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@ARTICLE{Brokman:611250,
      author       = {Brokman, Jonathan and Burger, Martin and Gilboa, Guy},
      title        = {{S}pectral {T}otal-{V}ariation {P}rocessing of {S}hapes -
                      {T}heory and {A}pplications},
      journal      = {ACM transactions on graphics},
      volume       = {43},
      number       = {2},
      issn         = {0730-0301},
      address      = {New York, NY [u.a.]},
      publisher    = {ACM},
      reportid     = {PUBDB-2024-04870, arXiv:2209.07517},
      pages        = {3641845},
      year         = {2024},
      note         = {Green open access version at arxiv,
                      https://arxiv.org/abs/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.},
      cin          = {FS-CI},
      ddc          = {004},
      cid          = {I:(DE-H253)FS-CI-20230420},
      pnm          = {623 - Data Management and Analysis (POF4-623) / NoMADS -
                      Nonlocal Methods for Arbitrary Data Sources (777826)},
      pid          = {G:(DE-HGF)POF4-623 / G:(EU-Grant)777826},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2209.07517},
      howpublished = {arXiv:2209.07517},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2209.07517;\%\%$},
      UT           = {WOS:001208809900009},
      doi          = {10.1145/3641845},
      url          = {https://bib-pubdb1.desy.de/record/611250},
}