Polynomial local shape descriptor on interest points for 3D part-in-whole matching

Part-in-whole 3D shape matching is to recognize query shapes as sub-parts of a target intact 3D object. It plays a pivotal role in a large number of engineering applications. The most critical component in a part-in-whole search system is the local shape descriptor which encapsulates the identified local feature on the query part and is matched with the local shape descriptors of the parts in the database. We propose a novel local shape descriptor based on the concept that the evolution pattern of geodesic iso-contour's length is a good representative for surface features. Our local shape descriptor enjoys a unique advantage over most existing ones by being sensitive to the geodesic radius of the local region, and thus is able to capture more comprehensive shape information if the query portion of the shape is larger and includes more complicated surface features. Through a simple approximation scheme, our local shape descriptor is defined as a vector piecewise polynomial function of the geodesic radius of the interest point, thus enabling local matching to be performed quickly by simple curve evaluations. We also introduce a new schema of interest points sampling so that we can reserve the most corresponding information of the model by a small number of local feature descriptors. The proposed part-in-whole matching approach outperforms many existing approaches in matching efficiency and requiring a smaller input region. It is a shortcut solution for incomplete model matching/retrieval.