# Color Deconvolution

This repository contains Mathematica notebooks for calculating both supervised and unsupervised color deconvolution of digital images. This work was intended to assist naive users in the analysis of stained histology samples by quatifying the amount of each stain in each pixel of the image.

## Supervised Methods

The canonical method is the unsupervised method of Ruifrok and Johnston in their paper "Quantification of Histochemical Staining by Color Deconvolution". A copy of the paper is included in the "Reference" directory.

The notebook "Ruifrok and Johnston Walkthrough" contains worked examples and code showing how the calculations can be done. It also includes some useful code showing how to display intermediate and final results.

The Ruifrok method works for our purposes, but requires a tedious and error prone series of staining procedures to generate calibration values for the color basis matrix of the dyes.

## Unsupervised Methods

A more useful method would be an unsupervised method capable of determining the color basis matrix without input from the operator.

The first of these methods to be examined was that of Newberg and Murphy in "A Framework for the Automated Analysis of Subcellular Patterns in Human Protein Atlas Images". A copy of the paper is in the "Reference" directory.

Again, notes containining worked examples and code are in the Mathematical notebook file "Newberg and Murphy Walkthrough". This paper included MATLAB code to do the calculations. The notes show how that code was translated to Mathematica as well.

This method was found to be extremely slow and unreliable. Additional work on this method was quickly abandoned.

The third method examined, and the most successful, was that of Macenko, et al., in the paper "A Method for Normalizing Histology Slides for Quantitative Analysis", a copy of which is also included in the "Reference" directory.

This method is the most intuitively satisfying in my opinion. A walkthrough is included in the Mathematica notebook entitled "Macenko et al Walkthrough". Although it does a good job of deconvolving the colors in an image, it does not always match the color basis that would be obtained by supervised methods. Of particular note is that, for the stain images examined, it can often be fooled by the presence of red blood cells in the image.

## Requirements

If you don't have Mathematica, you should be able to read the notebooks using the free Mathematica Viewer.

The images used in the walkthroughs are in the "Images" directory. If you wish to run or alter the notebooks, you may have to revised the hardwired paths to the images included in the notebook files.