Fuzzy “Along” Spatial Relation in 3D. Application to Anatomical Structures in Maxillofacial CBCT

Spatial relations have proved to be of great importance in computer vision and image understanding. One issue is their modeling in the image domain, hence allowing for their integration in segmentation and recognition algorithms. In this paper, we focus on the “along” spatial relation. Based on a previous work in 2D, we propose extensions to 3D. Starting from the inter-objects region, we demonstrate that the elongation of the interface between the objects and this region gives a good evaluation of the alongness degree. We also integrate distance information to take into account only close objects parts. Then we describe how to define the alongness relation within the fuzzy set theory. Our method gives a quantitative satisfaction degree of the relation, reliable for differentiating spatial situations. An original example on the maxillofacial area in Cone-Beam Computed Tomography (CBCT) illustrates how the proposed approach could be used to recognize elongated structures.