A generalized framework for stain separation in digital pathology applications

Microscopic examination of stained tissue sections obtained from biopsies forms the foundation of pathologically diagnosing diseased organs. Although offering a multi-scale view of the system pathology, interpretation is often subjective. Inter- and intra-observer variation in reporting due to limitations in tissue staining methods accounts for this subjectivity. Variation in stain uptake often leads to spectral overlap, variation in image intensities thus affecting the spectral signatures of imaged section and challenging computer assisted diagnosis. Stain density estimation techniques often referred to as digital stain separation have been introduced to overcome such limitations through quantification of amount of local stain uptake by a tissue. This is achieved by decorrelating the spectrally spread signal received by the color imaging sensor. Both blind and unblinded methods have been proposed with each having its own benefit. We focus on devising a framework for robust estimation of color deconvolution matrices as the basis for unblinded method. Here we propose a generalized framework using the Beer-Lambert intensity decay law for relating the stain uptake at a region to the resulting color and impose a Maxwellian chromaticity based regularization factor for solving the deconvolution matrix. The algorithm is trained and tested over different combinations of HE, VG and PAS stained cervical biopsy samples. The performance is validated using a 6-fold cross validation technique for each stain family and error in estimation measured across folds using MSE of stain uptake measurement. This generalized framework can be appropriately modified to other histopathological and immunohistochemical compound staining methods in brightfield microscopy.