Quantifying 3D shape similarity using maps: Recent trends, applications and perspectives

Shape similarity is an acute issue in Computer Vision and Computer Graphics that involves many aspects of human perception of the real world, including judged and perceived similarity concepts, deterministic and probabilistic decisions and their formalization. 3D models carry multiple information with them (e.g., geometry, topology, texture, time evolution, appearance), which can be thought as the filter that drives the recognition process. Assessing and quantifying the similarity between 3D shapes is necessary to explore large dataset of shapes, and tune the analysis framework to the user's needs. Many efforts have been done in this sense, including several attempts to formalize suitable notions of similarity and distance among 3D objects and their shapes. In the last years, 3D shape analysis knew a rapidly growing interest in a number of challenging issues, ranging from deformable shape similarity to partial matching and view-point selection. In this panorama, we focus on methods which quantify shape similarity (between two objects and sets of models) and compare these shapes in terms of their properties (i.e., global and local, geometric, differential and topological) conveyed by (sets of) maps. After presenting in detail the theoretical foundations underlying these methods, we review their usage in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Particular emphasis will be given to analyse the suitability of the different methods for specific classes of shapes (e.g. rigid or isometric shapes), as well as the flexibility of the various methods at the different stages of the shape comparison process. Finally, the most promising directions for future research developments are discussed.