TY - GEN
T1 - Stable spectral mesh filtering
AU - Kovnatsky, Artiom
AU - Bronstein, Michael M.
AU - Bronstein, Alexander M.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - 3D Mesh filtering
KW - Computational Geometry and Object Modeling
KW - Hierarchy and geometric transformations
KW - Laplace-Beltrami operator
UR - http://www.scopus.com/inward/record.url?scp=84867734131&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-33863-2_9
DO - https://doi.org/10.1007/978-3-642-33863-2_9
M3 - منشور من مؤتمر
SN - 9783642338625
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 83
EP - 91
BT - Computer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings
T2 - Computer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings
Y2 - 7 October 2012 through 13 October 2012
ER -