BCD-net: Stain separation of histological images using deep variational Bayesian blind color deconvolution

Histological images are often tainted with two or more stains to reveal their underlying structures. Blind Color Deconvolution (BCD) techniques separate colors (stains) and structural information (concentrations), which is useful for the processing, data augmentation, and classification of such images. Classical analytical BCD methods are typically computationally expensive in two distinct ways. First, estimating the colors and concentrations corresponding to a given image is a time-consuming process. Second, the entire estimation procedure must be performed independently for each image.In contrast, Deep Learning (DL) methods involve high training costs, but once trained, they are able to directly process unseen images. The application of DL to BCD has been limited by the absence of extensive databases containing ground truth color and concentrations. In this work, we propose BCD-Net, a deep variational Bayesian neural network for stain separation and concentration estimation. Under this framework, we address the challenge of lacking ground truth data by leveraging Bayesian modeling and inference techniques.We propose to use a prior distribution on the stain colors, and a simple flat prior on the concentrations. BCD -Net is trained by maximizing the evidence lower bound of the observed images. The loss function comprises two essential components: fidelity to the observed images and the Kullback-Leibler divergence between the estimated posterior distribution of colors and the selected prior.The model is trained, validated, and tested on two multicenter databases: Camelyon-17 and Warwick stain separation benchmark. The proposed approach is tested on image reconstruction, stain separation, and cancer classification. It performs well when contrasted with classical non-amortized methods and offers a substantial computational time advantage. This marks a significant step forward in the application of DL techniques to address BCD and paves the way for new approaches.