Incremental functional maps for accurate and smooth shape correspondence.

Incorporating multiscale spectral manifold wavelets preservation into the functional map framework for shape correspondence achieves great results in terms of both efficiency and effectiveness. However, fixing the dimension of the spectral embedding strategy in iterations of optimization is troublesome, such as missing high-frequency information when the dimension is small or getting trapped in local minima at a high dimension. In this paper, we present a simple and efficient method for refining correspondences from low frequency to high frequency with a theoretical guarantee. We formulate a strong constraint where the multiscale spectral manifold wavelets should be preserved at each scale correspondingly in the case of the arbitrary dimension of spectral embeddings. To solve the formula, we deduce two relaxed optimization subproblems and propose an incremental alternating iterative algorithm between the spatial and spectral domains via spectral up-sampling and filtering, computing the functional maps and pointwise maps in turn. Our results demonstrate that our method is robust to noisy initialization and scalable with regard to shape resolutions. The deformable shape correspondence benchmark experiments show our method produces more accurate and smoother results than state of the arts. [ABSTRACT FROM AUTHOR]