Discrete Methods for Image Analysis Applied to Molecular Biology

Abstract

The field of image analysis and signal processing originally developed in the engineering community and is thus dominated by methods appealing to continuous mathematics. As a discrete mathematician recently entering this domain in the context of analyzing biological images, primarily from various forms of microscopy, I have found that discrete techniques involving trees and graphs better solve some segmentation and tracking problems than their continuous competitors. We illustrate this with three examples: component trees for adaptively segmenting nuclei in C. elegans 3D stacks, progress graph merging for segmenting cells in a 2D image of a fly wing, and shortest paths for segmenting and modeling individual neurons in a fly brain.