OpenCV/opencv_contrib/modules/ximgproc/src/estimated_covariance.cpp

/*
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copy or use the software.


                          License Agreement
               For Open Source Computer Vision Library
                       (3-clause BSD License)

Copyright (C) 2000-2015, Intel Corporation, all rights reserved.
Copyright (C) 2009-2011, Willow Garage Inc., all rights reserved.
Copyright (C) 2009-2015, NVIDIA Corporation, all rights reserved.
Copyright (C) 2010-2013, Advanced Micro Devices, Inc., all rights reserved.
Copyright (C) 2015, OpenCV Foundation, all rights reserved.
Copyright (C) 2015, Itseez Inc., all rights reserved.
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are permitted provided that the following conditions are met:

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    this list of conditions and the following disclaimer.

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    this list of conditions and the following disclaimer in the documentation
    and/or other materials provided with the distribution.

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    may be used to endorse or promote products derived from this software
    without specific prior written permission.

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the use of this software, even if advised of the possibility of such damage.

Algorithmic details of this algorithm can be found at:
 * O. Green, Y. Birk, "A Computationally Efficient Algorithm for the 2D Covariance Method", ACM/IEEE International Conference on High Performance Computing, Networking, Storage and Analysis, Denver, Colorado, 2013
A previous and less efficient version of the algorithm can be found:
 * O. Green, L. David, A. Galperin, Y. Birk, "Efficient parallel computation of the estimated covariance matrix", arXiv, 2013


*/

#include "precomp.hpp"

using namespace cv;
using namespace std;


namespace cv{
namespace ximgproc{

class EstimateCovariance{

public:
    EstimateCovariance(int pr_, int pc_);
    ~EstimateCovariance();

    void computeEstimateCovariance(Mat inputData,Mat outputData);
    int combinationCount();

private:
    typedef struct {
        int mult1r;
        int mult1c;
        int mult2r;
        int mult2c;
        int type2; // 0 - for the first P*P. 1 - for the next (P-1)(P-1)
        int id;
    } Combination;

    void initInternalDataStructures();
    void buildCombinationsTable();

    void iterateCombinations(Mat inputData,Mat outputData);
    void computeOneCombination(int comb_id, Mat inputData , Mat outputData,
        Mat outputVector,std::vector<int> finalMatPosR, std::vector<int> finalMatPosC);

    inline void complexSubtract(std::complex<float>& src, std::complex<float>& dst){dst-=src;}
    inline void complexAdd(std::complex<float>& src, std::complex<float>& dst){dst+=src;}
    inline void complexConjMulAndAdd(std::complex<float>& a, std::complex<float>& b,
            std::complex<float>& dst){dst += a*b;}
    inline void complexConjMul(std::complex<float>& a, std::complex<float>& b,
            std::complex<float>& dst){dst = a*b;}

private:
    int nr;
    int nc;
    int pr;
    int pc;

    std::vector<Combination> combinationsTable;
};



EstimateCovariance::EstimateCovariance(int pr_, int pc_){
    pr=pr_; pc=pc_;
}

EstimateCovariance::~EstimateCovariance(){

}

void EstimateCovariance::initInternalDataStructures(){
    int combCount = combinationCount();
    combinationsTable.resize(combCount);
    buildCombinationsTable();
}

int EstimateCovariance::combinationCount(){
    return  (pr*pc+(pr-1)*(pc-1));
}

void EstimateCovariance::buildCombinationsTable()
{
    int idx_row,idx_col;
    int comb_idx = 0;
    Combination comb;

    // The first element of the product is [0,0] and the second is to down and to the right of it.
    for (idx_col=0; idx_col<pc; ++idx_col)  {
        for (idx_row=0; idx_row<pr; ++idx_row)      {
            comb.mult1r=0;
            comb.mult1c=0;
            comb.mult2r=idx_row;
            comb.mult2c=idx_col;
            comb.type2 = 0;
            comb.id = comb_idx;
            memcpy(&combinationsTable[comb_idx++], &comb, sizeof(Combination));
        }
    }

    // The first element is on the top right, and the second element is to the left and down of it.
    for (idx_row=1; idx_row<pr; ++idx_row)  {
        for (idx_col=1; idx_col<pc; ++idx_col)      {
            comb.mult1r=idx_row;
            comb.mult1c=0;
            comb.mult2r=0;
            comb.mult2c=idx_col;

            comb.type2 = 1;
            comb.id = comb_idx;
            memcpy(&combinationsTable[comb_idx++], &comb, sizeof(Combination));
        }
    }
}

void EstimateCovariance::computeEstimateCovariance(Mat inputData,Mat outputData){
    initInternalDataStructures();
    nr=inputData.rows;
    nc=inputData.cols;

    iterateCombinations(inputData,outputData);
}


void EstimateCovariance::iterateCombinations(Mat inputData,Mat outputData)
{
    Mat outputVector(pr*pc,1,  DataType<std::complex<float> >::type);

