How to compute 2D log-chromaticity?

Question

My goal is to remove shadows from image. I use C++ and OpenCV. Sure I lack enough math background and not being native English speaker makes everything harder to understand.

After reading different approaches to remove shadows I found method which should work for me but it relies on something they call "2D chromaticity" and "2D log-chromaticity space" but even this term seems to be inconsistent in different sources. Many papers on topic, few are listed here:

http://www.cs.cmu.edu/~efros/courses/LBMV09/Papers/finlayson-eccv-04.pdf http://www2.cmp.uea.ac.uk/Research/compvis/Papers/DrewFinHor_ICCV03.pdf http://www.cvc.uab.es/adas/publications/alvarez_2008.pdf http://ivrgwww.epfl.ch/alumni/fredemba/papers/FFICPR06.pdf

I teared Google into strips by searching right words and explanations. Best I found is Illumination invariant image which did not help me much.

I tried to repeat formula log(G/R), log(B/R) described in first paper, page 3 to get figures similar to 2b.

As input I used http://en.wikipedia.org/wiki/File:Gretag-Macbeth_ColorChecker.jpg

Output I get is

My source code:

#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include <iostream>
#include <stdio.h>

using namespace std;
using namespace cv;

int main( int argc, char** argv ) {
  Mat src;

  src = imread( argv[1], 1 );

  if( !src.data )
    { return -1; }

  Mat image( 600, 600, CV_8UC3, Scalar(127,127,127) );

  int cn = src.channels();
  uint8_t* pixelPtr = (uint8_t*)src.data;

  for(int i=0 ; i< src.rows;i++) {
      for(int j=0 ; j< src.cols;j++) {
          Scalar_<uint8_t> bgrPixel;
          bgrPixel.val[0] = pixelPtr[i*src.cols*cn + j*cn + 0]; // B
          bgrPixel.val[1] = pixelPtr[i*src.cols*cn + j*cn + 1]; // G
          bgrPixel.val[2] = pixelPtr[i*src.cols*cn + j*cn + 2]; // R
          if(bgrPixel.val[2] !=0 ) { // avoid division by zero
              float a= image.cols/2+50*(log((float)bgrPixel.val[0] / (float)bgrPixel.val[2])) ;
              float b= image.rows/2+50*(log((float)bgrPixel.val[1] / (float)bgrPixel.val[2])) ;
              if(!isinf(a) && !isinf(b))
                  image.at<Vec3b>(a,b)=Vec3b(255,2,3);
          }
      }
  }

  imshow("log-chroma", image );
  imwrite("log-chroma.png", image );
  waitKey(0);

}

What I am missing or misunderstand?

Answer 1

By reading the paper Recovery of Chromaticity Image Free from Shadows via Illumination Invariance that you've posted, and your code, I guess the problem is that your coordinate system (X/Y axis) are linear while in the paper the coordinate system are log(R/G) by log(B/G).