Part-in-whole matching of rigid 3D shapes using geodesic disk spectrum

Part-in-whole matching of rigid 3D shapes has attracted great interest in shape analysis and has various applications in computational archaeology. Rigid part-in-whole matching algorithms are mainly based on methods minimizing geometric distances and methods using local shape descriptors, which are challenging when the partial shapes are relatively small and smooth. This paper proposes a part-in-whole matching algorithm of rigid 3D shapes using geodesic disk spectrum (GDS), which achieves accurate matching results for partial shapes with arbitrary boundaries or smooth appearances. The largest enclosing geodesic disk of the partial shape and geodesic disks on the complete shape are extracted in the matching process. GDS is used as the matching descriptor, which is the distribution of shape index for enclosing points of the disk. The problem of matching partial surfaces with arbitrarily irregular boundaries to the complete shape is transformed into the matching of geodesic disks with the same radius using the proposed algorithm. GDS is discriminative, which can handle the situation when partial surfaces have few distinctive features. The proposed algorithm has been tested on various partial surfaces and obtained accurate matching results. A higher precision is achieved by comparing with existing part-in-whole matching algorithms, which proves the efficiency of the proposed algorithm.