Journal Article

PUBDB-2024-04870

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Spectral Total-Variation Processing of Shapes - Theory and Applications

Brokman, J. ; Burger, M.DESY* ; Gilboa, G.

2024
ACM New York, NY [u.a.]

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Please use a persistent id in citations: doi:10.1145/3641845  doi:10.3204/PUBDB-2024-04870

Report No.: arXiv:2209.07517

Abstract: We present a comprehensive analysis of total variation (TV) on non-Euclidean domains and its eigenfunctions. We specifically address parameterized surfaces, a natural representation of the shapes used in 3D graphics. Our work sheds new light on the celebrated Beltrami and Anisotropic TV flows and explains experimental findings from recent years on shape spectral TV [Fumero et al. 2020] and adaptive anisotropic spectral TV [Biton and Gilboa 2022]. A new notion of convexity on surfaces is derived by characterizing structures that are stable throughout the TV flow, performed on surfaces. We establish and numerically demonstrate quantitative relationships between TV, area, eigenvalue, and eigenfunctions of the TV operator on surfaces. Moreover, we expand the shape spectral TV toolkit to include zero-homogeneous flows, leading to efficient and versatile shape processing methods. These methods are exemplified through applications in smoothing, enhancement, and exaggeration filters. We introduce a novel method that, for the first time, addresses the shape deformation task using TV. This deformation technique is characterized by the concentration of deformation along geometrical bottlenecks, shown to coincide with the discontinuities of eigenfunctions. Overall, our findings elucidate recent experimental observations in spectral TV, provide a diverse framework for shape filtering, and present the first TV-based approach to shape deformation.

Note: Green open access version at arxiv, https://arxiv.org/abs/2209.07517

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)
2. NoMADS - Nonlocal Methods for Arbitrary Data Sources (777826) (777826)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; Essential Science Indicators ; IF >= 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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