Global conformal surface parameterization

By Xianfeng David Gu, Shing-Tung Yau. 2003

477 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0a6f2809dea0320db6bac1a58fc50fc856dc7ace

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Citations in the corpus

Geometrically Accurate Topology-Correction of Cortical Surfaces Using Nonseparating Loops (2007, methodology): “the closed curves; they have been extensively used in graphics [39], [53], [54], combinatorial and computational topology [52], [55]–[58], and medical imaging [40].”
Spatial regression models over two-dimensional manifolds (2016, background): “Such global parameterizations are available for a large class of two-dimensional manifolds, including surfaces with self-intersections or holes and other nontrivial geometries; see, e.g., Gu & Yau (2003).”
Genus zero surface conformal mapping and its application to brain surface mapping (2004, methodology): “Method Principle Comments Discrete Harmonic Maps [11]–[14] Minimize harmonic energy, Compute harmonic maps namely the Dirichlet energy for genus zero surfaces only Least-square Conformal Mapping [16] Approximate Cauchy-Riemann equation Equivalent to harmonic energy Laplace-Beltrami operator [17], [2”
Discrete differential forms for computational modeling (2005, background): “One usual way to calculate a cohomology basis is to calculate a Smith Normal Form to obtain the homology basis (cid:2)rst (possibly using progressive meshes [19]), with a worst case complexity of O ( n 3 ) , and then (cid:2)nd the corresponding cohomology basis derived from this homology basis.”
Image deformation using moving least squares (2006, background): “(Transformations that strictly preserve angle are called conformal transformations and have been studied extensively in [Gu and Yau 2003].)”
Differential Representations for Mesh Processing (2006, background): “This topic is outside of the scope of this paper; the reader is kindly referred to recent publications [6,50,51,52] for further information.”
Periodic global parameterization (2006, background): “Since two singular points located in the same region drastically increase the penalty function in that region, the augmented energy functional attempts to avoid those conﬁgurations and evenly distributes the singular points over the surface.”
Intrinsic shape context descriptors for deformable shapes (2012, background): “Such mappings can be established using multidimensional scaling (MDS) [6] or conformal mapping [19, 18, 39].”
Mesh parameterization: theory and practice (2007, methodology): “Still, the approach is constrained by the global nature of harmonic one-forms, in some sense, similar to the algorithm of Gu and Yau [Gu and Yau, 2003].”
Inter-surface mapping (2004, methodology): “Some techniques cut the surface into a single chart [e.g. Gu et al 2002; Sheffer et al 2002; Sorkine et al 2002], while others cut it into an atlas of charts [e.g. Maillot et al 1993; Sander et al 2001; Levy et al 2002; Gu and Yau 2003].”
Surface Parameterization: a Tutorial and Survey (2005, methodology): “Gu and Yau [28] have later proposed an iterative method which approximates a harmonic (and therefore conformal) map and avoids splitting.”