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opencv/modules/video/src/ecc.cpp

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/*M///////////////////////////////////////////////////////////////////////////////////////
//
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#include "precomp.hpp"
/****************************************************************************************\
* Image Alignment (ECC algorithm) *
\****************************************************************************************/
using namespace cv;
static void image_jacobian_homo_ECC(const Mat& src1, const Mat& src2,
const Mat& src3, const Mat& src4,
const Mat& src5, Mat& dst)
{
CV_Assert(src1.size() == src2.size());
CV_Assert(src1.size() == src3.size());
CV_Assert(src1.size() == src4.size());
CV_Assert( src1.rows == dst.rows);
CV_Assert(dst.cols == (src1.cols*8));
CV_Assert(dst.type() == CV_32FC1);
CV_Assert(src5.isContinuous());
const float* hptr = src5.ptr<float>(0);
const float h0_ = hptr[0];
const float h1_ = hptr[3];
const float h2_ = hptr[6];
const float h3_ = hptr[1];
const float h4_ = hptr[4];
const float h5_ = hptr[7];
const float h6_ = hptr[2];
const float h7_ = hptr[5];
const int w = src1.cols;
//create denominator for all points as a block
Mat den_ = src3*h2_ + src4*h5_ + 1.0;//check the time of this! otherwise use addWeighted
//create projected points
Mat hatX_ = -src3*h0_ - src4*h3_ - h6_;
divide(hatX_, den_, hatX_);
Mat hatY_ = -src3*h1_ - src4*h4_ - h7_;
divide(hatY_, den_, hatY_);
//instead of dividing each block with den,
//just pre-devide the block of gradients (it's more efficient)
Mat src1Divided_;
Mat src2Divided_;
divide(src1, den_, src1Divided_);
divide(src2, den_, src2Divided_);
//compute Jacobian blocks (8 blocks)
dst.colRange(0, w) = src1Divided_.mul(src3);//1
dst.colRange(w,2*w) = src2Divided_.mul(src3);//2
Mat temp_ = (hatX_.mul(src1Divided_)+hatY_.mul(src2Divided_));
dst.colRange(2*w,3*w) = temp_.mul(src3);//3
hatX_.release();
hatY_.release();
dst.colRange(3*w, 4*w) = src1Divided_.mul(src4);//4
dst.colRange(4*w, 5*w) = src2Divided_.mul(src4);//5
dst.colRange(5*w, 6*w) = temp_.mul(src4);//6
src1Divided_.copyTo(dst.colRange(6*w, 7*w));//7
src2Divided_.copyTo(dst.colRange(7*w, 8*w));//8
}
static void image_jacobian_euclidean_ECC(const Mat& src1, const Mat& src2,
const Mat& src3, const Mat& src4,
const Mat& src5, Mat& dst)
{
CV_Assert( src1.size()==src2.size());
CV_Assert( src1.size()==src3.size());
CV_Assert( src1.size()==src4.size());
CV_Assert( src1.rows == dst.rows);
CV_Assert(dst.cols == (src1.cols*3));
CV_Assert(dst.type() == CV_32FC1);
CV_Assert(src5.isContinuous());
const float* hptr = src5.ptr<float>(0);
const float h0 = hptr[0];//cos(theta)
const float h1 = hptr[3];//sin(theta)
const int w = src1.cols;
//create -sin(theta)*X -cos(theta)*Y for all points as a block -> hatX
Mat hatX = -(src3*h1) - (src4*h0);
//create cos(theta)*X -sin(theta)*Y for all points as a block -> hatY
Mat hatY = (src3*h0) - (src4*h1);
//compute Jacobian blocks (3 blocks)
