Curvature Based Robust Descriptors

Feature descriptors have enabled feature matching under varying imaging conditions, while mostly being backed by experimental evidence. In addition to imposing some restrictions in imaging conditions needed to ensure matching, extending the existing descriptors is not straightforward due to the lack of sound mathematical bases. In this work, by using a surface bending versus shape histogram based on the principal curvatures, we are able to produce a descriptor which is not sensitive to the errors in dominant orientation assignment. Experimental evaluations show that our descriptor outperforms existing descriptors in the areas of viewpoint, rotation, scale, zoom, lighting and compression changes, with the exception of resilience to blur. Further, we apply this descriptor for accuracy demanding applications such as homography estimation and pose estimation. The experimental results show significant improvements in estimated homography and pose in terms of residual error and Sampson distance respectively. Eigenvalues of Hessian matrix H are the principal curvatures λmax,λmin of a surface I(x,y) at any given point. Let ~p be any point in patch S. We introduce a metric the amount of bending m(~p) based on rotationally invariant principle curvatures as below