Blind colour separation of H&E stained histological images by linearly transforming the colour space

Blind source separation methods aim to split information into the original sources. In histology, each dye component attempts to specifically characterize different microscopic structures. In the case of the hematoxylin-eosin stain, universally used for routine examination, quantitative analysis may often require the inspection of different morphological signatures related mainly to nuclei patterns, but also to stroma distribution. Stain separation is usually a preprocessing operation that is transversal to different applications. This paper presents a novel colour separation method that finds the hematoxylin and eosin clusters by projecting the whole (r,g,b) space to a folded surface connecting the distributions of a series of [(r-b),g] planes that divide the cloud of H&E tones. The proposed method produces density maps closer to those obtained with the colour mixing matrices set by an expert, when comparing with the density maps obtained using nonnegative matrix factorization (NMF), independent component analysis (ICA) and a state-of-the-art method. The method has outperformed three baseline methods, NMF, Macenko and ICA, in about 8%, 12% and 52% for the eosin component, whereas this was about 4%, 8% and 26% for the hematoxylin component.