Learning the Geometric Structure of Manifolds with Singularities Using the Tensor Voting Graph

We present a general framework that addresses manifolds with singularities and multiple intersecting manifolds, which is also robust against a large number of outliers. We suggest a hybrid local–global method that leverages the algorithmic capabilities of the tensor voting framework and, unlike tensor voting, is capable of reliably inferring the global structure of complex manifolds by using a unique graph construction, called the tensor voting graph (TVG). Moreover, we propose to explicitly and directly resolve the ambiguities near the intersections with a novel algorithm, which uses the TVG and the positions of the points near the manifold intersections. Experimental results in estimating geodesic distances and clustering demonstrate that our framework outperforms the state of the art, especially on geometric complex settings such as when the tangent spaces at the intersections points are not orthogonal and in the presence of a large amount of outliers.