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switched back to FitEllipse algorithm by Dr. Daniel Weiss; improved its accuracy in some cases. It fixes #1638

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pull/13383/head
Vadim Pisarevsky 13 years ago
parent 7901879e48
commit 4eda1662aa
2 changed files with 59 additions and 202 deletions
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  1. 227
      modules/imgproc/src/shapedescr.cpp
  2. 34
      modules/imgproc/test/test_convhull.cpp

227
modules/imgproc/src/shapedescr.cpp
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@ -771,202 +771,6 @@ cvContourArea( const void *array, CvSlice slice, int oriented )
}
/* 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 void
icvFitEllipse_F( CvSeq* points, CvBox2D* box )
{
cv::Ptr<CvMat> D;
double S[36], C[36], T[36];
int i, j;
double eigenvalues[6], eigenvectors[36];
double a, b, c, d, e, f;
double x0, y0, idet, scale, offx = 0, offy = 0;
int n = points->total;
CvSeqReader reader;
int is_float = CV_SEQ_ELTYPE(points) == CV_32FC2;
CvMat matS = cvMat(6,6,CV_64F,S), matC = cvMat(6,6,CV_64F,C), matT = cvMat(6,6,CV_64F,T);
CvMat _EIGVECS = cvMat(6,6,CV_64F,eigenvectors), _EIGVALS = cvMat(6,1,CV_64F,eigenvalues);
/* create matrix D of input points */
D = cvCreateMat( n, 6, CV_64F );
cvStartReadSeq( points, &reader );
/* shift all points to zero */
for( i = 0; i < n; i++ )
{
if( !is_float )
{
offx += ((CvPoint*)reader.ptr)->x;
offy += ((CvPoint*)reader.ptr)->y;
}
else
{
offx += ((CvPoint2D32f*)reader.ptr)->x;
offy += ((CvPoint2D32f*)reader.ptr)->y;
}
CV_NEXT_SEQ_ELEM( points->elem_size, reader );
}
offx /= n;
offy /= n;
// fill matrix rows as (x*x, x*y, y*y, x, y, 1 )
for( i = 0; i < n; i++ )
{
double x, y;
double* Dptr = D->data.db + i*6;
if( !is_float )
{
x = ((CvPoint*)reader.ptr)->x - offx;
y = ((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 );
Dptr[0] = x * x;
Dptr[1] = x * y;
Dptr[2] = y * y;
Dptr[3] = x;
Dptr[4] = y;
Dptr[5] = 1.;
}
// S = D^t*D
cvMulTransposed( D, &matS, 1 );
cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
for( i = 0; i < 6; i++ )
{
double a = eigenvalues[i];
a = a < DBL_EPSILON ? 0 : 1./sqrt(sqrt(a));
for( j = 0; j < 6; j++ )
eigenvectors[i*6 + j] *= a;
}
// C = Q^-1 = transp(INVEIGV) * INVEIGV
cvMulTransposed( &_EIGVECS, &matC, 1 );
cvZero( &matS );
S[2] = 2.;
S[7] = -1.;
S[12] = 2.;
// S = Q^-1*S*Q^-1
cvMatMul( &matC, &matS, &matT );
cvMatMul( &matT, &matC, &matS );
// and find its eigenvalues and vectors too
//cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
cvEigenVV( &matS, &_EIGVECS, &_EIGVALS, 0 );
for( i = 0; i < 3; i++ )
if( eigenvalues[i] > 0 )
break;
if( i >= 3 /*eigenvalues[0] < DBL_EPSILON*/ )
{
box->center.x = box->center.y =
box->size.width = box->size.height =
box->angle = 0.f;
return;
}
// now find truthful eigenvector
_EIGVECS = cvMat( 6, 1, CV_64F, eigenvectors + 6*i );
matT = cvMat( 6, 1, CV_64F, T );
// Q^-1*eigenvecs[0]
cvMatMul( &matC, &_EIGVECS, &matT );
// extract vector components
a = T[0]; b = T[1]; c = T[2]; d = T[3]; e = T[4]; f = T[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 |
*/
idet = a * c - b * b * 0.25;
idet = idet > DBL_EPSILON ? 1./idet : 0;
// we must normalize (a b c d e f ) to fit (4ac-b^2=1)
scale = sqrt( 0.25 * idet );
if( scale < DBL_EPSILON )
{
box->center.x = (float)offx;
box->center.y = (float)offy;
box->size.width = box->size.height = box->angle = 0.f;
return;
}
a *= scale;
b *= scale;
c *= scale;
d *= scale;
e *= scale;
f *= scale;
x0 = (-d * c + e * b * 0.5) * 2.;
y0 = (-a * e + d * b * 0.5) * 2.;
// recover center
box->center.x = (float)(x0 + offx);
box->center.y = (float)(y0 + offy);
// 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( fabs(f) < DBL_EPSILON )
{
box->size.width = box->size.height = box->angle = 0.f;
return;
}
scale = -1. / f;
// normalize to f = 1
a *= scale;
b *= scale;
c *= scale;
// extract axis of ellipse
// one more eigenvalue operation
S[0] = a;
S[1] = S[2] = b * 0.5;
S[3] = c;
matS = cvMat( 2, 2, CV_64F, S );
_EIGVECS = cvMat( 2, 2, CV_64F, eigenvectors );
_EIGVALS = cvMat( 1, 2, CV_64F, eigenvalues );
cvSVD( &matS, &_EIGVALS, &_EIGVECS, 0, CV_SVD_MODIFY_A + CV_SVD_U_T );
// exteract axis length from eigenvectors
box->size.width = (float)(2./sqrt(eigenvalues[0]));
box->size.height = (float)(2./sqrt(eigenvalues[1]));
// calc angle
box->angle = (float)(180 - atan2(eigenvectors[2], eigenvectors[3])*180/CV_PI);
}
CV_IMPL CvBox2D
cvFitEllipse2( const CvArr* array )
{
@ -993,12 +797,11 @@ cvFitEllipse2( const CvArr* array )
n = ptseq->total;
if( n < 5 )
CV_Error( CV_StsBadSize, "Number of points should be >= 5" );
#if 1
icvFitEllipse_F( ptseq, &box );
#else
/*
* New fitellipse algorithm, contributed by Dr. Daniel Weiss
*/
CvPoint2D32f c = {0,0};
double gfp[5], rp[5], t;
CvMat A, b, x;
const double min_eps = 1e-6;
@ -1015,6 +818,23 @@ cvFitEllipse2( const CvArr* array )
cvStartReadSeq( ptseq, &reader );
is_float = CV_SEQ_ELTYPE(ptseq) == CV_32FC2;
for( i = 0; i < n; i++ )
{
CvPoint2D32f p;
if( is_float )
p = *(CvPoint2D32f*)(reader.ptr);
else
{
p.x = (float)((int*)reader.ptr)[0];
p.y = (float)((int*)reader.ptr)[1];
}
CV_NEXT_SEQ_ELEM( sizeof(p), reader );
c.x += p.x;
c.y += p.y;
}
c.x /= n;
c.y /= n;
for( i = 0; i < n; i++ )
{
@ -1027,6 +847,8 @@ cvFitEllipse2( const CvArr* array )
p.y = (float)((int*)reader.ptr)[1];
}
CV_NEXT_SEQ_ELEM( sizeof(p), reader );
p.x -= c.x;
p.y -= c.y;
bd[i] = 10000.0; // 1.0?
Ad[i*5] = -(double)p.x * p.x; // A - C signs inverted as proposed by APP
@ -1065,6 +887,8 @@ cvFitEllipse2( const CvArr* array )
p.y = (float)((int*)reader.ptr)[1];
}
CV_NEXT_SEQ_ELEM( sizeof(p), reader );
p.x -= c.x;
p.y -= c.y;
bd[i] = 1.0;
Ad[i * 3] = (p.x - rp[0]) * (p.x - rp[0]);
Ad[i * 3 + 1] = (p.y - rp[1]) * (p.y - rp[1]);
@ -1086,8 +910,8 @@ cvFitEllipse2( const CvArr* array )
if( rp[3] > min_eps )
rp[3] = sqrt(2.0 / rp[3]);
box.center.x = (float)rp[0];
box.center.y = (float)rp[1];
box.center.x = (float)rp[0] + c.x;
box.center.y = (float)rp[1] + c.y;
box.size.width = (float)(rp[2]*2);
box.size.height = (float)(rp[3]*2);
if( box.size.width > box.size.height )
@ -1100,7 +924,6 @@ cvFitEllipse2( const CvArr* array )
box.angle += 360;
if( box.angle > 360 )
box.angle -= 360;
#endif
return box;
}

