Imperial College London


Faculty of EngineeringDepartment of Computing

Chair in Machine Learning and Pattern Recognition



m.bronstein Website




569Huxley BuildingSouth Kensington Campus






BibTex format

author = {Kovnatsky, A and Bronstein, MM and Bronstein, AM},
doi = {10.1007/978-3-642-33863-2_9},
pages = {83--91},
title = {Stable spectral mesh filtering},
url = {},
year = {2012}

RIS format (EndNote, RefMan)

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. © 2012 Springer-Verlag.
AU - Kovnatsky,A
AU - Bronstein,MM
AU - Bronstein,AM
DO - 10.1007/978-3-642-33863-2_9
EP - 91
PY - 2012///
SN - 0302-9743
SP - 83
TI - Stable spectral mesh filtering
UR -
ER -