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Published in:
2013 | OriginalPaper | Chapter
The Laplace-Beltrami Operator: A Ubiquitous Tool for Image and Shape Processing
Authors : Aaron Wetzler, Yonathan Aflalo, Anastasia Dubrovina, Ron Kimmel
Published in: Mathematical Morphology and Its Applications to Signal and Image Processing
Publisher: Springer Berlin Heidelberg
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The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high dimensional embeddings of 2D manifolds and finally the possibility of viewing the framework of geodesic active contours as a surface minimization having the Laplace-Beltrami operator as its main ingredient.