/*F///////////////////////////////////////////////////////////////////////////////////////
// Name: cvConDensUpdateByTime
// Purpose: Performing Time Update routine for ConDensation algorithm
// Context:
// Parameters:
// Kalman - pointer to CvConDensation structure
// Returns:
// Notes:
//
//F*/
CV_IMPL void
cvConDensUpdateByTime( CvConDensation * ConDens )
{
int i, j;
float Sum = 0;
if( !ConDens )
CV_Error( CV_StsNullPtr, "" );
/* Sets Temp to Zero */
icvSetZero_32f( ConDens->Temp, ConDens->DP, 1 );
/* Calculating the Mean */
for( i = 0; i < ConDens->SamplesNum; i++ )
{
icvScaleVector_32f( ConDens->flSamples[i], ConDens->State, ConDens->DP,
ConDens->flConfidence[i] );
icvAddVector_32f( ConDens->Temp, ConDens->State, ConDens->Temp, ConDens->DP );
Sum += ConDens->flConfidence[i];
ConDens->flCumulative[i] = Sum;
}
/* Taking the new vector from transformation of mean by dynamics matrix */
icvScaleVector_32f( ConDens->Temp, ConDens->Temp, ConDens->DP, 1.f / Sum );
icvTransformVector_32f( ConDens->DynamMatr, ConDens->Temp, ConDens->State, ConDens->DP,
ConDens->DP );
Sum = Sum / ConDens->SamplesNum;
/* Updating the set of random samples */
for( i = 0; i < ConDens->SamplesNum; i++ )
{
j = 0;
while( (ConDens->flCumulative[j] <= (float) i * Sum)&&(j<ConDens->SamplesNum-1))
{
j++;
}
icvCopyVector_32f( ConDens->flSamples[j], ConDens->DP, ConDens->flNewSamples[i] );
}
/* Adding the random-generated vector to every vector in sample set */
for( i = 0; i < ConDens->SamplesNum; i++ )
{
for( j = 0; j < ConDens->DP; j++ )
{
cvbRand( ConDens->RandS + j, ConDens->RandomSample + j, 1 );
}
icvTransformVector_32f( ConDens->DynamMatr, ConDens->flNewSamples[i],
ConDens->flSamples[i], ConDens->DP, ConDens->DP );
icvAddVector_32f( ConDens->flSamples[i], ConDens->RandomSample, ConDens->flSamples[i],
ConDens->DP );
}
}
/* for now this function works bad with singular cases
You can see in the code, that when some troubles with
matrices or some variables occur -
box filled with zero values is returned.
However in general function works fine.
*/
static CvStatus icvFitEllipse_32f( CvSeq* points, CvBox2D* box )
{
CvStatus status = CV_OK;
float u[6];
CvMatr32f D = 0;
float S[36]; /* S = D' * D */
float C[36];
float INVQ[36];
/* transposed eigenvectors */
float INVEIGV[36];
/* auxulary matrices */
float TMP1[36];
float TMP2[36];
int i, index = -1;
float eigenvalues[6];
float a, b, c, d, e, f;
float offx, offy;
float *matr;
int n = points->total;
CvSeqReader reader;
int is_float = CV_SEQ_ELTYPE(points) == CV_32FC2;
CvMat _S, _EIGVECS, _EIGVALS;
/* create matrix D of input points */
D = icvCreateMatrix_32f( 6, n );
offx = offy = 0;
cvStartReadSeq( points, &reader );
/* shift all points to zero */
for( i = 0; i < n; i++ )
{
if( !is_float )
{
offx += (float)((CvPoint*)reader.ptr)->x;
offy += (float)((CvPoint*)reader.ptr)->y;
}
else
{
offx += ((CvPoint2D32f*)reader.ptr)->x;
offy += ((CvPoint2D32f*)reader.ptr)->y;
}
CV_NEXT_SEQ_ELEM( points->elem_size, reader );
}
c = 1.f / n;
offx *= c;
offy *= c;
/* fill matrix rows as (x*x, x*y, y*y, x, y, 1 ) */
matr = D;
for( i = 0; i < n; i++ )
{
float x, y;
if( !is_float )
{
x = (float)((CvPoint*)reader.ptr)->x - offx;
y = (float)((CvPoint*)reader.ptr)->y - offy;
}
else
{
x = ((CvPoint2D32f*)reader.ptr)->x - offx;
y = ((CvPoint2D32f*)reader.ptr)->y - offy;
}
CV_NEXT_SEQ_ELEM( points->elem_size, reader );
matr[0] = x * x;
matr[1] = x * y;
matr[2] = y * y;
matr[3] = x;
matr[4] = y;
matr[5] = 1.f;
matr += 6;
}
/* compute S */
icvMulTransMatrixR_32f( D, 6, n, S );
/* fill matrix C */
icvSetZero_32f( C, 6, 6 );
