV_ARE_SIZES_EQ(m1, m2) && CV_ARE_SIZES_EQ(m1, mask) );
if( count < modelPoints )
EXIT;
models = cvCreateMat( modelSize.height*maxBasicSolutions, modelSize.width, CV_64FC1 );
err = cvCreateMat( 1, count, CV_32FC1 );
if( count > modelPoints )
{
ms1 = cvCreateMat( 1, modelPoints, m1->type );
ms2 = cvCreateMat( 1, modelPoints, m2->type );
}
else
{
niters = 1;
ms1 = (CvMat*)m1;
ms2 = (CvMat*)m2;
}
niters = cvRound(log(1-confidence)/log(1-pow(1-outlierRatio,(double)modelPoints)));
niters = MIN( MAX(niters, 3), maxIters );
for( iter = 0; iter < niters; iter++ )
{
int i, nmodels;
if( count > modelPoints )
{
bool found = getSubset( m1, m2, ms1, ms2, 300 );
if( !found )
{
if( iter == 0 )
EXIT;
break;
}
}
nmodels = runKernel( ms1, ms2, models );
if( nmodels <= 0 )
continue;
for( i = 0; i < nmodels; i++ )
{
CvMat model_i;
cvGetRows( models, &model_i, i*modelSize.height, (i+1)*modelSize.height );
computeReprojError( m1, m2, &model_i, err );
icvSortDistances( err->data.i, count, 0 );
double median = count % 2 != 0 ?
err->data.fl[count/2] : (err->data.fl[count/2-1] + err->data.fl[count/2])*0.5;
if( median < minMedian )
{
minMedian = median;
cvCopy( &model_i, model );
}
}
}
if( minMedian < DBL_MAX )
{
sigma = 2.5*1.4826*(1 + 5./(count - modelPoints))*sqrt(minMedian);
sigma = MAX( sigma, FLT_EPSILON*100 );
count = findInliers( m1, m2, model, err, mask, sigma );
result = count >= modelPoints;
}
__END__;
if( ms1 != m1 )
cvReleaseMat( &ms1 );
if( ms2 != m2 )
cvReleaseMat( &ms2 );
cvReleaseMat( &models );
cvReleaseMat( &err );
return result;
}
bool CvModelEstimator2::getSubset( const CvMat* m1, const CvMat* m2,
CvMat* ms1, CvMat* ms2, int maxAttempts )
{
int* idx = (int*)cvStackAlloc( modelPoints*sizeof(idx[0]) );
int i, j, k, idx_i, iters = 0;
int type = CV_MAT_TYPE(m1->type), elemSize = CV_ELEM_SIZE(type);
const int *m1ptr = m1->data.i, *m2ptr = m2->data.i;
int *ms1ptr = ms1->data.i, *ms2ptr = ms2->data.i;
int count = m1->cols*m1->rows;
assert( CV_IS_MAT_CONT(m1->type & m2->type) && (elemSize % sizeof(int) == 0) );
elemSize /= sizeof(int);
for(;;)
{
for( i = 0; i < modelPoints && iters < maxAttempts; iters++ )
{
idx[i] = idx_i = cvRandInt(&rng) % count;
for( j = 0; j < i; j++ )
if( idx_i == idx[j] )
break;
if( j < i )
continue;
for( k = 0; k < elemSize; k++ )
{
ms1ptr[i*elemSize + k] = m1ptr[idx_i*elemSize + k];
ms2ptr[i*elemSize + k] = m2ptr[idx_i*elemSize + k];
}
if( checkPartialSubsets && (!checkSubset( ms1, i+1 ) || !checkSubset( ms2, i+1 )))
continue;
i++;
iters = 0;
}
if( !checkPartialSubsets && i == modelPoints &&
(!checkSubset( ms1, i+1 ) || !checkSubset( ms2, i+1 )))
continue;
break;
}
return i == modelPoints;
}
bool CvModelEstimator2::checkSubset( const CvMat* m, int count )
{
int j, k, i = count-1;
CvPoint2D64f* ptr = (CvPoint2D64f*)m->data.ptr;
assert( CV_MAT_TYPE(m->type) == CV_64FC2 );
// check that the i-th selected point does not belong
// to a line connecting some previously selected points
for( j = 0; j < i; j++ )
{
double dx1 = ptr[j].x - ptr[i].x;
double dy1 = ptr[j].y - ptr[i].y;
for( k = 0; k < j; k++ )
{
double dx2 = ptr[k].x - ptr[i].x;
double dy2 = ptr[k].y - ptr[i].y;
if( fabs(dx2*dy1 - dy2*dx1) < FLT_EPSILON*(fabs(dx1) + fabs(dy1) + fabs(dx2) + fabs(dy2)))
break;
}
if( k < j )
break;
}
return j == i;
}
class CvHomographyEstimator : public CvModelEstimator2
{
public:
CvHomographyEstimator( int modelPoints );
virtual int runKernel( const CvMat* m1, const CvMat* m2, CvMat* model );
virtual bool refine( const CvMat* m1, const CvMat* m2,
CvMat* model, int maxIters );
protected:
virtual void computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error );
};
CvHomographyEstimator::CvHomographyEstimator(int _modelPoints)
: CvModelEstimator2(_modelPoints, cvSize(3,3), 1)
{
assert( _modelPoints == 4 || _modelPoints == 5 );
}
