Robust 2D Shape Correspondence using Geodesic Shape Context

A meaningful correspondence and similarity measure between shapes is particularly useful in applications such as morphing, object recognition, shape registration and retrieval. In this paper, we present a robust shape descriptor for points along a 2D contour, based on the curvature distribution collected over bins arranged geodesically along the contour. Convolution, binning and hysteresis thresholding of curvatures are applied to render the descriptor more robust against noise and non-rigid shape deformation. Once the shape descriptor is computed for every point or feature vertex of the two shapes to be matched, a one-to-one correspondence can be quickly established through best matching of the descriptors, aided by a proximity heuristic. Our approach does not rely on the linear ordering of the points along a contour, facilitating its 3D generalization. It is also capable of matching all the points along the contour, not just a specified set of feature vertices. Our shape descriptor is intuitive, fast to compute, shape distinguishing, and easy to implement. The performance of our approach, when applied to shape correspondence and shape retrieval on the Brown database and the articulated shapes database of Ling et al., shows that it is robust against both rigid and common non-rigid transformations such as bending and moderate stretching.