First order logic with fuzzy semantics for describing and recognizing nerves in medical imaging

This article deals with the description and recognition of fiber bundles, in particular nerves, in medical imaging, based on the anatomical description of the fiber path. To this end, we propose a logical formalization. The intrinsically imprecise description of nerves, as found in anatomical textbooks, leads us to propose fuzzy semantics combined with first-order logic.We define a language representing spatial entities, relations between these entities and quantifiers. A formula in this language is then a formalization of the natural language description. The semantics are given by fuzzy representations in a concrete space and satisfaction degrees of relations. This formalization leads to spatial reasoning algorithms for segmentation and recognition of nerves from anatomical and diffusion MRI images, which are illustrated on pelvic nerves in pediatric imaging, enabling surgeons to plan surgery.