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opencv/modules/imgproc/src/shapedescr.cpp

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/*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 "precomp.hpp"
/* calculates length of a curve (e.g. contour perimeter) */
CV_IMPL double
cvArcLength( const void *array, CvSlice slice, int is_closed )
{
double perimeter = 0;
int i, j = 0, count;
const int N = 16;
float buf[N];
CvMat buffer = cvMat( 1, N, CV_32F, buf );
CvSeqReader reader;
CvContour contour_header;
CvSeq* contour = 0;
CvSeqBlock block;
if( CV_IS_SEQ( array ))
{
contour = (CvSeq*)array;
if( !CV_IS_SEQ_POLYLINE( contour ))
CV_Error( CV_StsBadArg, "Unsupported sequence type" );
if( is_closed < 0 )
is_closed = CV_IS_SEQ_CLOSED( contour );
}
else
{
is_closed = is_closed > 0;
contour = cvPointSeqFromMat(
CV_SEQ_KIND_CURVE | (is_closed ? CV_SEQ_FLAG_CLOSED : 0),
array, &contour_header, &block );
}
if( contour->total > 1 )
{
int is_float = CV_SEQ_ELTYPE( contour ) == CV_32FC2;
cvStartReadSeq( contour, &reader, 0 );
cvSetSeqReaderPos( &reader, slice.start_index );
count = cvSliceLength( slice, contour );
count -= !is_closed && count == contour->total;
/* scroll the reader by 1 point */
reader.prev_elem = reader.ptr;
CV_NEXT_SEQ_ELEM( sizeof(CvPoint), reader );
for( i = 0; i < count; i++ )
{
float dx, dy;
if( !is_float )
{
CvPoint* pt = (CvPoint*)reader.ptr;
CvPoint* prev_pt = (CvPoint*)reader.prev_elem;
dx = (float)pt->x - (float)prev_pt->x;
dy = (float)pt->y - (float)prev_pt->y;
}
else
{
CvPoint2D32f* pt = (CvPoint2D32f*)reader.ptr;
CvPoint2D32f* prev_pt = (CvPoint2D32f*)reader.prev_elem;
dx = pt->x - prev_pt->x;
dy = pt->y - prev_pt->y;
}
reader.prev_elem = reader.ptr;
CV_NEXT_SEQ_ELEM( contour->elem_size, reader );
buffer.data.fl[j] = dx * dx + dy * dy;
if( ++j == N || i == count - 1 )
{
buffer.cols = j;
cvPow( &buffer, &buffer, 0.5 );
for( ; j > 0; j-- )
perimeter += buffer.data.fl[j-1];
}
}
}
return perimeter;
}
static CvStatus
icvFindCircle( CvPoint2D32f pt0, CvPoint2D32f pt1,
CvPoint2D32f pt2, CvPoint2D32f * center, float *radius )
{
double x1 = (pt0.x + pt1.x) * 0.5;
double dy1 = pt0.x - pt1.x;
double x2 = (pt1.x + pt2.x) * 0.5;
double dy2 = pt1.x - pt2.x;
double y1 = (pt0.y + pt1.y) * 0.5;
double dx1 = pt1.y - pt0.y;
double y2 = (pt1.y + pt2.y) * 0.5;
double dx2 = pt2.y - pt1.y;
double t = 0;
CvStatus result = CV_OK;
if( icvIntersectLines( x1, dx1, y1, dy1, x2, dx2, y2, dy2, &t ) >= 0 )
{
center->x = (float) (x2 + dx2 * t);
center->y = (float) (y2 + dy2 * t);
*radius = (float) icvDistanceL2_32f( *center, pt0 );
}
else
{
center->x = center->y = 0.f;
radius = 0;
result = CV_NOTDEFINED_ERR;
}
return result;
}
CV_INLINE double icvIsPtInCircle( CvPoint2D32f pt, CvPoint2D32f center, float radius )
{
double dx = pt.x - center.x;
double dy = pt.y - center.y;
return (double)radius*radius - dx*dx - dy*dy;
}
