Functional correspondence by matrix completion
This addresses shape matching in computer vision and graphics, offering incremental improvements for non-rigid shape correspondence.
The paper tackles the problem of finding dense intrinsic correspondence between manifolds by formulating it as a matrix completion problem with geometric structure and L1 norm for localization, resulting in improved accuracy over state-of-the-art methods, especially with scarce data.
In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold geometric structure and inducing functional localization with the $L_1$ norm. We discuss efficient numerical procedures for the solution of our problem. Our method compares favorably to the accuracy of state-of-the-art correspondence algorithms on non-rigid shape matching benchmarks, and is especially advantageous in settings when only scarce data is available.