dst.colRange(0, w) = (src1.mul(hatX))+(src2.mul(hatY));//1
src1.copyTo(dst.colRange(w, 2*w));//2
src2.copyTo(dst.colRange(2*w, 3*w));//3
}
static void image_jacobian_affine_ECC(const Mat& src1, const Mat& src2,
const Mat& src3, const Mat& src4,
Mat& dst)
{
CV_Assert(src1.size() == src2.size());
CV_Assert(src1.size() == src3.size());
CV_Assert(src1.size() == src4.size());
CV_Assert(src1.rows == dst.rows);
CV_Assert(dst.cols == (6*src1.cols));
CV_Assert(dst.type() == CV_32FC1);
const int w = src1.cols;
//compute Jacobian blocks (6 blocks)
dst.colRange(0,w) = src1.mul(src3);//1
dst.colRange(w,2*w) = src2.mul(src3);//2
dst.colRange(2*w,3*w) = src1.mul(src4);//3
dst.colRange(3*w,4*w) = src2.mul(src4);//4
src1.copyTo(dst.colRange(4*w,5*w));//5
src2.copyTo(dst.colRange(5*w,6*w));//6
}
static void image_jacobian_translation_ECC(const Mat& src1, const Mat& src2, Mat& dst)
{
CV_Assert( src1.size()==src2.size());
CV_Assert( src1.rows == dst.rows);
CV_Assert(dst.cols == (src1.cols*2));
CV_Assert(dst.type() == CV_32FC1);
const int w = src1.cols;
//compute Jacobian blocks (2 blocks)
src1.copyTo(dst.colRange(0, w));
src2.copyTo(dst.colRange(w, 2*w));
}
static void project_onto_jacobian_ECC(const Mat& src1, const Mat& src2, Mat& dst)
{
/* this functions is used for two types of projections. If src1.cols ==src.cols
it does a blockwise multiplication (like in the outer product of vectors)
of the blocks in matrices src1 and src2 and dst
has size (number_of_blcks x number_of_blocks), otherwise dst is a vector of size
(number_of_blocks x 1) since src2 is "multiplied"(dot) with each block of src1.
The number_of_blocks is equal to the number of parameters we are lloking for
(i.e. rtanslation:2, euclidean: 3, affine: 6, homography: 8)
*/
CV_Assert(src1.rows == src2.rows);
CV_Assert((src1.cols % src2.cols) == 0);
int w;
float* dstPtr = dst.ptr<float>(0);
if (src1.cols !=src2.cols){//dst.cols==1
w = src2.cols;
for (int i=0; i<dst.rows; i++){
dstPtr[i] = (float) src2.dot(src1.colRange(i*w,(i+1)*w));
}
}
else {
CV_Assert(dst.cols == dst.rows); //dst is square (and symmetric)
w = src2.cols/dst.cols;
Mat mat;
for (int i=0; i<dst.rows; i++){
mat = Mat(src1.colRange(i*w, (i+1)*w));
dstPtr[i*(dst.rows+1)] = (float) pow(norm(mat),2); //diagonal elements
for (int j=i+1; j<dst.cols; j++){ //j starts from i+1
dstPtr[i*dst.cols+j] = (float) mat.dot(src2.colRange(j*w, (j+1)*w));
dstPtr[j*dst.cols+i] = dstPtr[i*dst.cols+j]; //due to symmetry
}
}
}
}
static void update_warping_matrix_ECC (Mat& map_matrix, const Mat& update, const int motionType)
{
CV_Assert (map_matrix.type() == CV_32FC1);
CV_Assert (update.type() == CV_32FC1);
CV_Assert (motionType == MOTION_TRANSLATION || motionType == MOTION_EUCLIDEAN ||
motionType == MOTION_AFFINE || motionType == MOTION_HOMOGRAPHY);
if (motionType == MOTION_HOMOGRAPHY)
CV_Assert (map_matrix.rows == 3 && update.rows == 8);
else if (motionType == MOTION_AFFINE)
CV_Assert(map_matrix.rows == 2 && update.rows == 6);
else if (motionType == MOTION_EUCLIDEAN)
