Tensor-based computation and modeling in multi-resolution digital pathology imaging: application to follicular lymphoma grading

In this work, we introduce a tensor-based computation and modeling framework for the analysis of digital pathology images at different resolutions. We represent digital pathology images as a third-order tensor (a three-way array) with modes: images, features and scales, by extracting features at different scales. The constructed tensor is then analyzed using the most popular tensor factorization methods, i.e., CANDECOMP/PARAFAC and Tucker. These tensor models enable us to extract the underlying patterns in each mode (i.e. images, features and scales) and examine how these patterns are related to each other. As a motivating example, we analyzed 500 follicular lymphoma images corresponding to high power fields, evaluated by three expert hematopathologists. Numerical experiments demonstrate that (i) tensor models capture easily-interpretable patterns showing the significant features and scales, and (ii) patterns extracted by the right tensor model, which in this case is the Tucker model commonly used for exploratory analysis of higher-order tensors, perform as well as the reduced dimensions captured by matrix factorization methods on unfolded data, in terms of follicular lymphoma grading.