static int
icvFindEnslosingCicle4pts_32f( CvPoint2D32f * pts, CvPoint2D32f * _center, float *_radius )
{
int shuffles[4][4] = { {0, 1, 2, 3}, {0, 1, 3, 2}, {2, 3, 0, 1}, {2, 3, 1, 0} };
int idxs[4] = { 0, 1, 2, 3 };
int i, j, k = 1, mi = 0;
float max_dist = 0;
CvPoint2D32f center;
CvPoint2D32f min_center;
float radius, min_radius = FLT_MAX;
CvPoint2D32f res_pts[4];
center = min_center = pts[0];
radius = 1.f;
for( i = 0; i < 4; i++ )
for( j = i + 1; j < 4; j++ )
{
float dist = icvDistanceL2_32f( pts[i], pts[j] );
if( max_dist < dist )
{
max_dist = dist;
idxs[0] = i;
idxs[1] = j;
}
}
if( max_dist == 0 )
goto function_exit;
k = 2;
for( i = 0; i < 4; i++ )
{
for( j = 0; j < k; j++ )
if( i == idxs[j] )
break;
if( j == k )
idxs[k++] = i;
}
center = cvPoint2D32f( (pts[idxs[0]].x + pts[idxs[1]].x)*0.5f,
(pts[idxs[0]].y + pts[idxs[1]].y)*0.5f );
radius = (float)(icvDistanceL2_32f( pts[idxs[0]], center )*1.03);
if( radius < 1.f )
radius = 1.f;
if( icvIsPtInCircle( pts[idxs[2]], center, radius ) >= 0 &&
icvIsPtInCircle( pts[idxs[3]], center, radius ) >= 0 )
{
k = 2; //rand()%2+2;
}
else
{
mi = -1;
for( i = 0; i < 4; i++ )
{
if( icvFindCircle( pts[shuffles[i][0]], pts[shuffles[i][1]],
pts[shuffles[i][2]], &center, &radius ) >= 0 )
{
radius *= 1.03f;
if( radius < 2.f )
radius = 2.f;
if( icvIsPtInCircle( pts[shuffles[i][3]], center, radius ) >= 0 &&
min_radius > radius )
{
min_radius = radius;
min_center = center;
mi = i;
}
}
}
assert( mi >= 0 );
if( mi < 0 )
mi = 0;
k = 3;
center = min_center;
radius = min_radius;
for( i = 0; i < 4; i++ )
idxs[i] = shuffles[mi][i];
}
function_exit:
*_center = center;
*_radius = radius;
/* reorder output points */
for( i = 0; i < 4; i++ )
res_pts[i] = pts[idxs[i]];
for( i = 0; i < 4; i++ )
{
pts[i] = res_pts[i];
assert( icvIsPtInCircle( pts[i], center, radius ) >= 0 );
}
return k;
}
CV_IMPL int
cvMinEnclosingCircle( const void* array, CvPoint2D32f * _center, float *_radius )
{
const int max_iters = 100;
const float eps = FLT_EPSILON*2;
CvPoint2D32f center = { 0, 0 };
float radius = 0;
int result = 0;
if( _center )
_center->x = _center->y = 0.f;
if( _radius )
*_radius = 0;
CvSeqReader reader;
int i, k, count;
CvPoint2D32f pts[8];
CvContour contour_header;
CvSeqBlock block;
CvSeq* sequence = 0;
int is_float;
if( !_center || !_radius )
CV_Error( CV_StsNullPtr, "Null center or radius pointers" );
if( CV_IS_SEQ(array) )
{
sequence = (CvSeq*)array;
if( !CV_IS_SEQ_POINT_SET( sequence ))
CV_Error( CV_StsBadArg, "The passed sequence is not a valid contour" );
}
else
{
sequence = cvPointSeqFromMat(
CV_SEQ_KIND_GENERIC, array, &contour_header, &block );
}
if( sequence->total <= 0 )
CV_Error( CV_StsBadSize, "" );
cvStartReadSeq( sequence, &reader, 0 );
count = sequence->total;
is_float = CV_SEQ_ELTYPE(sequence) == CV_32FC2;
if( !is_float )
{
CvPoint *pt_left, *pt_right, *pt_top, *pt_bottom;
CvPoint pt;