    std::vector<int> finalMatPosR(pr*pc,0);
    std::vector<int> finalMatPosC(pr*pc,0);
    int combs=combinationCount();
    for (int idx=0; idx<combs; idx++){
        outputVector.setTo(Scalar(0,0));
        for (unsigned x=0; x<finalMatPosR.size(); x++)
            finalMatPosR[x]=0;
        for (unsigned x=0; x<finalMatPosC.size(); x++)
            finalMatPosC[x]=0;
        computeOneCombination(idx++, inputData, outputData,
                outputVector,finalMatPosR, finalMatPosC);
    }
}

void EstimateCovariance::computeOneCombination(int comb_id,Mat inputData, Mat outputData,
            Mat outputVector,std::vector<int> finalMatPosR, std::vector<int> finalMatPosC)
{
    Combination* comb = &combinationsTable[comb_id];
    int type2 = comb->type2;
    int deltaR = (int)abs((int)(comb->mult1r-comb->mult2r));
    int deltaC = (int)abs((int)(comb->mult1c-comb->mult2c));
    int numElementsInBlock = pr-abs(deltaR);
    int numBlocks = pc-deltaC;
    const int DR= nr-pr;
    const int DC= nc-pc;

    int elementC=0;
    std::complex<float> temp_res = std::complex<float>(0,0);
    int i,j,r,c;

    if (!type2) {
        // Computing the first index of the combination.
        // This index is made up
        for(i=0; i<=( DR); i++) {
            int iPdr=i+deltaR;
            for(j=0; j<= (DC); j++) {
                int jPdc = j+deltaC;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(i,j), inputData.at<std::complex<float> >(iPdr,jPdc), temp_res);
            }
        }
    }else{
        // Computing the first index of the combination.
        for(i=0; i<=( DR); i++) {
            int iPdr=i+deltaR;
            for(j=0; j<= (DC); j++) {
                int jPdc = j+deltaC;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(iPdr,j), inputData.at<std::complex<float> >(i,jPdc), temp_res);
            }
        }
    }
    outputVector.at<std::complex<float> >(0,0) = temp_res;

    // Checking if the first element belongs to the first set of combinatons.
    // The combination that the first element is above the second.
    if (!type2) {
        finalMatPosR[0]=0;
        finalMatPosC[0]=pr*deltaC+deltaR;
        elementC++;
    }else{
        finalMatPosR[0]=deltaR;
        finalMatPosC[0]=pr*deltaC;
        elementC++;
    }

    for(r=1;r<(pr-deltaR);r++){
        std::complex<float> newRowSum = std::complex<float>(0,0),oldRowSum = std::complex<float>(0,0);
        std::complex<float> addRows  = std::complex<float>(0,0);

        int rM1 = r-1;
        int k = DR+1 + rM1;
        int kPdr = k+deltaR;
        int rM1Pdr = rM1 + deltaR;
        int cPdc;

        if (!type2) {
            for(c=0;c<=(DC); c++){
                cPdc = c+deltaC;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(k,c),inputData.at<std::complex<float> >(kPdr,cPdc),newRowSum);
                complexConjMulAndAdd(inputData.at<std::complex<float> >(rM1,c),inputData.at<std::complex<float> >(rM1Pdr,cPdc),oldRowSum);
            }
        }else{
            for(c=0;c<=(DC); c++){
                cPdc = c+deltaC;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(kPdr,c),inputData.at<std::complex<float> >(k,cPdc),newRowSum);
                complexConjMulAndAdd(inputData.at<std::complex<float> >(rM1Pdr,c),inputData.at<std::complex<float> >(rM1,cPdc),oldRowSum);
            }
        }
        complexAdd(newRowSum,addRows);
        complexSubtract(oldRowSum,addRows);
        complexAdd(outputVector.at<std::complex<float> >(rM1,0),outputVector.at<std::complex<float> >(r,0));
        complexAdd(addRows,outputVector.at<std::complex<float> >(r,0));

        finalMatPosR[elementC]=finalMatPosR[elementC-1]+1;;
        finalMatPosC[elementC]=finalMatPosC[elementC-1]+1;
        elementC++;
    }

    for(c=1; c<numBlocks; c++)  {
        std::complex<float> newColSum = std::complex<float>(0,0),oldColSum = std::complex<float>(0,0);
        std::complex<float> addCols  = std::complex<float>(0,0);