int CvHomographyEstimator::runKernel( const CvMat* m1, const CvMat* m2, CvMat* H )
{
int i, count = m1->rows*m1->cols;
const CvPoint2D64f* M = (const CvPoint2D64f*)m1->data.ptr;
const CvPoint2D64f* m = (const CvPoint2D64f*)m2->data.ptr;
double LtL[9][9], W[9][9], V[9][9];
CvMat _LtL = cvMat( 9, 9, CV_64F, LtL );
CvMat _W = cvMat( 9, 9, CV_64F, W );
CvMat _V = cvMat( 9, 9, CV_64F, V );
CvMat _H0 = cvMat( 3, 3, CV_64F, V[8] );
CvMat _Htemp = cvMat( 3, 3, CV_64F, V[7] );
CvPoint2D64f cM={0,0}, cm={0,0}, sM={0,0}, sm={0,0};
for( i = 0; i < count; i++ )
{
cm.x += m[i].x; cm.y += m[i].y;
cM.x += M[i].x; cM.y += M[i].y;
}
cm.x /= count; cm.y /= count;
cM.x /= count; cM.y /= count;
for( i = 0; i < count; i++ )
{
sm.x += fabs(m[i].x - cm.x);
sm.y += fabs(m[i].y - cm.y);
sM.x += fabs(M[i].x - cM.x);
sM.y += fabs(M[i].y - cM.y);
}
sm.x = count/sm.x; sm.y = count/sm.y;
sM.x = count/sM.x; sM.y = count/sM.y;
double invHnorm[9] = { 1./sm.x, 0, cm.x, 0, 1./sm.y, cm.y, 0, 0, 1 };
double Hnorm2[9] = { sM.x, 0, -cM.x*sM.x, 0, sM.y, -cM.y*sM.y, 0, 0, 1 };
CvMat _invHnorm = cvMat( 3, 3, CV_64FC1, invHnorm );
CvMat _Hnorm2 = cvMat( 3, 3, CV_64FC1, Hnorm2 );
cvZero( &_LtL );
for( i = 0; i < count; i++ )
{
double x = (m[i].x - cm.x)*sm.x, y = (m[i].y - cm.y)*sm.y;
double X = (M[i].x - cM.x)*sM.x, Y = (M[i].y - cM.y)*sM.y;
double Lx[] = { X, Y, 1, 0, 0, 0, -x*X, -x*Y, -x };
double Ly[] = { 0, 0, 0, X, Y, 1, -y*X, -y*Y, -y };
int j, k;
for( j = 0; j < 9; j++ )
for( k = j; k < 9; k++ )
LtL[j][k] += Lx[j]*Lx[k] + Ly[j]*Ly[k];
}
cvCompleteSymm( &_LtL );
cvSVD( &_LtL, &_W, 0, &_V, CV_SVD_MODIFY_A + CV_SVD_V_T );
cvMatMul( &_invHnorm, &_H0, &_Htemp );
cvMatMul( &_Htemp, &_Hnorm2, &_H0 );
cvConvertScale( &_H0, H, 1./_H0.data.db[8] );
return 1;
}
void CvHomographyEstimator::computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* _err )
{
int i, count = m1->rows*m1->cols;
const CvPoint2D64f* M = (const CvPoint2D64f*)m1->data.ptr;
const CvPoint2D64f* m = (const CvPoint2D64f*)m2->data.ptr;
const double* H = model->data.db;
float* err = _err->data.fl;
for( i = 0; i < count; i++ )
{
double ww = 1./(H[6]*M[i].x + H[7]*M[i].y + 1.);
double dx = (H[0]*M[i].x + H[1]*M[i].y + H[2])*ww - m[i].x;
double dy = (H[3]*M[i].x + H[4]*M[i].y + H[5])*ww - m[i].y;
err[i] = (float)(dx*dx + dy*dy);
}
}
bool CvHomographyEstimator::refine( const CvMat* m1, const CvMat* m2, CvMat* model, int maxIters )
{
CvLevMarq solver(8, 0, cvTermCriteria(CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, maxIters, DBL_EPSILON));
int i, j, k, count = m1->rows*m1->cols;
const CvPoint2D64f* M = (const CvPoint2D64f*)m1->data.ptr;
const CvPoint2D64f* m = (const CvPoint2D64f*)m2->data.ptr;
CvMat modelPart = cvMat( solver.param->rows, solver.param->cols, model->type, model->data.ptr );
cvCopy( &modelPart, solver.param );
for(;;)
{
const CvMat* _param = 0;
CvMat *_JtJ = 0, *_JtErr = 0;
double* _errNorm = 0;
if( !solver.updateAlt( _param, _JtJ, _JtErr, _errNorm ))
break;
for( i = 0; i < count; i++ )
{
const double* h = _param->data.db;
double Mx = M[i].x, My = M[i].y;
double ww = 1./(h[6]*Mx + h[7]*My + 1.);
double _xi = (h[0]*Mx + h[1]*My + h[2])*ww;
double _yi = (h[3]*Mx + h[4]*My + h[5])*ww;
double err[] = { _xi - m[i].x, _yi - m[i].y };
if( _JtJ || _JtErr )
{
double J[][8] =
{
{ Mx*ww, My*ww, ww, 0, 0, 0, -Mx*ww*_xi, -My*ww*_xi },
{ 0, 0, 0, Mx*ww, My*ww, ww, -Mx*ww*_yi, -My*ww*_yi }
};
for( j = 0; j < 8; j++ )
{
for( k = j; k < 8; k++ )
_JtJ->data.db[j*8+k] += J[0][j]*J[0][k] + J[1][j]*J[1][k];
_JtErr->data.db[j] += J[0][j]*err[0] + J[1][j]*err[1];
}
}
if( _errNorm )
*_errNorm += err[0]*err[0] + err[1]*err[1];
}
}
cvCopy( solver.param, &modelPart );
return true;
}
CV_IMPL int
cvFindHomography( const CvMat* objectPoints, const CvMat* imagePoints,
CvMat* __H, int method, double ransacReprojThreshold,
