AdaHOSVD: an adaptive higher-order singular value decomposition method for point cloud denoising

Higher-Order Singular Value Decomposition (HOSVD) is an effective method for point cloud denoising, however how to preserve the global and local structure during the denoising process and how to balance the denoising performance and its inherent large computational burden are still open questions in the field. To tackle these problems, an adaptive higher-order singular value decomposition method, AdaHOSVD including two sub-algorithms HOSVD-1 and HOSVD-2, is proposed in this work by adaptively setting the threshold value to truncate the kernel tensor, and by limiting the patch similarity searching within a search radius. Since point cloud is in 3D space rather than a 2D plane as in image cases, we extend the patch similarity detection in 3D space up to a 3D rigid motion; hence, more similar 3D patches could be detected, which in turn boosts its performance. We validate our method on two datasets. One is the 3D benchmark dataset including the ShapeNetCore and the 3D scanning repository of Stanford University, which contains a large body of diverse high quality shapes to assess its noise sensitivity, and the other is the Golden Temple and the Electric hook, which contains a large temple structure with abundant local repeated textural and shape patterns.