        // Index arithmetic
        int cM1 = c-1;
        int dcPc = DC+c;
        int q = DC+1 + cM1;
        int cM1PdeltaC = cM1 + deltaC;
        int dcPcPdeltaC = dcPc+deltaC;

        if (!type2) {
            for(r=0;r<=(DR); r++){
                int rPdr = r+deltaR;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(r,q),inputData.at<std::complex<float> >(rPdr,q+deltaC),newColSum);
                complexConjMulAndAdd(inputData.at<std::complex<float> >(r,cM1),inputData.at<std::complex<float> >(rPdr,cM1+deltaC),oldColSum);
            }
        }else{
            for(r=0;r<=(DR); r++){
                int rPdr = r+deltaR;
                complexConjMulAndAdd(inputData.at<std::complex<float> >(rPdr,q),inputData.at<std::complex<float> >(r,q+deltaC),newColSum);
                complexConjMulAndAdd(inputData.at<std::complex<float> >(rPdr,cM1),inputData.at<std::complex<float> >(r,cM1+deltaC),oldColSum);
            }
        }
        complexAdd(newColSum,addCols);
        complexSubtract(oldColSum,addCols);
        complexAdd(outputVector.at<std::complex<float> >((c-1)*numElementsInBlock,0),outputVector.at<std::complex<float> >(c*numElementsInBlock,0));
        complexAdd(addCols,outputVector.at<std::complex<float> >(c*numElementsInBlock,0));

        finalMatPosR[elementC]=finalMatPosR[elementC-numElementsInBlock]+pr;
        finalMatPosC[elementC]=finalMatPosC[elementC-numElementsInBlock]+pr;
        elementC++;

        for(r=1; r<numElementsInBlock; r++) {
            std::complex<float> w = std::complex<float>(0,0),x = std::complex<float>(0,0),
                y = std::complex<float>(0,0),z = std::complex<float>(0,0),deltaRowSum = std::complex<float>(0,0);
            std::complex<float> tempRes = std::complex<float>(0,0);
            // Index arithmetic
            int rM1 = r-1;
            int drPr = DR+r;
            int rM1PdeltaR = rM1 + deltaR;
            int drPrPdeltaR = drPr+deltaR;

            if (!type2) {
                complexConjMul(inputData.at<std::complex<float> >(rM1,cM1),inputData.at<std::complex<float> >(rM1PdeltaR,cM1PdeltaC),w);
                complexConjMul(inputData.at<std::complex<float> >(rM1,dcPc),inputData.at<std::complex<float> >(rM1PdeltaR,dcPcPdeltaC),x);
                complexConjMul(inputData.at<std::complex<float> >(drPr,cM1),inputData.at<std::complex<float> >(drPrPdeltaR,cM1PdeltaC),y);
                complexConjMul(inputData.at<std::complex<float> >(drPr,dcPc),inputData.at<std::complex<float> >(drPrPdeltaR,dcPcPdeltaC),z);
            }else{
                complexConjMul(inputData.at<std::complex<float> >(rM1PdeltaR,cM1),inputData.at<std::complex<float> >(rM1,cM1PdeltaC),w);
                complexConjMul(inputData.at<std::complex<float> >(rM1PdeltaR,dcPc),inputData.at<std::complex<float> >(rM1,dcPcPdeltaC),x);
                complexConjMul(inputData.at<std::complex<float> >(drPrPdeltaR,cM1),inputData.at<std::complex<float> >(drPr,cM1PdeltaC),y);
                complexConjMul(inputData.at<std::complex<float> >(drPrPdeltaR,dcPc),inputData.at<std::complex<float> >(drPr,dcPcPdeltaC),z);
            }
            complexAdd(w,tempRes);
            complexSubtract(x,tempRes);
            complexSubtract(y,tempRes);
            complexAdd(z,tempRes);

            complexAdd(outputVector.at<std::complex<float> >((c-1)*numElementsInBlock + r,0),deltaRowSum);
            complexSubtract(outputVector.at<std::complex<float> >((c-1)*numElementsInBlock+ rM1,0),deltaRowSum);

            complexAdd(deltaRowSum,tempRes);
            complexAdd(outputVector.at<std::complex<float> >(c*numElementsInBlock+rM1,0),tempRes);
            complexAdd(tempRes,outputVector.at<std::complex<float> >(c*numElementsInBlock+r,0));

            finalMatPosR[elementC]=finalMatPosR[elementC-1]+1;
            finalMatPosC[elementC]=finalMatPosC[elementC-1]+1;
            elementC++;
        }
    }

    for(i=0; i<numElementsInBlock*numBlocks; i++){
        outputData.at<std::complex<float> >(finalMatPosR[i],finalMatPosC[i])=outputVector.at<std::complex<float> >(i,0);
    }
}



void covarianceEstimation(InputArray input_, OutputArray output_,int windowRows, int windowCols){

    CV_Assert( input_.channels() <= 2);   // Does not take color images.

    Mat input;

    Mat temp=input_.getMat();
    if(temp.channels() == 1){
        temp.convertTo(temp,CV_32FC2);
        Mat zmat = Mat::zeros(temp.size(), CV_32F);
        Mat twoChannelsbefore[] = {temp,zmat};
        cv::merge(twoChannelsbefore,2,input);
    }else{
        temp.convertTo(input, CV_32FC2);

    }

    EstimateCovariance estCov(windowRows,windowCols);

    //input_.getMat().convertTo(input, CV_32FC2);

    output_.create(windowRows*windowCols,windowRows*windowCols,  DataType<std::complex<float> >::type);

    Mat output = output_.getMat();

    estCov.computeEstimateCovariance(input,output);
}

} // namespace ximgproc
} // namespace cv