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#include "precomp.hpp"
#include "opencv2/reg/mappergradaffine.hpp"
#include "opencv2/reg/mapaffine.hpp"

namespace cv {
namespace reg {


////////////////////////////////////////////////////////////////////////////////////////////////////
MapperGradAffine::MapperGradAffine(void)
{
}


////////////////////////////////////////////////////////////////////////////////////////////////////
MapperGradAffine::~MapperGradAffine(void)
{
}


////////////////////////////////////////////////////////////////////////////////////////////////////
void MapperGradAffine::calculate(
    const cv::Mat& img1, const cv::Mat& image2, cv::Ptr<Map>& res) const
{
    Mat gradx, grady, imgDiff;
    Mat img2;

    CV_DbgAssert(img1.size() == image2.size());
    CV_DbgAssert(img1.channels() == image2.channels());
    CV_DbgAssert(img1.channels() == 1 || img1.channels() == 3);

    if(!res.empty()) {
        // We have initial values for the registration: we move img2 to that initial reference
        res->inverseWarp(image2, img2);
    } else {
        img2 = image2;
    }

    // Get gradient in all channels
    gradient(img1, img2, gradx, grady, imgDiff);

    // Matrices with reference frame coordinates
    Mat grid_r, grid_c;
    grid(img1, grid_r, grid_c);

    // Calculate parameters using least squares
    Matx<double, 6, 6> A;
    Vec<double, 6> b;
    // For each value in A, all the matrix elements are added and then the channels are also added,
    // so we have two calls to "sum". The result can be found in the first element of the final
    // Scalar object.
    Mat xIx = grid_c.mul(gradx);
    Mat xIy = grid_c.mul(grady);
    Mat yIx = grid_r.mul(gradx);
    Mat yIy = grid_r.mul(grady);
    Mat Ix2 = gradx.mul(gradx);
    Mat Iy2 = grady.mul(grady);
    Mat xy = grid_c.mul(grid_r);
    Mat IxIy = gradx.mul(grady);
    A(0, 0) = sum(sum(sqr(xIx)))[0];
    A(0, 1) = sum(sum(xy.mul(Ix2)))[0];
    A(0, 2) = sum(sum(grid_c.mul(Ix2)))[0];
    A(0, 3) = sum(sum(sqr(grid_c).mul(IxIy)))[0];
    A(0, 4) = sum(sum(xy.mul(IxIy)))[0];
    A(0, 5) = sum(sum(grid_c.mul(IxIy)))[0];
    A(1, 1) = sum(sum(sqr(yIx)))[0];
    A(1, 2) = sum(sum(grid_r.mul(Ix2)))[0];
    A(1, 3) = A(0, 4);
    A(1, 4) = sum(sum(sqr(grid_r).mul(IxIy)))[0];
    A(1, 5) = sum(sum(grid_r.mul(IxIy)))[0];
    A(2, 2) = sum(sum(Ix2))[0];
    A(2, 3) = A(0, 5);
    A(2, 4) = A(1, 5);
    A(2, 5) = sum(sum(IxIy))[0];
    A(3, 3) = sum(sum(sqr(xIy)))[0];
    A(3, 4) = sum(sum(xy.mul(Iy2)))[0];
    A(3, 5) = sum(sum(grid_c.mul(Iy2)))[0];
    A(4, 4) = sum(sum(sqr(yIy)))[0];
    A(4, 5) = sum(sum(grid_r.mul(Iy2)))[0];
    A(5, 5) = sum(sum(Iy2))[0];
    // Lower half values (A is symmetric)
    A(1, 0) = A(0, 1);
    A(2, 0) = A(0, 2);
    A(2, 1) = A(1, 2);
    A(3, 0) = A(0, 3);
    A(3, 1) = A(1, 3);
    A(3, 2) = A(2, 3);
    A(4, 0) = A(0, 4);
    A(4, 1) = A(1, 4);
    A(4, 2) = A(2, 4);
    A(4, 3) = A(3, 4);
    A(5, 0) = A(0, 5);
    A(5, 1) = A(1, 5);
    A(5, 2) = A(2, 5);
    A(5, 3) = A(3, 5);
    A(5, 4) = A(4, 5);

    // Calculation of b
    b(0) = -sum(sum(imgDiff.mul(xIx)))[0];
    b(1) = -sum(sum(imgDiff.mul(yIx)))[0];
    b(2) = -sum(sum(imgDiff.mul(gradx)))[0];
    b(3) = -sum(sum(imgDiff.mul(xIy)))[0];
    b(4) = -sum(sum(imgDiff.mul(yIy)))[0];
    b(5) = -sum(sum(imgDiff.mul(grady)))[0];

    // Calculate affine transformation. We use Cholesky decomposition, as A is symmetric.
    Vec<double, 6> k = A.inv(DECOMP_CHOLESKY)*b;

    Matx<double, 2, 2> linTr(k(0) + 1., k(1), k(3), k(4) + 1.);
    Vec<double, 2> shift(k(2), k(5));
    if(res.empty()) {
        res = Ptr<Map>(new MapAffine(linTr, shift));
    } else {
        MapAffine newTr(linTr, shift);
        res->compose(newTr);
   }
}

////////////////////////////////////////////////////////////////////////////////////////////////////
cv::Ptr<Map> MapperGradAffine::getMap(void) const
{
    return cv::Ptr<Map>(new MapAffine());
}


}}  // namespace cv::reg
