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opencv/modules/imgproc/src/moments.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.
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// 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
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//
//M*/
#include "precomp.hpp"
// The function calculates center of gravity and the central second order moments
static void icvCompleteMomentState( CvMoments* moments )
{
double cx = 0, cy = 0;
double mu20, mu11, mu02;
assert( moments != 0 );
moments->inv_sqrt_m00 = 0;
if( fabs(moments->m00) > DBL_EPSILON )
{
double inv_m00 = 1. / moments->m00;
cx = moments->m10 * inv_m00;
cy = moments->m01 * inv_m00;
moments->inv_sqrt_m00 = std::sqrt( fabs(inv_m00) );
}
// mu20 = m20 - m10*cx
mu20 = moments->m20 - moments->m10 * cx;
// mu11 = m11 - m10*cy
mu11 = moments->m11 - moments->m10 * cy;
// mu02 = m02 - m01*cy
mu02 = moments->m02 - moments->m01 * cy;
moments->mu20 = mu20;
moments->mu11 = mu11;
moments->mu02 = mu02;
// mu30 = m30 - cx*(3*mu20 + cx*m10)
moments->mu30 = moments->m30 - cx * (3 * mu20 + cx * moments->m10);
mu11 += mu11;
// mu21 = m21 - cx*(2*mu11 + cx*m01) - cy*mu20
moments->mu21 = moments->m21 - cx * (mu11 + cx * moments->m01) - cy * mu20;
// mu12 = m12 - cy*(2*mu11 + cy*m10) - cx*mu02
moments->mu12 = moments->m12 - cy * (mu11 + cy * moments->m10) - cx * mu02;
// mu03 = m03 - cy*(3*mu02 + cy*m01)
moments->mu03 = moments->m03 - cy * (3 * mu02 + cy * moments->m01);
}
static void icvContourMoments( CvSeq* contour, CvMoments* moments )
{
int is_float = CV_SEQ_ELTYPE(contour) == CV_32FC2;
if( contour->total )
{
CvSeqReader reader;
double a00, a10, a01, a20, a11, a02, a30, a21, a12, a03;
double xi, yi, xi2, yi2, xi_1, yi_1, xi_12, yi_12, dxy, xii_1, yii_1;
int lpt = contour->total;
a00 = a10 = a01 = a20 = a11 = a02 = a30 = a21 = a12 = a03 = 0;
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 );
xi_12 = xi_1 * xi_1;
yi_12 = yi_1 * yi_1;
while( lpt-- > 0 )
{
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 );
xi2 = xi * xi;
yi2 = yi * yi;
dxy = xi_1 * yi - xi * yi_1;
xii_1 = xi_1 + xi;
yii_1 = yi_1 + yi;
a00 += dxy;
a10 += dxy * xii_1;
a01 += dxy * yii_1;
a20 += dxy * (xi_1 * xii_1 + xi2);
a11 += dxy * (xi_1 * (yii_1 + yi_1) + xi * (yii_1 + yi));
a02 += dxy * (yi_1 * yii_1 + yi2);
a30 += dxy * xii_1 * (xi_12 + xi2);
a03 += dxy * yii_1 * (yi_12 + yi2);
a21 +=
dxy * (xi_12 * (3 * yi_1 + yi) + 2 * xi * xi_1 * yii_1 +
xi2 * (yi_1 + 3 * yi));
a12 +=
dxy * (yi_12 * (3 * xi_1 + xi) + 2 * yi * yi_1 * xii_1 +
yi2 * (xi_1 + 3 * xi));
xi_1 = xi;
yi_1 = yi;
xi_12 = xi2;
yi_12 = yi2;
}
double db1_2, db1_6, db1_12, db1_24, db1_20, db1_60;
if( fabs(a00) > FLT_EPSILON )
{
if( a00 > 0 )
{
db1_2 = 0.5;
db1_6 = 0.16666666666666666666666666666667;