CV_Assert (map_matrix.rows == 2 && update.rows == 3);
else
CV_Assert (map_matrix.rows == 2 && update.rows == 2);
CV_Assert (update.cols == 1);
CV_Assert( map_matrix.isContinuous());
CV_Assert( update.isContinuous() );
float* mapPtr = map_matrix.ptr<float>(0);
const float* updatePtr = update.ptr<float>(0);
if (motionType == MOTION_TRANSLATION){
mapPtr[2] += updatePtr[0];
mapPtr[5] += updatePtr[1];
}
if (motionType == MOTION_AFFINE) {
mapPtr[0] += updatePtr[0];
mapPtr[3] += updatePtr[1];
mapPtr[1] += updatePtr[2];
mapPtr[4] += updatePtr[3];
mapPtr[2] += updatePtr[4];
mapPtr[5] += updatePtr[5];
}
if (motionType == MOTION_HOMOGRAPHY) {
mapPtr[0] += updatePtr[0];
mapPtr[3] += updatePtr[1];
mapPtr[6] += updatePtr[2];
mapPtr[1] += updatePtr[3];
mapPtr[4] += updatePtr[4];
mapPtr[7] += updatePtr[5];
mapPtr[2] += updatePtr[6];
mapPtr[5] += updatePtr[7];
}
if (motionType == MOTION_EUCLIDEAN) {
double new_theta = updatePtr[0];
new_theta += asin(mapPtr[3]);
mapPtr[2] += updatePtr[1];
mapPtr[5] += updatePtr[2];
mapPtr[0] = mapPtr[4] = (float) cos(new_theta);
mapPtr[3] = (float) sin(new_theta);
mapPtr[1] = -mapPtr[3];
}
}
double cv::findTransformECC(InputArray templateImage,
InputArray inputImage,
InputOutputArray warpMatrix,
int motionType,
TermCriteria criteria,
InputArray inputMask)
{
Mat src = templateImage.getMat();//template iamge
Mat dst = inputImage.getMat(); //input image (to be warped)
Mat map = warpMatrix.getMat(); //warp (transformation)
CV_Assert(!src.empty());
CV_Assert(!dst.empty());
if( ! (src.type()==dst.type()))
CV_Error( Error::StsUnmatchedFormats, "Both input images must have the same data type" );
//accept only 1-channel images
if( src.type() != CV_8UC1 && src.type()!= CV_32FC1)
CV_Error( Error::StsUnsupportedFormat, "Images must have 8uC1 or 32fC1 type");
if( map.type() != CV_32FC1)
CV_Error( Error::StsUnsupportedFormat, "warpMatrix must be single-channel floating-point matrix");
CV_Assert (map.cols == 3);
CV_Assert (map.rows == 2 || map.rows ==3);
CV_Assert (motionType == MOTION_AFFINE || motionType == MOTION_HOMOGRAPHY ||
motionType == MOTION_EUCLIDEAN || motionType == MOTION_TRANSLATION);
if (motionType == MOTION_HOMOGRAPHY){
CV_Assert (map.rows ==3);
}
CV_Assert (criteria.type & TermCriteria::COUNT || criteria.type & TermCriteria::EPS);
const int numberOfIterations = (criteria.type & TermCriteria::COUNT) ? criteria.maxCount : 200;
const double termination_eps = (criteria.type & TermCriteria::EPS) ? criteria.epsilon : -1;
int paramTemp = 6;//default: affine
switch (motionType){
case MOTION_TRANSLATION:
paramTemp = 2;
break;
case MOTION_EUCLIDEAN:
paramTemp = 3;
break;
case MOTION_HOMOGRAPHY:
paramTemp = 8;
break;
}
const int numberOfParameters = paramTemp;
const int ws = src.cols;
const int hs = src.rows;
const int wd = dst.cols;
const int hd = dst.rows;
Mat Xcoord = Mat(1, ws, CV_32F);
Mat Ycoord = Mat(hs, 1, CV_32F);
Mat Xgrid = Mat(hs, ws, CV_32F);
Mat Ygrid = Mat(hs, ws, CV_32F);
float* XcoPtr = Xcoord.ptr<float>(0);
float* YcoPtr = Ycoord.ptr<float>(0);
int j;
