Structural descriptors for 3d shapes

Assessing the similarity among 3D shapes is a challenging research topic, and effective shape descriptions have to be devised in order to support the matching process. There is a growing consensus that shapes are recognized and coded mentally in terms of relevant parts and their spatial configuration, or structure. The presentation will discuss the definition and use of structural descriptions for assessing shape similarity. The idea is to define a shape description framework based on results of differential topology which deal with the description of shapes by means of the properties of one, or more, real-valued functions defined over the shape. Studying these properties, several topological descriptions of the shape can be defined, which may also encode different geometric and morphological attributes that globally and locally describe the shape. Examples and results will be discussed and ongoing work outlined.