Spatial logics and model checking for medical imaging

Recent research on spatial and spatio-temporal model checking provides novel image analysis methodologies, rooted in logical methods for topological spaces. Medical imaging (MI) is a field where such methods show potential for ground-breaking innovation. Our starting point is SLCS, the Spatial Logic for Closure Spaces--closure spaces being a generalisation of topological spaces, covering also discrete space structures--and topochecker, a model checker for SLCS (and extensions thereof). We introduce the logical language ImgQL ("Image Query Language"). ImgQL extends SLCS with logical operators describing distance and region similarity. The spatio-temporal model checker topochecker is correspondingly enhanced with state-of-the-art algorithms, borrowed from computational image processing, for efficient implementation of distance-based operators, namely distance transforms. Similarity between regions is defined by means of a statistical similarity operator, based on notions from statistical texture analysis. We illustrate our approach by means of an example of analysis of Magnetic Resonance images: segmentation of glioblastoma and its oedema.