Shift-invariant ring feature for 3D shape

In this paper, we present a shift-invariant ring feature for 3D shape, which can encode multiple low-level descriptors and provide high-discriminative representation of local region for 3D shape. First, several iso-geodesic rings are created at equal intervals, and then low-level descriptors on the sampling rings are used to represent the property of a feature point. In order to boost the descriptive capability of raw descriptors, we formulate the unsupervised basis learning into an L1-penalized optimization problem, which uses convolution operation to address the rotation ambiguity of descriptors resulting from different starting points in rings. In the following extraction procedure of high-level feature, we use the learned bases to calculate the sparse coefficients by solving the optimization problem. Furthermore, to make the coefficients irrelevant with the sequential order in ring, we use Fourier transform to achieve circular-shift invariant ring feature. Experiments on 3D shape correspondence and retrieval demonstrate the satisfactory performance of the proposed intrinsic feature.