for (j=0; j<ws; j++)
XcoPtr[j] = (float) j;
for (j=0; j<hs; j++)
YcoPtr[j] = (float) j;
repeat(Xcoord, hs, 1, Xgrid);
repeat(Ycoord, 1, ws, Ygrid);
Xcoord.release();
Ycoord.release();
Mat templateZM = Mat(hs, ws, CV_32F);// to store the (smoothed)zero-mean version of template
Mat templateFloat = Mat(hs, ws, CV_32F);// to store the (smoothed) template
Mat imageFloat = Mat(hd, wd, CV_32F);// to store the (smoothed) input image
Mat imageWarped = Mat(hs, ws, CV_32F);// to store the warped zero-mean input image
Mat imageMask = Mat(hs, ws, CV_8U); //to store the final mask
Mat inputMaskMat = inputMask.getMat();
//to use it for mask warping
Mat preMask;
if(inputMask.empty())
preMask = Mat::ones(hd, wd, CV_8U);
else
threshold(inputMask, preMask, 0, 1, THRESH_BINARY);
//gaussian filtering is optional
src.convertTo(templateFloat, templateFloat.type());
GaussianBlur(templateFloat, templateFloat, Size(5, 5), 0, 0);
Mat preMaskFloat;
preMask.convertTo(preMaskFloat, CV_32F);
GaussianBlur(preMaskFloat, preMaskFloat, Size(5, 5), 0, 0);
// Change threshold.
preMaskFloat *= (0.5/0.95);
// Rounding conversion.
preMaskFloat.convertTo(preMask, preMask.type());
preMask.convertTo(preMaskFloat, preMaskFloat.type());
dst.convertTo(imageFloat, imageFloat.type());
GaussianBlur(imageFloat, imageFloat, Size(5, 5), 0, 0);
// needed matrices for gradients and warped gradients
Mat gradientX = Mat::zeros(hd, wd, CV_32FC1);
Mat gradientY = Mat::zeros(hd, wd, CV_32FC1);
Mat gradientXWarped = Mat(hs, ws, CV_32FC1);
Mat gradientYWarped = Mat(hs, ws, CV_32FC1);
// calculate first order image derivatives
Matx13f dx(-0.5f, 0.0f, 0.5f);
filter2D(imageFloat, gradientX, -1, dx);
filter2D(imageFloat, gradientY, -1, dx.t());
gradientX = gradientX.mul(preMaskFloat);
gradientY = gradientY.mul(preMaskFloat);
// matrices needed for solving linear equation system for maximizing ECC
Mat jacobian = Mat(hs, ws*numberOfParameters, CV_32F);
Mat hessian = Mat(numberOfParameters, numberOfParameters, CV_32F);
Mat hessianInv = Mat(numberOfParameters, numberOfParameters, CV_32F);
Mat imageProjection = Mat(numberOfParameters, 1, CV_32F);
Mat templateProjection = Mat(numberOfParameters, 1, CV_32F);
Mat imageProjectionHessian = Mat(numberOfParameters, 1, CV_32F);
Mat errorProjection = Mat(numberOfParameters, 1, CV_32F);
Mat deltaP = Mat(numberOfParameters, 1, CV_32F);//transformation parameter correction
Mat error = Mat(hs, ws, CV_32F);//error as 2D matrix
const int imageFlags = INTER_LINEAR + WARP_INVERSE_MAP;
const int maskFlags = INTER_NEAREST + WARP_INVERSE_MAP;
// iteratively update map_matrix
double rho = -1;
double last_rho = - termination_eps;
for (int i = 1; (i <= numberOfIterations) && (fabs(rho-last_rho)>= termination_eps); i++)
{
// warp-back portion of the inputImage and gradients to the coordinate space of the templateImage
if (motionType != MOTION_HOMOGRAPHY)
{
warpAffine(imageFloat, imageWarped, map, imageWarped.size(), imageFlags);
warpAffine(gradientX, gradientXWarped, map, gradientXWarped.size(), imageFlags);