pt_left = pt_right = pt_top = pt_bottom = (CvPoint *)(reader.ptr);
CV_READ_SEQ_ELEM( pt, reader );
for( i = 1; i < count; i++ )
{
CvPoint* pt_ptr = (CvPoint*)reader.ptr;
CV_READ_SEQ_ELEM( pt, reader );
if( pt.x < pt_left->x )
pt_left = pt_ptr;
if( pt.x > pt_right->x )
pt_right = pt_ptr;
if( pt.y < pt_top->y )
pt_top = pt_ptr;
if( pt.y > pt_bottom->y )
pt_bottom = pt_ptr;
}
pts[0] = cvPointTo32f( *pt_left );
pts[1] = cvPointTo32f( *pt_right );
pts[2] = cvPointTo32f( *pt_top );
pts[3] = cvPointTo32f( *pt_bottom );
}
else
{
CvPoint2D32f *pt_left, *pt_right, *pt_top, *pt_bottom;
CvPoint2D32f pt;
pt_left = pt_right = pt_top = pt_bottom = (CvPoint2D32f *) (reader.ptr);
CV_READ_SEQ_ELEM( pt, reader );
for( i = 1; i < count; i++ )
{
CvPoint2D32f* pt_ptr = (CvPoint2D32f*)reader.ptr;
CV_READ_SEQ_ELEM( pt, reader );
if( pt.x < pt_left->x )
pt_left = pt_ptr;
if( pt.x > pt_right->x )
pt_right = pt_ptr;
if( pt.y < pt_top->y )
pt_top = pt_ptr;
if( pt.y > pt_bottom->y )
pt_bottom = pt_ptr;
}
pts[0] = *pt_left;
pts[1] = *pt_right;
pts[2] = *pt_top;
pts[3] = *pt_bottom;
}
for( k = 0; k < max_iters; k++ )
{
double min_delta = 0, delta;
CvPoint2D32f ptfl;
icvFindEnslosingCicle4pts_32f( pts, &center, &radius );
cvStartReadSeq( sequence, &reader, 0 );
for( i = 0; i < count; i++ )
{
if( !is_float )
{
ptfl.x = (float)((CvPoint*)reader.ptr)->x;
ptfl.y = (float)((CvPoint*)reader.ptr)->y;
}
else
{
ptfl = *(CvPoint2D32f*)reader.ptr;
}
CV_NEXT_SEQ_ELEM( sequence->elem_size, reader );
delta = icvIsPtInCircle( ptfl, center, radius );
if( delta < min_delta )
{
min_delta = delta;
pts[3] = ptfl;
}
}
result = min_delta >= 0;
if( result )
break;
}
if( !result )
{
cvStartReadSeq( sequence, &reader, 0 );
radius = 0.f;
for( i = 0; i < count; i++ )
{
CvPoint2D32f ptfl;
float t, dx, dy;
if( !is_float )
{
ptfl.x = (float)((CvPoint*)reader.ptr)->x;
ptfl.y = (float)((CvPoint*)reader.ptr)->y;
}
else
{
ptfl = *(CvPoint2D32f*)reader.ptr;
}
CV_NEXT_SEQ_ELEM( sequence->elem_size, reader );
dx = center.x - ptfl.x;
dy = center.y - ptfl.y;
t = dx*dx + dy*dy;
radius = MAX(radius,t);
}
radius = (float)(sqrt(radius)*(1 + eps));
result = 1;
}
*_center = center;
*_radius = radius;
return result;
}
/* area of a whole sequence */
static CvStatus
icvContourArea( const CvSeq* contour, double *area )
{
if( contour->total )
{
CvSeqReader reader;
int lpt = contour->total;
double a00 = 0, xi_1, yi_1;
int is_float = CV_SEQ_ELTYPE(contour) == CV_32FC2;
cvStartReadSeq( contour, &reader, 0 );
if( !is_float )
{
xi_1 = ((CvPoint*)(reader.ptr))->x;
yi_1 = ((CvPoint*)(reader.ptr))->y;
}
else
{
xi_1 = ((CvPoint2D32f*)(reader.ptr))->x;
yi_1 = ((CvPoint2D32f*)(reader.ptr))->y;
}
CV_NEXT_SEQ_ELEM( contour->elem_size, reader );
while( lpt-- > 0 )
{
double dxy, xi, yi;
if( !is_float )
{
xi = ((CvPoint*)(reader.ptr))->x;
yi = ((CvPoint*)(reader.ptr))->y;
}
else
{
xi = ((CvPoint2D32f*)(reader.ptr))->x;