CvMat* mask )
{
const double confidence = 0.99;
bool result = false;
CvMat *m = 0, *M = 0, *tempMask = 0;
CV_FUNCNAME( "cvFindHomography" );
__BEGIN__;
double H[9];
CvMat _H = cvMat( 3, 3, CV_64FC1, H );
int count;
CV_ASSERT( CV_IS_MAT(imagePoints) && CV_IS_MAT(objectPoints) );
count = MAX(imagePoints->cols, imagePoints->rows);
CV_ASSERT( count >= 4 );
m = cvCreateMat( 1, count, CV_64FC2 );
cvConvertPointsHomogeneous( imagePoints, m );
M = cvCreateMat( 1, count, CV_64FC2 );
cvConvertPointsHomogeneous( objectPoints, M );
if( mask )
{
CV_ASSERT( CV_IS_MASK_ARR(mask) && CV_IS_MAT_CONT(mask->type) &&
(mask->rows == 1 || mask->cols == 1) &&
mask->rows*mask->cols == count );
tempMask = mask;
}
else if( count > 4 )
tempMask = cvCreateMat( 1, count, CV_8U );
if( tempMask )
cvSet( tempMask, cvScalarAll(1.) );
{
CvHomographyEstimator estimator( MIN(count, 5) );
if( count == 4 )
method = 0;
if( method == CV_LMEDS )
result = estimator.runLMeDS( M, m, &_H, tempMask, confidence );
else if( method == CV_RANSAC )
result = estimator.runRANSAC( M, m, &_H, tempMask, ransacReprojThreshold, confidence );
else
result = estimator.runKernel( M, m, &_H ) > 0;
if( result && count > 4 )
{
icvCompressPoints( (CvPoint2D64f*)M->data.ptr, tempMask->data.ptr, 1, count );
count = icvCompressPoints( (CvPoint2D64f*)m->data.ptr, tempMask->data.ptr, 1, count );
M->cols = m->cols = count;
estimator.refine( M, m, &_H, 10 );
}
}
if( result )
cvConvert( &_H, __H );
__END__;
cvReleaseMat( &m );
cvReleaseMat( &M );
if( tempMask != mask )
cvReleaseMat( &tempMask );
return (int)result;
}
/* Evaluation of Fundamental Matrix from point correspondences.
The original code has been written by Valery Mosyagin */
/* The algorithms (except for RANSAC) and the notation have been taken from
Zhengyou Zhang's research report
"Determining the Epipolar Geometry and its Uncertainty: A Review"
that can be found at http://www-sop.inria.fr/robotvis/personnel/zzhang/zzhang-eng.html */
/************************************** 7-point algorithm *******************************/
class CvFMEstimator : public CvModelEstimator2
{
public:
CvFMEstimator( int _modelPoints );
virtual int runKernel( const CvMat* m1, const CvMat* m2, CvMat* model );
virtual int run7Point( const CvMat* m1, const CvMat* m2, CvMat* model );
virtual int run8Point( const CvMat* m1, const CvMat* m2, CvMat* model );
protected:
virtual void computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error );
};
CvFMEstimator::CvFMEstimator( int _modelPoints )
: CvModelEstimator2( _modelPoints, cvSize(3,3), _modelPoints == 7 ? 3 : 1 )
{
assert( _modelPoints == 7 || _modelPoints == 8 );
}
int CvFMEstimator::runKernel( const CvMat* m1, const CvMat* m2, CvMat* model )
{
return modelPoints == 7 ? run7Point( m1, m2, model ) : run8Point( m1, m2, model );
}
int CvFMEstimator::run7Point( const CvMat* _m1, const CvMat* _m2, CvMat* _fmatrix )
{
double a[7*9], w[7], v[9*9], c[4], r[3];
double* f1, *f2;
double t0, t1, t2;
CvMat A = cvMat( 7, 9, CV_64F, a );
CvMat V = cvMat( 9, 9, CV_64F, v );
CvMat W = cvMat( 7, 1, CV_64F, w );
CvMat coeffs = cvMat( 1, 4, CV_64F, c );
CvMat roots = cvMat( 1, 3, CV_64F, r );
const CvPoint2D64f* m1 = (const CvPoint2D64f*)_m1->data.ptr;
const CvPoint2D64f* m2 = (const CvPoint2D64f*)_m2->data.ptr;
double* fmatrix = _fmatrix->data.db;
int i, k, n;
// form a linear system: i-th row of A(=a) represents
// the equation: (m2[i], 1)'*F*(m1[i], 1) = 0
for( i = 0; i < 7; i++ )
{
double x0 = m1[i].x, y0 = m1[i].y;
double x1 = m2[i].x, y1 = m2[i].y;
a[i*9+0] = x1*x0;
a[i*9+1] = x1*y0;
a[i*9+2] = x1;
a[i*9+3] = y1*x0;
a[i*9+4] = y1*y0;
a[i*9+5] = y1;
a[i*9+6] = x0;
a[i*9+7] = y0;
a[i*9+8] = 1;
}
// A*(f11 f12 ... f33)' = 0 is singular (7 equations for 9 variables), so
// the solution is linear subspace of dimensionality 2.
