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@PHDTHESIS{Schmidt:1003249,
      author       = {Schmidt, Patrick},
      othercontributors = {Kobbelt, Leif and Ben-Chen, Mirela},
      title        = {{I}ntrinsic optimization of maps between surfaces},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2025-00939},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2025; Dissertation, RWTH Aachen University, 2024},
      abstract     = {This thesis addresses the construction and optimization of
                      high-quality maps between the surfaces of 3D shapes. Within
                      the field of geometry processing, there is an increasing
                      demand for methods that, instead of operating on individual
                      shapes in isolation, process entire shape collections in
                      correspondence. A key component in such scenarios are
                      surface maps: functions defining a geometric point-to-point
                      relationship between two or more surfaces. Such maps open
                      the door to numerous applications ranging from attribute
                      transfer, over spatial and temporal shape interpolation, to
                      co-analysis and co-synthesis of surface data, or the
                      generation of common base domains for higher-level
                      processing algorithms. In this work, we tackle the intricate
                      tasks of generating surface homeomorphisms (a class of maps
                      that strictly ensure continuity and bijectivity) and
                      optimizing them for low intrinsic mapping distortion. In
                      contrast to previous approaches, which were only able to
                      either guarantee homeomorphisms or minimize distortion, we
                      establish a novel algorithmic framework that allows
                      combining both aspects. To set the stage for our
                      contributions, we start by reviewing a wide range of
                      approaches to the surface mapping problem. Along the way, we
                      provide in-depth introductions to concepts from surface
                      parametrization, geometry processing in spherical and
                      hyperbolic domains, as well as non-linear continuous
                      optimization. We then present three methods targeting
                      different scenarios: maps between disk-topology surfaces in
                      a free-boundary setting, maps between closed surfaces of
                      arbitrary genus, and multi-resolution maps within
                      collections of genus-0 shapes. We conclude by providing a
                      tool for automatic differentiation that not only powers
                      these surface mapping methods but makes non-linear
                      optimization techniques practically available in a much
                      broader range of geometry processing tasks.},
      cin          = {122310 / 120000},
      ddc          = {004},
      cid          = {$I:(DE-82)122310_20140620$ / $I:(DE-82)120000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2025-00939},
      url          = {https://publications.rwth-aachen.de/record/1003249},
}