yi = ((CvPoint2D32f*)(reader.ptr))->y;
}
CV_NEXT_SEQ_ELEM( contour->elem_size, reader );
dxy = xi_1 * yi - xi * yi_1;
a00 += dxy;
xi_1 = xi;
yi_1 = yi;
}
*area = a00 * 0.5;
}
else
*area = 0;
return CV_OK;
}
/****************************************************************************************\
copy data from one buffer to other buffer
\****************************************************************************************/
static CvStatus
icvMemCopy( double **buf1, double **buf2, double **buf3, int *b_max )
{
int bb;
if( (*buf1 == NULL && *buf2 == NULL) || *buf3 == NULL )
return CV_NULLPTR_ERR;
bb = *b_max;
if( *buf2 == NULL )
{
*b_max = 2 * (*b_max);
*buf2 = (double *)cvAlloc( (*b_max) * sizeof( double ));
if( *buf2 == NULL )
return CV_OUTOFMEM_ERR;
memcpy( *buf2, *buf3, bb * sizeof( double ));
*buf3 = *buf2;
cvFree( buf1 );
*buf1 = NULL;
}
else
{
*b_max = 2 * (*b_max);
*buf1 = (double *) cvAlloc( (*b_max) * sizeof( double ));
if( *buf1 == NULL )
return CV_OUTOFMEM_ERR;
memcpy( *buf1, *buf3, bb * sizeof( double ));
*buf3 = *buf1;
cvFree( buf2 );
*buf2 = NULL;
}
return CV_OK;
}
/* area of a contour sector */
static CvStatus icvContourSecArea( CvSeq * contour, CvSlice slice, double *area )
{
CvPoint pt; /* pointer to points */
CvPoint pt_s, pt_e; /* first and last points */
CvSeqReader reader; /* points reader of contour */
int p_max = 2, p_ind;
int lpt, flag, i;
double a00; /* unnormalized moments m00 */
double xi, yi, xi_1, yi_1, x0, y0, dxy, sk, sk1, t;
double x_s, y_s, nx, ny, dx, dy, du, dv;
double eps = 1.e-5;
double *p_are1, *p_are2, *p_are;
assert( contour != NULL );
if( contour == NULL )
return CV_NULLPTR_ERR;
if( !CV_IS_SEQ_POINT_SET( contour ))
return CV_BADFLAG_ERR;
lpt = cvSliceLength( slice, contour );
/*if( n2 >= n1 )
lpt = n2 - n1 + 1;
else
lpt = contour->total - n1 + n2 + 1;*/
if( contour->total && lpt > 2 )
{
a00 = x0 = y0 = xi_1 = yi_1 = 0;
sk1 = 0;
flag = 0;
dxy = 0;
p_are1 = (double *) cvAlloc( p_max * sizeof( double ));
if( p_are1 == NULL )
return CV_OUTOFMEM_ERR;
p_are = p_are1;
p_are2 = NULL;
cvStartReadSeq( contour, &reader, 0 );
cvSetSeqReaderPos( &reader, slice.start_index );
CV_READ_SEQ_ELEM( pt_s, reader );
p_ind = 0;
cvSetSeqReaderPos( &reader, slice.end_index );
CV_READ_SEQ_ELEM( pt_e, reader );
/* normal coefficients */
nx = pt_s.y - pt_e.y;
ny = pt_e.x - pt_s.x;
cvSetSeqReaderPos( &reader, slice.start_index );
while( lpt-- > 0 )
{
CV_READ_SEQ_ELEM( pt, reader );
if( flag == 0 )
{
xi_1 = (double) pt.x;
yi_1 = (double) pt.y;
x0 = xi_1;
y0 = yi_1;
sk1 = 0;
flag = 1;
}
else
{
xi = (double) pt.x;
yi = (double) pt.y;
/**************** edges intersection examination **************************/
sk = nx * (xi - pt_s.x) + ny * (yi - pt_s.y);
if( (fabs( sk ) < eps && lpt > 0) || sk * sk1 < -eps )
{
if( fabs( sk ) < eps )
{
dxy = xi_1 * yi - xi * yi_1;
a00 = a00 + dxy;
dxy = xi * y0 - x0 * yi;