// => use the last two singular vectors as a basis of the space
// (according to SVD properties)
cvSVD( &A, &W, 0, &V, CV_SVD_MODIFY_A + CV_SVD_V_T );
f1 = v + 7*9;
f2 = v + 8*9;
// f1, f2 is a basis => lambda*f1 + mu*f2 is an arbitrary f. matrix.
// as it is determined up to a scale, normalize lambda & mu (lambda + mu = 1),
// so f ~ lambda*f1 + (1 - lambda)*f2.
// use the additional constraint det(f) = det(lambda*f1 + (1-lambda)*f2) to find lambda.
// it will be a cubic equation.
// find c - polynomial coefficients.
for( i = 0; i < 9; i++ )
f1[i] -= f2[i];
t0 = f2[4]*f2[8] - f2[5]*f2[7];
t1 = f2[3]*f2[8] - f2[5]*f2[6];
t2 = f2[3]*f2[7] - f2[4]*f2[6];
c[3] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2;
c[2] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2 -
f1[3]*(f2[1]*f2[8] - f2[2]*f2[7]) +
f1[4]*(f2[0]*f2[8] - f2[2]*f2[6]) -
f1[5]*(f2[0]*f2[7] - f2[1]*f2[6]) +
f1[6]*(f2[1]*f2[5] - f2[2]*f2[4]) -
f1[7]*(f2[0]*f2[5] - f2[2]*f2[3]) +
f1[8]*(f2[0]*f2[4] - f2[1]*f2[3]);
t0 = f1[4]*f1[8] - f1[5]*f1[7];
t1 = f1[3]*f1[8] - f1[5]*f1[6];
t2 = f1[3]*f1[7] - f1[4]*f1[6];
c[1] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2 -
f2[3]*(f1[1]*f1[8] - f1[2]*f1[7]) +
f2[4]*(f1[0]*f1[8] - f1[2]*f1[6]) -
f2[5]*(f1[0]*f1[7] - f1[1]*f1[6]) +
f2[6]*(f1[1]*f1[5] - f1[2]*f1[4]) -
f2[7]*(f1[0]*f1[5] - f1[2]*f1[3]) +
f2[8]*(f1[0]*f1[4] - f1[1]*f1[3]);
c[0] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2;
// solve the cubic equation; there can be 1 to 3 roots ...
n = cvSolveCubic( &coeffs, &roots );
if( n < 1 || n > 3 )
return n;
for( k = 0; k < n; k++, fmatrix += 9 )
{
// for each root form the fundamental matrix
double lambda = r[k], mu = 1.;
double s = f1[8]*r[k] + f2[8];
// normalize each matrix, so that F(3,3) (~fmatrix[8]) == 1
if( fabs(s) > DBL_EPSILON )
{
mu = 1./s;
lambda *= mu;
fmatrix[8] = 1.;
}
else
fmatrix[8] = 0.;
for( i = 0; i < 8; i++ )
fmatrix[i] = f1[i]*lambda + f2[i]*mu;
}
return n;
}
int CvFMEstimator::run8Point( const CvMat* _m1, const CvMat* _m2, CvMat* _fmatrix )
{
double a[9*9], w[9], v[9*9];
CvMat W = cvMat( 1, 9, CV_64F, w );
CvMat V = cvMat( 9, 9, CV_64F, v );
CvMat A = cvMat( 9, 9, CV_64F, a );
CvMat U, F0, TF;
CvPoint2D64f m0c = {0,0}, m1c = {0,0};
double t, scale0 = 0, scale1 = 0;
const CvPoint2D64f* m1 = (const CvPoint2D64f*)_m1->data.ptr;
const CvPoint2D64f* m2 = (const CvPoint2D64f*)_m2->data.ptr;
double* fmatrix = _fmatrix->data.db;
int i, j, k, count = _m1->cols*_m1->rows;
// compute centers and average distances for each of the two point sets
for( i = 0; i < count; i++ )
{
double x = m1[i].x, y = m1[i].y;
m0c.x += x; m0c.y += y;
x = m2[i].x, y = m2[i].y;
m1c.x += x; m1c.y += y;
}
// calculate the normalizing transformations for each of the point sets:
// after the transformation each set will have the mass center at the coordinate origin
// and the average distance from the origin will be ~sqrt(2).