C[2] = 2.f; //icvSetElement_32f( C, 6, 6, 0, 2, 2.f );
C[7] = -1.f; //icvSetElement_32f( C, 6, 6, 1, 1, -1.f );
C[12] = 2.f; //icvSetElement_32f( C, 6, 6, 2, 0, 2.f );
/* find eigenvalues */
//status1 = icvJacobiEigens_32f( S, INVEIGV, eigenvalues, 6, 0.f );
//assert( status1 == CV_OK );
_S = cvMat( 6, 6, CV_32F, S );
_EIGVECS = cvMat( 6, 6, CV_32F, INVEIGV );
_EIGVALS = cvMat( 6, 1, CV_32F, eigenvalues );
cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );
//avoid troubles with small negative values
for( i = 0; i < 6; i++ )
eigenvalues[i] = (float)fabs(eigenvalues[i]);
cvbSqrt( eigenvalues, eigenvalues, 6 );
cvbInvSqrt( eigenvalues, eigenvalues, 6 );
for( i = 0; i < 6; i++ )
icvScaleVector_32f( &INVEIGV[i * 6], &INVEIGV[i * 6], 6, eigenvalues[i] );
// INVQ = transp(INVEIGV) * INVEIGV
icvMulTransMatrixR_32f( INVEIGV, 6, 6, INVQ );
/* create matrix INVQ*C*INVQ */
icvMulMatrix_32f( INVQ, 6, 6, C, 6, 6, TMP1 );
icvMulMatrix_32f( TMP1, 6, 6, INVQ, 6, 6, TMP2 );
/* find its eigenvalues and vectors */
//status1 = icvJacobiEigens_32f( TMP2, INVEIGV, eigenvalues, 6, 0.f );
//assert( status1 == CV_OK );
_S = cvMat( 6, 6, CV_32F, TMP2 );
cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );
/* search for positive eigenvalue */
for( i = 0; i < 3; i++ )
{
if( eigenvalues[i] > 0 )
{
index = i;
break;
}
}
/* only 3 eigenvalues must be not zero
and only one of them must be positive
if it is not true - return zero result
*/
if( index == -1 )
{
box->center.x = box->center.y =
box->size.width = box->size.height =
box->angle = 0.f;
goto error;
}
/* now find truthful eigenvector */
icvTransformVector_32f( INVQ, &INVEIGV[index * 6], u, 6, 6 );
/* extract vector components */
a = u[0];
b = u[1];
c = u[2];
d = u[3];
e = u[4];
f = u[5];
{
/* extract ellipse axes from above values */
/*
1) find center of ellipse
it satisfy equation
| a b/2 | * | x0 | + | d/2 | = |0 |
| b/2 c | | y0 | | e/2 | |0 |
*/
float x0, y0;
float idet = 1.f / (a * c - b * b * 0.25f);
/* we must normalize (a b c d e f ) to fit (4ac-b^2=1) */
float scale = cvSqrt( 0.25f * idet );
if (!scale)
{
box->center.x = box->center.y =
box->size.width = box->size.height =
box->angle = 0.f;
goto error;
}
a *= scale;
b *= scale;
c *= scale;
d *= scale;
e *= scale;
f *= scale;
//x0 = box->center.x = (-d * c * 0.5f + e * b * 0.25f) * 4.f;
//y0 = box->center.y = (-a * e * 0.5f + d * b * 0.25f) * 4.f;
x0 = box->center.x = (-d * c + e * b * 0.5f) * 2.f;
y0 = box->center.y = (-a * e + d * b * 0.5f) * 2.f;
/* offset ellipse to (x0,y0) */
/* new f == F(x0,y0) */
f += a * x0 * x0 + b * x0 * y0 + c * y0 * y0 + d * x0 + e * y0;
if (!f)
{
box->center.x = box->center.y =
box->size.width = box->size.height =
box->angle = 0.f;
goto error;
}
scale = -1.f / f;
/* normalize to f = 1 */
a *= scale;
b *= scale;
c *= scale;
}
/* recover center */
box->center.x += offx;
box->center.y += offy;
/* extract axis of ellipse */
/* one more eigenvalue operation */
TMP1[0] = a;
TMP1[1] = TMP1[2] = b * 0.5f;
TMP1[3] = c;
//status1 = icvJacobiEigens_32f( TMP1, INVEIGV, eigenvalues, 2, 0.f );
//assert( status1 == CV_OK );
_S = cvMat( 2, 2, CV_32F, TMP1 );
_EIGVECS = cvMat( 2, 2, CV_32F, INVEIGV );
_EIGVALS = cvMat( 2, 1, CV_32F, eigenvalues );
cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );
/* exteract axis length from eigenvectors */
box->size.height = 2 * cvInvSqrt( eigenvalues[0] );
box->size.width = 2 * cvInvSqrt( eigenvalues[1] );
if ( !(box->size.height && box->size.width) )
{
assert(0);
}
/* calc angle */
box->angle = cvFastArctan( INVEIGV[3], INVEIGV[2] );
error:
if( D )
icvDeleteMatrix( D );
return status;
}