34
modules/imgproc/test/test_convhull.cpp
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@ -1134,6 +1134,8 @@ int CV_FitEllipseTest::validate_test_results( int test_case_idx )
_exit_:
#if 0
if( code < 0 )
{
cvNamedWindow( "test", 0 );
IplImage* img = cvCreateImage( cvSize(cvRound(low_high_range*4),
cvRound(low_high_range*4)), 8, 3 );
@ -1154,6 +1156,7 @@ _exit_:
cvShowImage( "test", img );
cvReleaseImage( &img );
cvWaitKey(0);
}
#endif
if( code < 0 )
@ -1164,6 +1167,36 @@ _exit_:
}
class CV_FitEllipseSmallTest : public cvtest::BaseTest
{
public:
CV_FitEllipseSmallTest() {}
~CV_FitEllipseSmallTest() {}
protected:
void run(int)
{
Size sz(50, 50);
vector<vector<Point> > c;
c.push_back(vector<Point>());
int scale = 1;
Point ofs = Point(0,0);//sz.width/2, sz.height/2) - Point(4,4)*scale;
c[0].push_back(Point(2, 0)*scale+ofs);
c[0].push_back(Point(0, 2)*scale+ofs);
c[0].push_back(Point(0, 6)*scale+ofs);
c[0].push_back(Point(2, 8)*scale+ofs);
c[0].push_back(Point(6, 8)*scale+ofs);
c[0].push_back(Point(8, 6)*scale+ofs);
c[0].push_back(Point(8, 2)*scale+ofs);
c[0].push_back(Point(6, 0)*scale+ofs);
RotatedRect e = fitEllipse(c[0]);
CV_Assert( fabs(e.center.x - 4) <= 1. &&
fabs(e.center.y - 4) <= 1. &&
fabs(e.size.width - 9) <= 1. &&
fabs(e.size.height - 9) <= 1. );
}
};
/****************************************************************************************\
* FitLine Test *
\****************************************************************************************/
@ -1664,6 +1697,7 @@ TEST(Imgproc_FitEllipse, accuracy) { CV_FitEllipseTest test; test.safe_run(); }
TEST(Imgproc_FitLine, accuracy) { CV_FitLineTest test; test.safe_run(); }
TEST(Imgproc_ContourMoments, accuracy) { CV_ContourMomentsTest test; test.safe_run(); }
TEST(Imgproc_ContourPerimeterSlice, accuracy) { CV_PerimeterAreaSliceTest test; test.safe_run(); }
TEST(Imgproc_FitEllipse, small) { CV_FitEllipseSmallTest test; test.safe_run(); }
/* End of file. */

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