Stable Spectral Mesh Filtering

conference paper Stable Spectral Mesh Filtering LNCS published yes Artiom Kovnatsky author Michael M. Bronstein author Alexander Bronstein author 58f3726e-7cba-11ef-ad8b-e6e8cb3904e60000-0001-9699-8730 ECCV: European Conference on Computer Vision The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean space; it is thus possible to formulate signal analysis and synthesis in the manifold harmonics basis. In particular, geometry filtering can be carried out in the manifold harmonics domain by decomposing the embedding coordinates of the shape in this basis. However, since the basis functions depend on the shape itself, such filtering is valid only for weak (near all-pass) filters, and produces severe artifacts otherwise. In this paper, we analyze this problem and propose the fractional filtering approach, wherein we apply iteratively weak fractional powers of the filter, followed by the update of the basis functions. Experimental results show that such a process produces more plausible and meaningful results. Springer Nature2012Florence, Italy eng Computer Vision, ECCV 2012 - Workshops and Demonstrations 0302-9743 1611-3349 9783642338625 978364233863210.1007/978-3-642-33863-2_9 7583Part 183-91 yes A. Kovnatsky, M. M. Bronstein, and A. M. Bronstein, “Stable Spectral Mesh Filtering,” in Computer Vision, ECCV 2012 - Workshops and Demonstrations, Florence, Italy, 2012, vol. 7583, no. Part 1, pp. 83–91. Kovnatsky, Artiom, et al. “Stable Spectral Mesh Filtering.” Computer Vision, ECCV 2012 - Workshops and Demonstrations, vol. 7583, no. Part 1, Springer Nature, 2012, pp. 83–91, doi:<a href="https://doi.org/10.1007/978-3-642-33863-2_9">10.1007/978-3-642-33863-2_9</a>. Kovnatsky, A., Bronstein, M. M., & Bronstein, A. M. (2012). Stable Spectral Mesh Filtering. In Computer Vision, ECCV 2012 - Workshops and Demonstrations (Vol. 7583, pp. 83–91). Florence, Italy: Springer Nature. <a href="https://doi.org/10.1007/978-3-642-33863-2_9">https://doi.org/10.1007/978-3-642-33863-2_9</a> Kovnatsky, Artiom, Michael M. Bronstein, and Alex M. Bronstein. “Stable Spectral Mesh Filtering.” In Computer Vision, ECCV 2012 - Workshops and Demonstrations, 7583:83–91. Springer Nature, 2012. <a href="https://doi.org/10.1007/978-3-642-33863-2_9">https://doi.org/10.1007/978-3-642-33863-2_9</a>. Kovnatsky A, Bronstein MM, Bronstein AM. 2012. Stable Spectral Mesh Filtering. Computer Vision, ECCV 2012 - Workshops and Demonstrations. ECCV: European Conference on Computer Vision, LNCS, vol. 7583, 83–91. A. Kovnatsky, M.M. Bronstein, A.M. Bronstein, in:, Computer Vision, ECCV 2012 - Workshops and Demonstrations, Springer Nature, 2012, pp. 83–91. Kovnatsky A, Bronstein MM, Bronstein AM. Stable Spectral Mesh Filtering. In: Computer Vision, ECCV 2012 - Workshops and Demonstrations. Vol 7583. Springer Nature; 2012:83-91. doi:<a href="https://doi.org/10.1007/978-3-642-33863-2_9">10.1007/978-3-642-33863-2_9</a> 183492024-10-15T11:20:54Z2025-01-16T11:49:13Z