Möbius voting for surface correspondence

By Yaron Lipman, Thomas A. Funkhouser. ACM Transactions on Graphics, 2009

397 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/2d30768d0a3b3f895b37f806a8a0b65d870bb054

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Schelling points on 3D surface meshes (2012, background): “2008], local maxima of Gaussian curvature [Lipman and Funkhouser 2009], properties of the Heat Kernel Signature [Sun et al.”
3D-CODED: 3D Correspondences by Deep Deformation (2018, methodology): “…of this problem have been proposed such as: formulating it as Markov random ﬁeld and using linear programming relaxation [13], optimizing for soft correspondence [40,21,41], re-stricting correspondence space to conformal maps [23,22], heat kernel maps [32], and aligning functional bases [33].”
FAUST: Dataset and Evaluation for 3D Mesh Registration (2014, methodology): “Common intrinsic representations include Generalized Multi-Dimensional Scaling (GMDS) [8], Möbius transformations [13, 15], and heat kernel maps [16].”
Image Matching from Handcrafted to Deep Features: A Survey (2020, background): “Notably, another work developed conformal mapping approaches that also use embedding space (Lipman and Funkhouser 2009; Kim et al. 2011; Zeng et al. 2010).”
Dense Human Body Correspondences Using Convolutional Networks (2015, methodology): “When both source and target shapes are full models, an automatic mapping between shapes with considerable deformations becomes possible as shown in [20, 25, 33, 10].”
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013, background): “These saliency measures include: differential properties [56], rareness [48], scale space analysis on geometry [17] and features [48], size and curvature based on visual saliency [53], multiscale slippage [57] and maximally stable extremal regions (MSER) [58].”
Intrinsic shape context descriptors for deformable shapes (2012, background): “Also, the use of conformal factors has been proposed [27].”
Conformal Wasserstein distances: Comparing surfaces in polynomial time (2011, methodology): “ce the (hyperbolic) density functions and are known, it suces to identify m2M Dsuch that (m(z)) and (z) coincide (or \nearly" coincide, in a sense to be made precise). This was exploited in [6] to construct fast algorithms to nd corresponding points between two given surfaces. In the next secti”
One Point Isometric Matching with the Heat Kernel (2010, positive): “Finally our isometry veriﬁcation step follows the paradigm proposed in geometric hashing [WR97], and used in [LF09].”
Blended intrinsic maps (2011, methodology): “Please refer to [Lipman and Funkhouser 2009; Kim et al. 2010] for details.”
Learning Spectral Descriptors for Deformable Shape Correspondence (2014, neutral): “[12].”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, background): “[17, 16] suggested to compare neighborhoods of points in the framework of conformal geometry.”
Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery (2013, methodology): “(Bronstein et al., 2011; Funkhouser and Shilane, 2006; Gelfand et al., 2005; Lipman and Funkhouser, 2009; Wang et al., 2010; Windheuser et al., 2011; Zeng et al., 2010; Zhang et al., 2008), the only fully-automatic non-rigid approaches to intra-operative registration of range data in abdominal proce”
Style-content separation by anisotropic part scales (2010, background): “A few more recent papers [Zhang et al. 2008; Lipman and Funkhouser 2009] attempt to handle large shape deformations, but like most previous works, they focus on organic shapes and rely on extracted surface feature points to deﬁne a meaningful correspondence.”
Functional maps (2012, methodology): “The majority of existing methods try to tackle these challenges by limiting their search for correspondences between a small set of landmark points and extending those to a dense set of correspondences on entire shapes during final post-processing ([Bronstein et al. 2006; Huang et al. 2008; Lipman a”