db1_12 = 0.083333333333333333333333333333333;
db1_24 = 0.041666666666666666666666666666667;
db1_20 = 0.05;
db1_60 = 0.016666666666666666666666666666667;
}
else
{
db1_2 = -0.5;
db1_6 = -0.16666666666666666666666666666667;
db1_12 = -0.083333333333333333333333333333333;
db1_24 = -0.041666666666666666666666666666667;
db1_20 = -0.05;
db1_60 = -0.016666666666666666666666666666667;
}
// spatial moments
moments->m00 = a00 * db1_2;
moments->m10 = a10 * db1_6;
moments->m01 = a01 * db1_6;
moments->m20 = a20 * db1_12;
moments->m11 = a11 * db1_24;
moments->m02 = a02 * db1_12;
moments->m30 = a30 * db1_20;
moments->m21 = a21 * db1_60;
moments->m12 = a12 * db1_60;
moments->m03 = a03 * db1_20;
icvCompleteMomentState( moments );
}
}
}
/****************************************************************************************\
* Spatial Raster Moments *
\****************************************************************************************/
template<typename T, typename WT, typename MT>
static void momentsInTile( const cv::Mat& img, double* moments )
{
cv::Size size = img.size();
int x, y;
MT mom[10] = {0,0,0,0,0,0,0,0,0,0};
for( y = 0; y < size.height; y++ )
{
const T* ptr = (const T*)(img.data + y*img.step);
WT x0 = 0, x1 = 0, x2 = 0;
MT x3 = 0;
for( x = 0; x < size.width; x++ )
{
WT p = ptr[x];
WT xp = x * p, xxp;
x0 += p;
x1 += xp;
xxp = xp * x;
x2 += xxp;
x3 += xxp * x;
}
WT py = y * x0, sy = y*y;
mom[9] += ((MT)py) * sy; // m03
mom[8] += ((MT)x1) * sy; // m12
mom[7] += ((MT)x2) * y; // m21
mom[6] += x3; // m30
mom[5] += x0 * sy; // m02
mom[4] += x1 * y; // m11
mom[3] += x2; // m20
mom[2] += py; // m01
mom[1] += x1; // m10
mom[0] += x0; // m00
}
for( x = 0; x < 10; x++ )
moments[x] = (double)mom[x];
}
#if CV_SSE2
template<> void momentsInTile<uchar, int, int>( const cv::Mat& img, double* moments )
{
typedef uchar T;
typedef int WT;
typedef int MT;
cv::Size size = img.size();
int x, y;
MT mom[10] = {0,0,0,0,0,0,0,0,0,0};
bool useSIMD = cv::checkHardwareSupport(CV_CPU_SSE2);
for( y = 0; y < size.height; y++ )
{
const T* ptr = img.ptr<T>(y);
int x0 = 0, x1 = 0, x2 = 0, x3 = 0, x = 0;
if( useSIMD )
{
__m128i qx_init = _mm_setr_epi16(0, 1, 2, 3, 4, 5, 6, 7);
__m128i dx = _mm_set1_epi16(8);
__m128i z = _mm_setzero_si128(), qx0 = z, qx1 = z, qx2 = z, qx3 = z, qx = qx_init;
for( ; x <= size.width - 8; x += 8 )
{
__m128i p = _mm_unpacklo_epi8(_mm_loadl_epi64((const __m128i*)(ptr + x)), z);
qx0 = _mm_add_epi32(qx0, _mm_sad_epu8(p, z));
__m128i px = _mm_mullo_epi16(p, qx);
__m128i sx = _mm_mullo_epi16(qx, qx);
qx1 = _mm_add_epi32(qx1, _mm_madd_epi16(p, qx));
qx2 = _mm_add_epi32(qx2, _mm_madd_epi16(p, sx));
qx3 = _mm_add_epi32(qx3, _mm_madd_epi16(px, sx));
qx = _mm_add_epi16(qx, dx);
}
int CV_DECL_ALIGNED(16) buf[4];
_mm_store_si128((__m128i*)buf, qx0);
x0 = buf[0] + buf[1] + buf[2] + buf[3];