warpAffine(gradientY, gradientYWarped, map, gradientYWarped.size(), imageFlags);
warpAffine(preMask, imageMask, map, imageMask.size(), maskFlags);
}
else
{
warpPerspective(imageFloat, imageWarped, map, imageWarped.size(), imageFlags);
warpPerspective(gradientX, gradientXWarped, map, gradientXWarped.size(), imageFlags);
warpPerspective(gradientY, gradientYWarped, map, gradientYWarped.size(), imageFlags);
warpPerspective(preMask, imageMask, map, imageMask.size(), maskFlags);
}
Scalar imgMean, imgStd, tmpMean, tmpStd;
meanStdDev(imageWarped, imgMean, imgStd, imageMask);
meanStdDev(templateFloat, tmpMean, tmpStd, imageMask);
subtract(imageWarped, imgMean, imageWarped, imageMask);//zero-mean input
templateZM = Mat::zeros(templateZM.rows, templateZM.cols, templateZM.type());
subtract(templateFloat, tmpMean, templateZM, imageMask);//zero-mean template
const double tmpNorm = std::sqrt(countNonZero(imageMask)*(tmpStd.val[0])*(tmpStd.val[0]));
const double imgNorm = std::sqrt(countNonZero(imageMask)*(imgStd.val[0])*(imgStd.val[0]));
// calculate jacobian of image wrt parameters
switch (motionType){
case MOTION_AFFINE:
image_jacobian_affine_ECC(gradientXWarped, gradientYWarped, Xgrid, Ygrid, jacobian);
break;
case MOTION_HOMOGRAPHY:
image_jacobian_homo_ECC(gradientXWarped, gradientYWarped, Xgrid, Ygrid, map, jacobian);
break;
case MOTION_TRANSLATION:
image_jacobian_translation_ECC(gradientXWarped, gradientYWarped, jacobian);
break;
case MOTION_EUCLIDEAN:
image_jacobian_euclidean_ECC(gradientXWarped, gradientYWarped, Xgrid, Ygrid, map, jacobian);
break;
}
// calculate Hessian and its inverse
project_onto_jacobian_ECC(jacobian, jacobian, hessian);
hessianInv = hessian.inv();
const double correlation = templateZM.dot(imageWarped);
// calculate enhanced correlation coefficiont (ECC)->rho
last_rho = rho;
rho = correlation/(imgNorm*tmpNorm);
if (cvIsNaN(rho)) {
CV_Error(Error::StsNoConv, "NaN encountered.");
}
// project images into jacobian
project_onto_jacobian_ECC( jacobian, imageWarped, imageProjection);
project_onto_jacobian_ECC(jacobian, templateZM, templateProjection);
// calculate the parameter lambda to account for illumination variation
imageProjectionHessian = hessianInv*imageProjection;
const double lambda_n = (imgNorm*imgNorm) - imageProjection.dot(imageProjectionHessian);
const double lambda_d = correlation - templateProjection.dot(imageProjectionHessian);
if (lambda_d <= 0.0)
{
rho = -1;
CV_Error(Error::StsNoConv, "The algorithm stopped before its convergence. The correlation is going to be minimized. Images may be uncorrelated or non-overlapped");
}
const double lambda = (lambda_n/lambda_d);
// estimate the update step delta_p
error = lambda*templateZM - imageWarped;
project_onto_jacobian_ECC(jacobian, error, errorProjection);
deltaP = hessianInv * errorProjection;
// update warping matrix
update_warping_matrix_ECC( map, deltaP, motionType);
}
// return final correlation coefficient
return rho;
}
/* End of file. */
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