Discrete Mereotopology for Spatial Reasoning in Automated Histological Image Analysis.

Discrete mereotopology (DM) is a first-order spatial logic that fuses together mereology (the theory of parthood relations) and topology to model discrete space. We show how a set of quasitopological functions defined within DM can be mapped to specific operators defined in mathematical morphology (MM) and easily implemented in scientific image processing programs. These functions provide the means to model topological properties of individual regions and spatial relations between them such as contact, overlap, and the relation of part to whole.

Morphologic characterization of cell neighborhoods in neoplastic and preneoplastic epithelium.

Objective: To explore tissue organization based on the geometry of cell neighborhoods in histologic preparations.

Study Design: Local complexity of solid tissues was measured in images of discrete tissue compartments. Exclusive areas associated with cell nuclei (v-cells) were computed using a watershed transform of the nuclear staining intensity.