a00 = a00 + dxy;
if( p_ind >= p_max )
icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );
p_are[p_ind] = a00 / 2.;
p_ind++;
a00 = 0;
sk1 = 0;
x0 = xi;
y0 = yi;
dxy = 0;
}
else
{
/* define intersection point */
dv = yi - yi_1;
du = xi - xi_1;
dx = ny;
dy = -nx;
if( fabs( du ) > eps )
t = ((yi_1 - pt_s.y) * du + dv * (pt_s.x - xi_1)) /
(du * dy - dx * dv);
else
t = (xi_1 - pt_s.x) / dx;
if( t > eps && t < 1 - eps )
{
x_s = pt_s.x + t * dx;
y_s = pt_s.y + t * dy;
dxy = xi_1 * y_s - x_s * yi_1;
a00 += dxy;
dxy = x_s * y0 - x0 * y_s;
a00 += dxy;
if( p_ind >= p_max )
icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );
p_are[p_ind] = a00 / 2.;
p_ind++;
a00 = 0;
sk1 = 0;
x0 = x_s;
y0 = y_s;
dxy = x_s * yi - xi * y_s;
}
}
}
else
dxy = xi_1 * yi - xi * yi_1;
a00 += dxy;
xi_1 = xi;
yi_1 = yi;
sk1 = sk;
}
}
xi = x0;
yi = y0;
dxy = xi_1 * yi - xi * yi_1;
a00 += dxy;
if( p_ind >= p_max )
icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );
p_are[p_ind] = a00 / 2.;
p_ind++;
/* common area calculation */
*area = 0;
for( i = 0; i < p_ind; i++ )
(*area) += fabs( p_are[i] );
if( p_are1 != NULL )
cvFree( &p_are1 );
else if( p_are2 != NULL )
cvFree( &p_are2 );
return CV_OK;
}
else
return CV_BADSIZE_ERR;
}
/* external contour area function */
CV_IMPL double
cvContourArea( const void *array, CvSlice slice, int oriented )
{
double area = 0;
CvContour contour_header;
CvSeq* contour = 0;
CvSeqBlock block;
if( CV_IS_SEQ( array ))
{
contour = (CvSeq*)array;
if( !CV_IS_SEQ_POLYLINE( contour ))
CV_Error( CV_StsBadArg, "Unsupported sequence type" );
}
else
{
contour = cvPointSeqFromMat( CV_SEQ_KIND_CURVE, array, &contour_header, &block );
}
if( cvSliceLength( slice, contour ) == contour->total )
{
IPPI_CALL( icvContourArea( contour, &area ));
}
else
{
if( CV_SEQ_ELTYPE( contour ) != CV_32SC2 )
CV_Error( CV_StsUnsupportedFormat,
"Only curves with integer coordinates are supported in case of contour slice" );
IPPI_CALL( icvContourSecArea( contour, slice, &area ));
}
return oriented ? area : fabs(area);
}
/* 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 )
{
CvBox2D box;
cv::AutoBuffer<double> Ad, bd;
memset( &box, 0, sizeof(box));
CvContour contour_header;
CvSeq* ptseq = 0;
CvSeqBlock block;
int n;
if( CV_IS_SEQ( array ))
{
ptseq = (CvSeq*)array;
if( !CV_IS_SEQ_POINT_SET( ptseq ))
CV_Error( CV_StsBadArg, "Unsupported sequence type" );
}
else
{
ptseq = cvPointSeqFromMat(CV_SEQ_KIND_GENERIC, array, &contour_header, &block);
}
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
*/
double gfp[5], rp[5], t;
CvMat A, b, x;
const double min_eps = 1e-6;
int i, is_float;
CvSeqReader reader;
Ad.allocate(n*5);
bd.allocate(n);
// first fit for parameters A - E
A = cvMat( n, 5, CV_64F, Ad );
b = cvMat( n, 1, CV_64F, bd );
x = cvMat( 5, 1, CV_64F, gfp );
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 );
bd[i] = 10000.0; // 1.0?
