Abstract
In this paper, we apply Nyström method, a sub-sampling and reconstruction technique, to speed up spectral mesh processing. We first relate this method to Kernel Principal Component Analysis (KPCA). This enables us to derive a novel measure in the form of a matrix trace, based soly on sampled data, to quantify the quality of Nyström approximation. The measure is efficient to compute, well-grounded in the context of KPCA, and leads directly to a greedy sampling scheme via trace maximization. On the other hand, analyses show that it also motivates the use of the max-min farthest point sampling, which is a more efficient alternative. We demonstrate the effectiveness of Nyström method with farthest point sampling, compared with random sampling, using two applications: mesh segmentation and mesh correspondence.
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Liu, R., Jain, V., Zhang, H. (2006). Sub-sampling for Efficient Spectral Mesh Processing. In: Nishita, T., Peng, Q., Seidel, HP. (eds) Advances in Computer Graphics. CGI 2006. Lecture Notes in Computer Science, vol 4035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784203_15
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DOI: https://doi.org/10.1007/11784203_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35638-7
Online ISBN: 978-3-540-35639-4
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