t = 1./count;
m0c.x *= t; m0c.y *= t;
m1c.x *= t; m1c.y *= t;
for( i = 0; i < count; i++ )
{
double x = m1[i].x - m0c.x, y = m1[i].y - m0c.y;
scale0 += sqrt(x*x + y*y);
x = fabs(m2[i].x - m1c.x), y = fabs(m2[i].y - m1c.y);
scale1 += sqrt(x*x + y*y);
}
scale0 *= t;
scale1 *= t;
if( scale0 < FLT_EPSILON || scale1 < FLT_EPSILON )
return 0;
scale0 = sqrt(2.)/scale0;
scale1 = sqrt(2.)/scale1;
cvZero( &A );
// form a linear system Ax=0: for each selected pair of points m1 & m2,
// the row of A(=a) represents the coefficients of equation: (m2, 1)'*F*(m1, 1) = 0
// to save computation time, we compute (At*A) instead of A and then solve (At*A)x=0.
for( i = 0; i < count; i++ )
{
double x0 = (m1[i].x - m0c.x)*scale0;
double y0 = (m1[i].y - m0c.y)*scale0;
double x1 = (m2[i].x - m1c.x)*scale1;
double y1 = (m2[i].y - m1c.y)*scale1;
double r[9] = { x1*x0, x1*y0, x1, y1*x0, y1*y0, y1, x0, y0, 1 };
for( j = 0; j < 9; j++ )
for( k = 0; k < 9; k++ )
a[j*9+k] += r[j]*r[k];
}
cvSVD( &A, &W, 0, &V, CV_SVD_MODIFY_A + CV_SVD_V_T );
for( i = 0; i < 8; i++ )
{
if( fabs(w[i]) < DBL_EPSILON )
break;
}
if( i < 7 )
return 0;
F0 = cvMat( 3, 3, CV_64F, v + 9*8 ); // take the last column of v as a solution of Af = 0
// make F0 singular (of rank 2) by decomposing it with SVD,
// zeroing the last diagonal element of W and then composing the matrices back.
// use v as a temporary storage for different 3x3 matrices
W = U = V = TF = F0;
W.data.db = v;
U.data.db = v + 9;
V.data.db = v + 18;
TF.data.db = v + 27;
cvSVD( &F0, &W, &U, &V, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T );
W.data.db[8] = 0.;
// F0 <- U*diag([W(1), W(2), 0])*V'
cvGEMM( &U, &W, 1., 0, 0., &TF, CV_GEMM_A_T );
cvGEMM( &TF, &V, 1., 0, 0., &F0, 0/*CV_GEMM_B_T*/ );
// apply the transformation that is inverse
// to what we used to normalize the point coordinates
{
double tt0[] = { scale0, 0, -scale0*m0c.x, 0, scale0, -scale0*m0c.y, 0, 0, 1 };
double tt1[] = { scale1, 0, -scale1*m1c.x, 0, scale1, -scale1*m1c.y, 0, 0, 1 };
CvMat T0, T1;
T0 = T1 = F0;
T0.data.db = tt0;
T1.data.db = tt1;
// F0 <- T1'*F0*T0
cvGEMM( &T1, &F0, 1., 0, 0., &TF, CV_GEMM_A_T );
F0.data.db = fmatrix;
cvGEMM( &TF, &T0, 1., 0, 0., &F0, 0 );
// make F(3,3) = 1
if( fabs(F0.data.db[8]) > FLT_EPSILON )
cvScale( &F0, &F0, 1./F0.data.db[8] );
}
return 1;
}
void CvFMEstimator::computeReprojError( const CvMat* _m1, const CvMat* _m2,
const CvMat* model, CvMat* _err )
{
int i, count = _m1->rows*_m1->cols;
const CvPoint2D64f* m1 = (const CvPoint2D64f*)_m1->data.ptr;
const CvPoint2D64f* m2 = (const CvPoint2D64f*)_m2->data.ptr;
const double* F = model->data.db;
float* err = _err->data.fl;
for( i = 0; i < count; i++ )
{
double a, b, c, d1, d2, s1, s2;
a = F[0]*m1[i].x + F[1]*m1[i].y + F[2];
b = F[3]*m1[i].x + F[4]*m1[i].y + F[5];
c = F[6]*m1[i].x + F[7]*m1[i].y + F[8];
s2 = 1./(a*a + b*b);
d2 = m2[i].x*a + m2[i].y*b + c;
a = F[0]*m2[i].x + F[3]*m2[i].y + F[6];
b = F[1]*m2[i].x + F[4]*m2[i].y + F[7];
c = F[2]*m2[i].x + F[5]*m2[i].y + F[8];
s1 = 1./(a*a + b*b);
d1 = m1[i].x*a + m1[i].y*b + c;
err[i] = (float)(d1*d1*s1 + d2*d2*s2);
}
}
CV_IMPL int
cvFindFundamentalMat( const CvMat* points1, const CvMat* points2,
CvMat* fmatrix, int method,
double param1, double param2, CvMat* mask )
{
int result = 0;
CvMat *m1 = 0, *m2 = 0, *tempMask = 0;
CV_FUNCNAME( "cvFindFundamentalMat" );
__BEGIN__;
double F[3*9];
CvMat _F3x3 = cvMat( 3, 3, CV_64FC1, F ), _F9x3 = cvMat( 9, 3, CV_64FC1, F );
int count;
CV_ASSERT( CV_IS_MAT(points1) && CV_IS_MAT(points2) && CV_ARE_SIZES_EQ(points1, points2) );
CV_ASSERT( CV_IS_MAT(fmatrix) && fmatrix->cols == 3 &&
(fmatrix->rows == 3 || (fmatrix->rows == 9 && method == CV_FM_7POINT)) );
