Abstract
This paper is concerned with the semantic segmentation within domain-specific contexts, such as those pertaining to biology, physics, or material science. Under these circumstances, the objects of interest are often irregular and have fine structure, i.e., detail at arbitrarily small scales. Empirically, they are often understood as self-similar processes, a concept grounded in Multifractal Analysis. We find that this multifractal behaviour is carried out through a convolutional neural network (CNN), if we view its channel-wise responses as self-similar measures. A function of the local singularities of each measure we call Singularity Stregth Recalibration (SSR) is set forth to modulate the response at each layer of the CNN. SSR is a lightweight, plug-in module for CNNs. We observe that it improves a baseline U-Net in two biomedical tasks: skin lesion and colonic polyp segmentation, by an average of 1.36% and 1.12% Dice score, respectively. To the best of our knowledge, this is the first time multifractal-analysis is conducted end-to-end for semantic segmentation.

Abstract