Full and partial shape similarity through sparse descriptor reconstruction

Lili Wan, Changqing Zou, Hao Zhang

Abstract: We introduce a novel approach to measuring similarity between two shapes based on sparse reconstruction of shape descriptors. The main feature of our approach is its applicability in situations where either of the two shapes may have moderate to significant portions of its data missing. Let the two shapes be A and B. Without loss of generality, we characterize A by learning a sparse dictionary from its local descriptors. The similarity between A and B is defined by the error incurred when reconstructing B’s descriptor set using the basis signals from A’s dictionary. Benefits of using sparse dictionary learning and reconstruction are twofold. First, sparse dictionary learning reduces data redundancy and facilitates similarity computations. More importantly, the reconstruction error is expected to be small as long as B is similar to A, regardless of whether the similarity is full or partial. Our proposed approach achieves significant improvements over previous works when retrieving non-rigid shapes with missing data, and it is also comparable to state-of-the-art methods on the retrieval of complete non-rigid shapes.