count = MAX(points1->cols, points1->rows);
if( count < 7 )
EXIT;
m1 = cvCreateMat( 1, count, CV_64FC2 );
cvConvertPointsHomogeneous( points1, m1 );
m2 = cvCreateMat( 1, count, CV_64FC2 );
cvConvertPointsHomogeneous( points2, m2 );
if( mask )
{
CV_ASSERT( CV_IS_MASK_ARR(mask) && CV_IS_MAT_CONT(mask->type) &&
(mask->rows == 1 || mask->cols == 1) &&
mask->rows*mask->cols == count );
tempMask = mask;
}
else if( count > 8 )
tempMask = cvCreateMat( 1, count, CV_8U );
if( tempMask )
cvSet( tempMask, cvScalarAll(1.) );
{
CvFMEstimator estimator( MIN(count, (method & 3) == CV_FM_7POINT ? 7 : 8) );
if( count == 7 )
result = estimator.run7Point(m1, m2, &_F9x3);
else if( count == 8 || method == CV_FM_8POINT )
result = estimator.run8Point(m1, m2, &_F3x3);
else if( count > 8 )
{
if( param1 <= 0 )
param1 = 3;
if( param2 < DBL_EPSILON || param2 > 1 - DBL_EPSILON )
param2 = 0.99;
if( (method & ~3) == CV_RANSAC )
result = estimator.runRANSAC(m1, m2, &_F3x3, tempMask, param1, param2 );
else
result = estimator.runLMeDS(m1, m2, &_F3x3, tempMask, param2 );
if( result <= 0 )
EXIT;
icvCompressPoints( (CvPoint2D64f*)m1->data.ptr, tempMask->data.ptr, 1, count );
count = icvCompressPoints( (CvPoint2D64f*)m2->data.ptr, tempMask->data.ptr, 1, count );
assert( count >= 8 );
m1->cols = m2->cols = count;
estimator.run8Point(m1, m2, &_F3x3);
}
}
if( result )
cvConvert( fmatrix->rows == 3 ? &_F3x3 : &_F9x3, fmatrix );
__END__;
cvReleaseMat( &m1 );
cvReleaseMat( &m2 );
if( tempMask != mask )
cvReleaseMat( &tempMask );
return result;
}
CV_IMPL void
cvComputeCorrespondEpilines( const CvMat* points, int pointImageID,
const CvMat* fmatrix, CvMat* lines )
{
CV_FUNCNAME( "cvComputeCorrespondEpilines" );
__BEGIN__;
int abc_stride, abc_plane_stride, abc_elem_size;
int plane_stride, stride, elem_size;
int i, dims, count, depth, cn, abc_dims, abc_count, abc_depth, abc_cn;
uchar *ap, *bp, *cp;
const uchar *xp, *yp, *zp;
double f[9];
CvMat F = cvMat( 3, 3, CV_64F, f );
if( !CV_IS_MAT(points) )
CV_ERROR( !points ? CV_StsNullPtr : CV_StsBadArg, "points parameter is not a valid matrix" );
depth = CV_MAT_DEPTH(points->type);
cn = CV_MAT_CN(points->type);
if( (depth != CV_32F && depth != CV_64F) || (cn != 1 && cn != 2 && cn != 3) )
CV_ERROR( CV_StsUnsupportedFormat, "The format of point matrix is unsupported" );
if( points->rows > points->cols )
{
dims = cn*points->cols;
count = points->rows;
}
else
{
if( (points->rows > 1 && cn > 1) || (points->rows == 1 && cn == 1) )
CV_ERROR( CV_StsBadSize, "The point matrix does not have a proper layout (2xn, 3xn, nx2 or nx3)" );
dims = cn * points->rows;
count = points->cols;
}
if( dims != 2 && dims != 3 )
CV_ERROR( CV_StsOutOfRange, "The dimensionality of points must be 2 or 3" );
if( !CV_IS_MAT(fmatrix) )
CV_ERROR( !fmatrix ? CV_StsNullPtr : CV_StsBadArg, "fmatrix is not a valid matrix" );
if( CV_MAT_TYPE(fmatrix->type) != CV_32FC1 && CV_MAT_TYPE(fmatrix->type) != CV_64FC1 )
CV_ERROR( CV_StsUnsupportedFormat, "fundamental matrix must have 32fC1 or 64fC1 type" );
if( fmatrix->cols != 3 || fmatrix->rows != 3 )
CV_ERROR( CV_StsBadSize, "fundamental matrix must be 3x3" );
if( !CV_IS_MAT(lines) )
CV_ERROR( !lines ? CV_StsNullPtr : CV_StsBadArg, "lines parameter is not a valid matrix" );
abc_depth = CV_MAT_DEPTH(lines->type);
abc_cn = CV_MAT_CN(lines->type);
if( (abc_depth != CV_32F && abc_depth != CV_64F) || (abc_cn != 1 && abc_cn != 3) )
CV_ERROR( CV_StsUnsupportedFormat, "The format of the matrix of lines is unsupported" );
if( lines->rows > lines->cols )
{
abc_dims = abc_cn*lines->cols;
abc_count = lines->rows;
}
else
{
if( (lines->rows > 1 && abc_cn > 1) || (lines->rows == 1 && abc_cn == 1) )