_mm_store_si128((__m128i*)buf, qx1);
x1 = buf[0] + buf[1] + buf[2] + buf[3];
_mm_store_si128((__m128i*)buf, qx2);
x2 = buf[0] + buf[1] + buf[2] + buf[3];
_mm_store_si128((__m128i*)buf, qx3);
x3 = buf[0] + buf[1] + buf[2] + buf[3];
}
for( ; x < size.width; x++ )
{
WT p = ptr[x];
WT xp = x * p, xxp;
x0 += p;
x1 += xp;
xxp = xp * x;
x2 += xxp;
x3 += xxp * x;
}
WT py = y * x0, sy = y*y;
mom[9] += ((MT)py) * sy; // m03
mom[8] += ((MT)x1) * sy; // m12
mom[7] += ((MT)x2) * y; // m21
mom[6] += x3; // m30
mom[5] += x0 * sy; // m02
mom[4] += x1 * y; // m11
mom[3] += x2; // m20
mom[2] += py; // m01
mom[1] += x1; // m10
mom[0] += x0; // m00
}
for( x = 0; x < 10; x++ )
moments[x] = (double)mom[x];
}
#endif
typedef void (*CvMomentsInTileFunc)(const cv::Mat& img, double* moments);
CV_IMPL void cvMoments( const void* array, CvMoments* moments, int binary )
{
const int TILE_SIZE = 32;
int type, depth, cn, coi = 0;
CvMat stub, *mat = (CvMat*)array;
CvMomentsInTileFunc func = 0;
CvContour contourHeader;
CvSeq* contour = 0;
CvSeqBlock block;
double buf[TILE_SIZE*TILE_SIZE];
uchar nzbuf[TILE_SIZE*TILE_SIZE];
if( CV_IS_SEQ( array ))
{
contour = (CvSeq*)array;
if( !CV_IS_SEQ_POINT_SET( contour ))
CV_Error( CV_StsBadArg, "The passed sequence is not a valid contour" );
}
if( !moments )
CV_Error( CV_StsNullPtr, "" );
memset( moments, 0, sizeof(*moments));
if( !contour )
{
mat = cvGetMat( mat, &stub, &coi );
type = CV_MAT_TYPE( mat->type );
if( type == CV_32SC2 || type == CV_32FC2 )
{
contour = cvPointSeqFromMat(
CV_SEQ_KIND_CURVE | CV_SEQ_FLAG_CLOSED,
mat, &contourHeader, &block );
}
}
if( contour )
{
icvContourMoments( contour, moments );
return;
}
type = CV_MAT_TYPE( mat->type );
depth = CV_MAT_DEPTH( type );
cn = CV_MAT_CN( type );
cv::Size size = cvGetMatSize( mat );
if( cn > 1 && coi == 0 )
CV_Error( CV_StsBadArg, "Invalid image type" );
if( size.width <= 0 || size.height <= 0 )
return;
if( binary || depth == CV_8U )
func = momentsInTile<uchar, int, int>;
else if( depth == CV_16U )
func = momentsInTile<ushort, int, int64>;
else if( depth == CV_16S )
func = momentsInTile<short, int, int64>;
else if( depth == CV_32F )
func = momentsInTile<float, double, double>;
else if( depth == CV_64F )
func = momentsInTile<double, double, double>;
else
CV_Error( CV_StsUnsupportedFormat, "" );
cv::Mat src0(mat);
for( int y = 0; y < size.height; y += TILE_SIZE )
{
cv::Size tileSize;
tileSize.height = std::min(TILE_SIZE, size.height - y);
for( int x = 0; x < size.width; x += TILE_SIZE )
{
tileSize.width = std::min(TILE_SIZE, size.width - x);
cv::Mat src(src0, cv::Rect(x, y, tileSize.width, tileSize.height));
if( coi > 0 )
{
cv::Mat tmp(tileSize, depth, buf);
int pairs[] = {coi-1, 0};
cv::mixChannels(&src, 1, &tmp, 1, pairs, 1);
src = tmp;
}
if( binary )
{
cv::Mat tmp(tileSize, CV_8U, nzbuf);
