Inferring a third spatial dimension from 2D histological images

Histological images are obtained by transmitting light through a tissue specimen that has been stained in order to produce contrast. This process results in 2D images of the specimen that has a three-dimensional structure. In this paper, we propose a method to infer how the stains are distributed in the direction perpendicular to the surface of the slide for a given 2D image in order to obtain a 3D representation of the tissue. This inference is achieved by decomposition of the staining concentration maps under constraints that ensure realistic decomposition and reconstruction of the original 2D images. Our study shows that it is possible to generate realistic 3D images making this method a potential tool for data augmentation when training deep learning models.