CV_ERROR( CV_StsBadSize, "The lines matrix does not have a proper layout (3xn or nx3)" );
abc_dims = abc_cn * lines->rows;
abc_count = lines->cols;
}
if( abc_dims != 3 )
CV_ERROR( CV_StsOutOfRange, "The lines matrix does not have a proper layout (3xn or nx3)" );
if( abc_count != count )
CV_ERROR( CV_StsUnmatchedSizes, "The numbers of points and lines are different" );
elem_size = CV_ELEM_SIZE(depth);
abc_elem_size = CV_ELEM_SIZE(abc_depth);
if( points->rows == dims )
{
plane_stride = points->step;
stride = elem_size;
}
else
{
plane_stride = elem_size;
stride = points->rows == 1 ? dims*elem_size : points->step;
}
if( lines->rows == 3 )
{
abc_plane_stride = lines->step;
abc_stride = abc_elem_size;
}
else
{
abc_plane_stride = abc_elem_size;
abc_stride = lines->rows == 1 ? 3*abc_elem_size : lines->step;
}
CV_CALL( cvConvert( fmatrix, &F ));
if( pointImageID == 2 )
cvTranspose( &F, &F );
xp = points->data.ptr;
yp = xp + plane_stride;
zp = dims == 3 ? yp + plane_stride : 0;
ap = lines->data.ptr;
bp = ap + abc_plane_stride;
cp = bp + abc_plane_stride;
for( i = 0; i < count; i++ )
{
double x, y, z = 1.;
double a, b, c, nu;
if( depth == CV_32F )
{
x = *(float*)xp; y = *(float*)yp;
if( zp )
z = *(float*)zp, zp += stride;
}
else
{
x = *(double*)xp; y = *(double*)yp;
if( zp )
z = *(double*)zp, zp += stride;
}
xp += stride; yp += stride;
a = f[0]*x + f[1]*y + f[2]*z;
b = f[3]*x + f[4]*y + f[5]*z;
c = f[6]*x + f[7]*y + f[8]*z;
nu = a*a + b*b;
nu = nu ? 1./sqrt(nu) : 1.;
a *= nu; b *= nu; c *= nu;
if( abc_depth == CV_32F )
{
*(float*)ap = (float)a;
*(float*)bp = (float)b;
*(float*)cp = (float)c;
}
else
{
*(double*)ap = a;
*(double*)bp = b;
*(double*)cp = c;
}
ap += abc_stride;
bp += abc_stride;
cp += abc_stride;
}
__END__;
}
CV_IMPL void
cvConvertPointsHomogeneous( const CvMat* src, CvMat* dst )
{
CvMat* temp = 0;
CvMat* denom = 0;
CV_FUNCNAME( "cvConvertPointsHomogeneous" );
__BEGIN__;
int i, s_count, s_dims, d_count, d_dims;
CvMat _src, _dst, _ones;
CvMat* ones = 0;
if( !CV_IS_MAT(src) )
CV_ERROR( !src ? CV_StsNullPtr : CV_StsBadArg,
"The input parameter is not a valid matrix" );
if( !CV_IS_MAT(dst) )
CV_ERROR( !dst ? CV_StsNullPtr : CV_StsBadArg,
"The output parameter is not a valid matrix" );
if( src == dst || src->data.ptr == dst->data.ptr )
{
if( src != dst && (!CV_ARE_TYPES_EQ(src, dst) || !CV_ARE_SIZES_EQ(src,dst)) )
CV_ERROR( CV_StsBadArg, "Invalid inplace operation" );
EXIT;
}
if( src->rows > src->cols )
{
if( !((src->cols > 1) ^ (CV_MAT_CN(src->type) > 1)) )
CV_ERROR( CV_StsBadSize, "Either the number of channels or columns or rows must be =1" );
s_dims = CV_MAT_CN(src->type)*src->cols;
s_count = src->rows;
}
else
{
if( !((src->rows > 1) ^ (CV_MAT_CN(src->type) > 1)) )
CV_ERROR( CV_StsBadSize, "Either the number of channels or columns or rows must be =1" );
s_dims = CV_MAT_CN(src->type)*src->rows;
s_count = src->cols;
}
if( src->rows == 1 || src->cols == 1 )
src = cvReshape( src, &_src, 1, s_count );
if( dst->rows > dst->cols )
{
if( !((dst->cols > 1) ^ (CV_MAT_CN(dst->type) > 1)) )
CV_ERROR( CV_StsBadSize,
"Either the number of channels or columns or rows in the input matrix must be =1" );
d_dims = CV_MAT_CN(dst->type)*dst->cols;
d_count = dst->rows;
}
else
{
if( !((dst->rows > 1) ^ (CV_MAT_CN(dst->type) > 1)) )
CV_ERROR( CV_StsBadSize,
"Either the number of channels or columns or rows in the output matrix must be =1" );
d_dims = CV_MAT_CN(dst->type)*dst->rows;
d_count = dst->cols;
}
if( dst->rows == 1 || dst->cols == 1 )
dst = cvReshape( dst, &_dst, 1, d_count );
if( s_count != d_count )
CV_ERROR( CV_StsUnmatchedSizes, "Both matrices must have the same number of points" );
