Optimal Transport Driven Asymmetric Image-to-Image Translation for Nuclei Segmentation of Histological Images

Segmentation of nuclei regions from histological images enables morphometric analysis of nuclei structures, which in turn helps in the detection and diagnosis of diseases under consideration. To develop a nuclei segmentation algorithm, applicable to different types of target domain representations, image-to-image translation networks can be considered as they are invariant to target domain image representations. One of the important issues with image-to-image translation models is that they fail miserably when the information content between two image domains are asymmetric in nature. In this regard, the paper introduces a new deep generative model for segmenting nuclei structures from histological images. The proposed model considers an embedding space for handling information-disparity between information-rich histological image space and information-poor segmentation map domain. Integrating judiciously the concepts of optimal transport and measure theory, the model develops an invertible generator, which provides an efficient optimization framework with lower network complexity. The concept of invertible generator automatically eliminates the need of any explicit cycle-consistency loss. The proposed model also introduces a spatially-constrained squeeze operation within the framework of invertible generator to maintain spatial continuity within the image patches. The model provides a better trade-off between network complexity and model performance compared to other existing models having complex network architectures. The performance of the proposed deep generative model, along with a comparison with state-of-the-art nuclei segmentation methods, is demonstrated on publicly available histological image data sets.