Ad[i*5] = -(double)p.x * p.x; // A - C signs inverted as proposed by APP
Ad[i*5 + 1] = -(double)p.y * p.y;
Ad[i*5 + 2] = -(double)p.x * p.y;
Ad[i*5 + 3] = p.x;
Ad[i*5 + 4] = p.y;
}
cvSolve( &A, &b, &x, CV_SVD );
// now use general-form parameters A - E to find the ellipse center:
// differentiate general form wrt x/y to get two equations for cx and cy
A = cvMat( 2, 2, CV_64F, Ad );
b = cvMat( 2, 1, CV_64F, bd );
x = cvMat( 2, 1, CV_64F, rp );
Ad[0] = 2 * gfp[0];
Ad[1] = Ad[2] = gfp[2];
Ad[3] = 2 * gfp[1];
bd[0] = gfp[3];
bd[1] = gfp[4];
cvSolve( &A, &b, &x, CV_SVD );
// re-fit for parameters A - C with those center coordinates
A = cvMat( n, 3, CV_64F, Ad );
b = cvMat( n, 1, CV_64F, bd );
x = cvMat( 3, 1, CV_64F, gfp );
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 );
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]);
Ad[i * 3 + 2] = (p.x - rp[0]) * (p.y - rp[1]);
}
cvSolve(&A, &b, &x, CV_SVD);
// store angle and radii
rp[4] = -0.5 * atan2(gfp[2], gfp[1] - gfp[0]); // convert from APP angle usage
t = sin(-2.0 * rp[4]);
if( fabs(t) > fabs(gfp[2])*min_eps )
t = gfp[2]/t;
else
t = gfp[1] - gfp[0];
rp[2] = fabs(gfp[0] + gfp[1] - t);
if( rp[2] > min_eps )
rp[2] = sqrt(2.0 / rp[2]);
rp[3] = fabs(gfp[0] + gfp[1] + t);
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.size.width = (float)(rp[2]*2);
box.size.height = (float)(rp[3]*2);
if( box.size.width > box.size.height )
{
float tmp;
CV_SWAP( box.size.width, box.size.height, tmp );
box.angle = (float)(90 + rp[4]*180/CV_PI);
}
if( box.angle < -180 )
box.angle += 360;
if( box.angle > 360 )
box.angle -= 360;
#endif
return box;
}
/* Calculates bounding rectagnle of a point set or retrieves already calculated */
CV_IMPL CvRect
cvBoundingRect( CvArr* array, int update )
{
CvSeqReader reader;
CvRect rect = { 0, 0, 0, 0 };
CvContour contour_header;
CvSeq* ptseq = 0;
CvSeqBlock block;
CvMat stub, *mat = 0;
int xmin = 0, ymin = 0, xmax = -1, ymax = -1, i, j, k;
int calculate = update;
if( CV_IS_SEQ( array ))
{
ptseq = (CvSeq*)array;
if( !CV_IS_SEQ_POINT_SET( ptseq ))
CV_Error( CV_StsBadArg, "Unsupported sequence type" );
if( ptseq->header_size < (int)sizeof(CvContour))
{
/*if( update == 1 )
CV_Error( CV_StsBadArg, "The header is too small to fit the rectangle, "
"so it could not be updated" );*/
update = 0;
calculate = 1;
}
}
else
{
mat = cvGetMat( array, &stub );
if( CV_MAT_TYPE(mat->type) == CV_32SC2 ||
CV_MAT_TYPE(mat->type) == CV_32FC2 )
{
ptseq = cvPointSeqFromMat(CV_SEQ_KIND_GENERIC, mat, &contour_header, &block);
mat = 0;
}
else if( CV_MAT_TYPE(mat->type) != CV_8UC1 &&
CV_MAT_TYPE(mat->type) != CV_8SC1 )
CV_Error( CV_StsUnsupportedFormat,
"The image/matrix format is not supported by the function" );
