One Point Isometric Matching with the Heat Kernel

By M. Ovsjanikov, Quentin Mérigot, Facundo M'emoli, Leonidas J. Guibas. Computer graphics forum (Print), 2010

361 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/645abbf4e0ce72f2b65eae5a6d3d9a9021cf206d

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

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].”
Learning Structural Node Embeddings via Diffusion Wavelets (2017, methodology): “Kernels have been shown to efﬁciently capture geometrical properties and have been successfully used for shape detection in the image processing community (Sun et al., 2009; Ovsjanikov et al., 2010; Aubry et al., 2011).”
Functional maps (2012, methodology): “Given a pair of candidate segment matches s1, s2 on M and N respectively, we construct a set of functional constraints using the Heat Kernel Map [Ovsjanikov et al. 2010] based on segment correspondences.”
PointNetLK: Robust & Efficient Point Cloud Registration Using PointNet (2019, background): “For instance, scale invariant curvature descriptors [9], oriented descriptors [10], extended Gaussian images [19], fast point feature histograms [32], color intensity-based descriptors [11], global point signatures [6], heat kernels [25], etc.”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, methodology): “Minimumdistortion methods establish the matching by minimizing some structure distortion, which can include similarity of local features [30, 11, 6, 44], geodesic [27, 10, 12] or diffusion distances [14], or a combination thereof [40].”
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013, methodology): “[40] suggest that by fixing one correspondence, all other correspondences can be inferred for nonrigid shapes.”
FAUST: Dataset and Evaluation for 3D Mesh Registration (2014, background): “Common intrinsic representations include Generalized Multi-Dimensional Scaling (GMDS) [8], Möbius transformations [13, 15], and heat kernel maps [16].”
Product Manifold Filter: Non-rigid Shape Correspondence via Kernel Density Estimation in the Product Space (2017, methodology): “Minimum-distortion methods establish the matching by minimizing some structure distortion, which can include similarity of local features [32, 14, 8, 45], geodesic [29, 13, 15] or diffusion distances [17], or a combination thereof [41].”
Dense Human Body Correspondences Using Convolutional Networks (2015, background): “A recent focus is on spectral shape embedding and induced descriptors [17, 39, 30, 5, 28].”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “proved that the set of all HKS on the shape “almost always” characterizes it up to isometry, see [23] for details and [23,36–39] for applications of this invariant on shape analysis tasks.”
Blended intrinsic maps (2011, methodology): “For example, [Ovsjanikov et al. 2010] showed that a single correspondence can define a Heat Kernel Map (HKM), a high dimensional embedding of a surface invariant under isometry.”
Dense Non-rigid Shape Correspondence Using Random Forests (2014, background): “Most dense approaches [8, 14, 19, 15] are well-defined in the quasi-isometric and conformal cases only; instances of inter-class matching were considered in [8], but the success of the method depends on the specific choice of (usually hand-picked) feature points used in the subsequent optimization.”
Learning class‐specific descriptors for deformable shapes using localized spectral convolutional networks (2015, methodology): “…the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the surface [BBG94, CL06, Lév06]; popular methods include shapeDNA [RWP06], global point signature (GPS) [Rus07], heat kernel signatures (HKS) [SOG09,GBAL09], wave kernel signatures (WKS) [ASC11], and heat kernel maps [OMMG10].”