if( CV_MAT_DEPTH(src->type) < CV_32F || CV_MAT_DEPTH(dst->type) < CV_32F )
CV_ERROR( CV_StsUnsupportedFormat,
"Both matrices must be floating-point (single or double precision)" );
if( s_dims < 2 || s_dims > 4 || d_dims < 2 || d_dims > 4 )
CV_ERROR( CV_StsOutOfRange,
"Both input and output point dimensionality must be 2, 3 or 4" );
if( s_dims < d_dims - 1 || s_dims > d_dims + 1 )
CV_ERROR( CV_StsUnmatchedSizes,
"The dimensionalities of input and output point sets differ too much" );
if( s_dims == d_dims - 1 )
{
if( d_count == dst->rows )
{
ones = cvGetSubRect( dst, &_ones, cvRect( s_dims, 0, 1, d_count ));
dst = cvGetSubRect( dst, &_dst, cvRect( 0, 0, s_dims, d_count ));
}
else
{
ones = cvGetSubRect( dst, &_ones, cvRect( 0, s_dims, d_count, 1 ));
dst = cvGetSubRect( dst, &_dst, cvRect( 0, 0, d_count, s_dims ));
}
}
if( s_dims <= d_dims )
{
if( src->rows == dst->rows && src->cols == dst->cols )
{
if( CV_ARE_TYPES_EQ( src, dst ) )
cvCopy( src, dst );
else
cvConvert( src, dst );
}
else
{
if( !CV_ARE_TYPES_EQ( src, dst ))
{
CV_CALL( temp = cvCreateMat( src->rows, src->cols, dst->type ));
cvConvert( src, temp );
src = temp;
}
cvTranspose( src, dst );
}
if( ones )
cvSet( ones, cvRealScalar(1.) );
}
else
{
int s_plane_stride, s_stride, d_plane_stride, d_stride, elem_size;
if( !CV_ARE_TYPES_EQ( src, dst ))
{
CV_CALL( temp = cvCreateMat( src->rows, src->cols, dst->type ));
cvConvert( src, temp );
src = temp;
}
elem_size = CV_ELEM_SIZE(src->type);
if( s_count == src->cols )
s_plane_stride = src->step / elem_size, s_stride = 1;
else
s_stride = src->step / elem_size, s_plane_stride = 1;
if( d_count == dst->cols )
d_plane_stride = dst->step / elem_size, d_stride = 1;
else
d_stride = dst->step / elem_size, d_plane_stride = 1;
CV_CALL( denom = cvCreateMat( 1, d_count, dst->type ));
if( CV_MAT_DEPTH(dst->type) == CV_32F )
{
const float* xs = src->data.fl;
const float* ys = xs + s_plane_stride;
const float* zs = 0;
const float* ws = xs + (s_dims - 1)*s_plane_stride;
float* iw = denom->data.fl;
float* xd = dst->data.fl;
float* yd = xd + d_plane_stride;
float* zd = 0;
if( d_dims == 3 )
{
zs = ys + s_plane_stride;
zd = yd + d_plane_stride;
}
for( i = 0; i < d_count; i++, ws += s_stride )
{
float t = *ws;
iw[i] = t ? t : 1.f;
}
cvDiv( 0, denom, denom );
if( d_dims == 3 )
for( i = 0; i < d_count; i++ )
{
float w = iw[i];
float x = *xs * w, y = *ys * w, z = *zs * w;
xs += s_stride; ys += s_stride; zs += s_stride;
*xd = x; *yd = y; *zd = z;
xd += d_stride; yd += d_stride; zd += d_stride;
}
else
for( i = 0; i < d_count; i++ )
{
float w = iw[i];
float x = *xs * w, y = *ys * w;
xs += s_stride; ys += s_stride;
*xd = x; *yd = y;
xd += d_stride; yd += d_stride;
}
}
else
{
const double* xs = src->data.db;
const double* ys = xs + s_plane_stride;
const double* zs = 0;
const double* ws = xs + (s_dims - 1)*s_plane_stride;
double* iw = denom->data.db;
double* xd = dst->data.db;
double* yd = xd + d_plane_stride;
double* zd = 0;
if( d_dims == 3 )
{
zs = ys + s_plane_stride;
zd = yd + d_plane_stride;
}
for( i = 0; i < d_count; i++, ws += s_stride )
{
double t = *ws;
iw[i] = t ? t : 1.;
}
cvDiv( 0, denom, denom );
if( d_dims == 3 )
for( i = 0; i < d_count; i++ )
{
double w = iw[i];
double x = *xs * w, y = *ys * w, z = *zs * w;
xs += s_stride; ys += s_stride; zs += s_stride;
*xd = x; *yd = y; *zd = z;
xd += d_stride; yd += d_stride; zd += d_stride;
}
else
for( i = 0; i < d_count; i++ )
{
double w = iw[i];
double x = *xs * w, y = *ys * w;
xs += s_stride; ys += s_stride;
*xd = x; *yd = y;
xd += d_stride; yd += d_stride;
}
}
}
__END__;
cvReleaseMat( &denom );
cvReleaseMat( &temp );
}
/* End of file. */