First Order Logic with Fuzzy Semantics for Describing and Recognizing Nerves in Medical Images

This article deals with the description and recognition of fiber bundles, in particular nerves, in medical images, based on the anatomical description of the fiber trajectories. To this end, we propose a logical formalization of this anatomical knowledge. 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 domain and satisfaction degrees of relations. Based on this formalization, a spatial reasoning algorithm is proposed for segmentation and recognition of nerves from anatomical and diffusion magnetic resonance images, which is illustrated on pelvic nerves in pediatric imaging, enabling surgeons to plan surgery.