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.

高阶奇异值分解（HOSVD）是点云去噪的有效方法，但是如何在去噪过程中保留全局和局部结构以及如何平衡去噪性能与其固有的大量计算负担仍然是该领域的悬而未决的问题。场地。为了解决这些问题，提出了一种自适应高阶奇异值分解方法AdaHOSVD ，包括两个子算法HOSVD-1和HOSVD-2，在这项工作中提出，通过自适应设置阈值来截断核张量，并通过将补丁相似度搜索限制在搜索半径内。由于点云位于 3D 空间而不是图像情况中的 2D 平面，因此我们将 3D 空间中的块相似性检测扩展到 3D 刚性运动；因此，可以检测到更多相似的 3D 补丁，从而提高其性能。我们在两个数据集上验证我们的方法。一个是 3D 基准数据集，包括 ShapeNetCore 和斯坦福大学的 3D 扫描存储库，其中包含大量不同的高质量形状，用于评估其噪声敏感度；另一个是 Golden Temple 和 Electric hook，其中包含大量的寺庙结构具有丰富的当地重复的纹理和形状图案。