update = 0;
calculate = 1;
}
if( !calculate )
return ((CvContour*)ptseq)->rect;
if( mat )
{
CvSize size = cvGetMatSize(mat);
xmin = size.width;
ymin = -1;
for( i = 0; i < size.height; i++ )
{
uchar* _ptr = mat->data.ptr + i*mat->step;
uchar* ptr = (uchar*)cvAlignPtr(_ptr, 4);
int have_nz = 0, k_min, offset = (int)(ptr - _ptr);
j = 0;
offset = MIN(offset, size.width);
for( ; j < offset; j++ )
if( _ptr[j] )
{
have_nz = 1;
break;
}
if( j < offset )
{
if( j < xmin )
xmin = j;
if( j > xmax )
xmax = j;
}
if( offset < size.width )
{
xmin -= offset;
xmax -= offset;
size.width -= offset;
j = 0;
for( ; j <= xmin - 4; j += 4 )
if( *((int*)(ptr+j)) )
break;
for( ; j < xmin; j++ )
if( ptr[j] )
{
xmin = j;
if( j > xmax )
xmax = j;
have_nz = 1;
break;
}
k_min = MAX(j-1, xmax);
k = size.width - 1;
for( ; k > k_min && (k&3) != 3; k-- )
if( ptr[k] )
break;
if( k > k_min && (k&3) == 3 )
{
for( ; k > k_min+3; k -= 4 )
if( *((int*)(ptr+k-3)) )
break;
}
for( ; k > k_min; k-- )
if( ptr[k] )
{
xmax = k;
have_nz = 1;
break;
}
if( !have_nz )
{
j &= ~3;
for( ; j <= k - 3; j += 4 )
if( *((int*)(ptr+j)) )
break;
for( ; j <= k; j++ )
if( ptr[j] )
{
have_nz = 1;
break;
}
}
xmin += offset;
xmax += offset;
size.width += offset;
}
if( have_nz )
{
if( ymin < 0 )
ymin = i;
ymax = i;
}
}
if( xmin >= size.width )
xmin = ymin = 0;
}
else if( ptseq->total )
{
int is_float = CV_SEQ_ELTYPE(ptseq) == CV_32FC2;
cvStartReadSeq( ptseq, &reader, 0 );
if( !is_float )
{
CvPoint pt;
/* init values */
CV_READ_SEQ_ELEM( pt, reader );
xmin = xmax = pt.x;
ymin = ymax = pt.y;
for( i = 1; i < ptseq->total; i++ )
{
CV_READ_SEQ_ELEM( pt, reader );
if( xmin > pt.x )
xmin = pt.x;
if( xmax < pt.x )
xmax = pt.x;
if( ymin > pt.y )
ymin = pt.y;
if( ymax < pt.y )
ymax = pt.y;
}
}
else
{
CvPoint pt;
Cv32suf v;
/* init values */
CV_READ_SEQ_ELEM( pt, reader );
xmin = xmax = CV_TOGGLE_FLT(pt.x);
ymin = ymax = CV_TOGGLE_FLT(pt.y);
for( i = 1; i < ptseq->total; i++ )
{
CV_READ_SEQ_ELEM( pt, reader );
pt.x = CV_TOGGLE_FLT(pt.x);
pt.y = CV_TOGGLE_FLT(pt.y);
if( xmin > pt.x )
xmin = pt.x;
if( xmax < pt.x )
xmax = pt.x;
if( ymin > pt.y )
ymin = pt.y;
if( ymax < pt.y )
ymax = pt.y;
}
v.i = CV_TOGGLE_FLT(xmin); xmin = cvFloor(v.f);
v.i = CV_TOGGLE_FLT(ymin); ymin = cvFloor(v.f);
/* because right and bottom sides of
the bounding rectangle are not inclusive
(note +1 in width and height calculation below),
cvFloor is used here instead of cvCeil */
v.i = CV_TOGGLE_FLT(xmax); xmax = cvFloor(v.f);
v.i = CV_TOGGLE_FLT(ymax); ymax = cvFloor(v.f);
}
}
rect.x = xmin;
rect.y = ymin;
rect.width = xmax - xmin + 1;
rect.height = ymax - ymin + 1;
if( update )
((CvContour*)ptseq)->rect = rect;
return rect;
}
/* End of file. */