cv::compare( src, 0, tmp, CV_CMP_NE );
src = tmp;
}
double mom[10];
func( src, mom );
if(binary)
{
double s = 1./255;
for( int k = 0; k < 10; k++ )
mom[k] *= s;
}
double xm = x * mom[0], ym = y * mom[0];
// accumulate moments computed in each tile
// + m00 ( = m00' )
moments->m00 += mom[0];
// + m10 ( = m10' + x*m00' )
moments->m10 += mom[1] + xm;
// + m01 ( = m01' + y*m00' )
moments->m01 += mom[2] + ym;
// + m20 ( = m20' + 2*x*m10' + x*x*m00' )
moments->m20 += mom[3] + x * (mom[1] * 2 + xm);
// + m11 ( = m11' + x*m01' + y*m10' + x*y*m00' )
moments->m11 += mom[4] + x * (mom[2] + ym) + y * mom[1];
// + m02 ( = m02' + 2*y*m01' + y*y*m00' )
moments->m02 += mom[5] + y * (mom[2] * 2 + ym);
// + m30 ( = m30' + 3*x*m20' + 3*x*x*m10' + x*x*x*m00' )
moments->m30 += mom[6] + x * (3. * mom[3] + x * (3. * mom[1] + xm));
// + m21 ( = m21' + x*(2*m11' + 2*y*m10' + x*m01' + x*y*m00') + y*m20')
moments->m21 += mom[7] + x * (2 * (mom[4] + y * mom[1]) + x * (mom[2] + ym)) + y * mom[3];
// + m12 ( = m12' + y*(2*m11' + 2*x*m01' + y*m10' + x*y*m00') + x*m02')
moments->m12 += mom[8] + y * (2 * (mom[4] + x * mom[2]) + y * (mom[1] + xm)) + x * mom[5];
// + m03 ( = m03' + 3*y*m02' + 3*y*y*m01' + y*y*y*m00' )
moments->m03 += mom[9] + y * (3. * mom[5] + y * (3. * mom[2] + ym));
}
}
icvCompleteMomentState( moments );
}
CV_IMPL void cvGetHuMoments( CvMoments * mState, CvHuMoments * HuState )
{
if( !mState || !HuState )
CV_Error( CV_StsNullPtr, "" );
double m00s = mState->inv_sqrt_m00, m00 = m00s * m00s, s2 = m00 * m00, s3 = s2 * m00s;
double nu20 = mState->mu20 * s2,
nu11 = mState->mu11 * s2,
nu02 = mState->mu02 * s2,
nu30 = mState->mu30 * s3,
nu21 = mState->mu21 * s3, nu12 = mState->mu12 * s3, nu03 = mState->mu03 * s3;
double t0 = nu30 + nu12;
double t1 = nu21 + nu03;
double q0 = t0 * t0, q1 = t1 * t1;
double n4 = 4 * nu11;
double s = nu20 + nu02;
double d = nu20 - nu02;
HuState->hu1 = s;
HuState->hu2 = d * d + n4 * nu11;
HuState->hu4 = q0 + q1;
HuState->hu6 = d * (q0 - q1) + n4 * t0 * t1;
t0 *= q0 - 3 * q1;
t1 *= 3 * q0 - q1;
q0 = nu30 - 3 * nu12;
q1 = 3 * nu21 - nu03;
HuState->hu3 = q0 * q0 + q1 * q1;
HuState->hu5 = q0 * t0 + q1 * t1;
HuState->hu7 = q1 * t0 - q0 * t1;
}
CV_IMPL double cvGetSpatialMoment( CvMoments * moments, int x_order, int y_order )
{
int order = x_order + y_order;
if( !moments )
CV_Error( CV_StsNullPtr, "" );
if( (x_order | y_order) < 0 || order > 3 )
CV_Error( CV_StsOutOfRange, "" );
return (&(moments->m00))[order + (order >> 1) + (order > 2) * 2 + y_order];
}
CV_IMPL double cvGetCentralMoment( CvMoments * moments, int x_order, int y_order )
{
int order = x_order + y_order;
if( !moments )
CV_Error( CV_StsNullPtr, "" );
if( (x_order | y_order) < 0 || order > 3 )
CV_Error( CV_StsOutOfRange, "" );
return order >= 2 ? (&(moments->m00))[4 + order * 3 + y_order] :
order == 0 ? moments->m00 : 0;
}
CV_IMPL double cvGetNormalizedCentralMoment( CvMoments * moments, int x_order, int y_order )
{
int order = x_order + y_order;
double mu = cvGetCentralMoment( moments, x_order, y_order );
double m00s = moments->inv_sqrt_m00;
while( --order >= 0 )
mu *= m00s;
return mu * m00s * m00s;
}
namespace cv
{
Moments::Moments()
{
m00 = m10 = m01 = m20 = m11 = m02 = m30 = m21 = m12 = m03 =
mu20 = mu11 = mu02 = mu30 = mu21 = mu12 = mu03 =
nu20 = nu11 = nu02 = nu30 = nu21 = nu12 = nu03 = 0.;
}
Moments::Moments( double _m00, double _m10, double _m01, double _m20, double _m11,
double _m02, double _m30, double _m21, double _m12, double _m03 )
{
m00 = _m00; m10 = _m10; m01 = _m01;
m20 = _m20; m11 = _m11; m02 = _m02;
m30 = _m30; m21 = _m21; m12 = _m12; m03 = _m03;
double cx = 0, cy = 0, inv_m00 = 0;
if( std::abs(m00) > DBL_EPSILON )
{
inv_m00 = 1./m00;
cx = m10*inv_m00; cy = m01*inv_m00;
}
mu20 = m20 - m10*cx;
mu11 = m11 - m10*cy;
mu02 = m02 - m01*cy;
mu30 = m30 - cx*(3*mu20 + cx*m10);
mu21 = m21 - cx*(2*mu11 + cx*m01) - cy*mu20;
mu12 = m12 - cy*(2*mu11 + cy*m10) - cx*mu02;
mu03 = m03 - cy*(3*mu02 + cy*m01);
double inv_sqrt_m00 = std::sqrt(std::abs(inv_m00));
double s2 = inv_m00*inv_m00, s3 = s2*inv_sqrt_m00;
nu20 = mu20*s2; nu11 = mu11*s2; nu02 = mu02*s2;
nu30 = mu30*s3; nu21 = mu21*s3; nu12 = mu12*s3; nu03 = mu03*s3;
}
Moments::Moments( const CvMoments& m )
{
*this = Moments(m.m00, m.m10, m.m01, m.m20, m.m11, m.m02, m.m30, m.m21, m.m12, m.m03);
}
Moments::operator CvMoments() const
{
CvMoments m;
m.m00 = m00; m.m10 = m10; m.m01 = m01;
m.m20 = m20; m.m11 = m11; m.m02 = m02;
m.m30 = m30; m.m21 = m21; m.m12 = m12; m.m03 = m03;
m.mu20 = mu20; m.mu11 = mu11; m.mu02 = mu02;
m.mu30 = mu30; m.mu21 = mu21; m.mu12 = mu12; m.mu03 = mu03;
double am00 = std::abs(m00);
m.inv_sqrt_m00 = am00 > DBL_EPSILON ? 1./std::sqrt(am00) : 0;
return m;
}
}
cv::Moments cv::moments( InputArray _array, bool binaryImage )
{
CvMoments om;
Mat arr = _array.getMat();
CvMat c_array = arr;
cvMoments(&c_array, &om, binaryImage);
return om;
}
void cv::HuMoments( const Moments& m, double hu[7] )
{
double t0 = m.nu30 + m.nu12;
double t1 = m.nu21 + m.nu03;
double q0 = t0 * t0, q1 = t1 * t1;
double n4 = 4 * m.nu11;
double s = m.nu20 + m.nu02;
double d = m.nu20 - m.nu02;
hu[0] = s;
hu[1] = d * d + n4 * m.nu11;
hu[3] = q0 + q1;
hu[5] = d * (q0 - q1) + n4 * t0 * t1;
t0 *= q0 - 3 * q1;
t1 *= 3 * q0 - q1;
q0 = m.nu30 - 3 * m.nu12;
q1 = 3 * m.nu21 - m.nu03;
hu[2] = q0 * q0 + q1 * q1;
hu[4] = q0 * t0 + q1 * t1;
hu[6] = q1 * t0 - q0 * t1;
}
void cv::HuMoments( const Moments& m, OutputArray _hu )
{
_hu.create(7, 1, CV_64F);
Mat hu = _hu.getMat();
CV_Assert( hu.isContinuous() );
HuMoments(m, (double*)hu.data);
}
/* End of file. */
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