Laplace-Beltrami eigenfunctions for deformation invariant shape representation

By Raif M. Rustamov. 2007

722 citations recorded by the source corpus.

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Citations in the corpus

Dynamic Graph CNN for Learning on Point Clouds (2018, background): “nating from each connected vertex. expressed in terms of the metric are invariant to isometric deformation. Representatives of this class include spectral descriptors such as global point signatures [Rustamov 2007], the heat and wave kernel signatures [Aubry et al. 2011; Sun et al. 2009], and varian”
Dense Non-rigid Shape Correspondence Using Random Forests (2014, methodology): “Among the wide range of available choices [18, 21] we have opted for the recently introduced Wave Kernel Signature (WKS) [1].”
Intrinsic shape context descriptors for deformable shapes (2012, background): “These distances as well as other diffusion geometric constructs [33, 10] have been shown sig-niﬁcantly more robust compared to their geodesic counter-parts.”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, methodology): “Inspired by the work [4], Rustamov [23] used the Laplace eigenfunctions to define an embedding of the surface in the space of convergent sequences 2 (R).”
Anisotropic Laplace-Beltrami Operators for Shape Analysis (2014, unknown): “Computing the LB operator directly on meshes with approaches such as [18, 15, 20], numerous works exploit the information contained in its eigen-decomposition to build a new representation of a shape, either by explicit formulas [23, 24, 1] or by learning [13, 22].”
Functional maps (2012, methodology): “Our use of spectral quantities is also closely related to spectral embeddings [Rustamov 2007] and their application in shape matching [Jain et al. 2007; Mateus et al. 2008; Ovsjanikov et al. 2008].”
Interior Distance Using Barycentric Coordinates (2009, background): “Diffusion distance [CLL ∗ 05] and GPS distance [Rus07] are such examples.”
A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching (2010, methodology): “…framework with geodesic distances (Bronstein et al. 2006b; Mémoli and Sapiro 2005b), canonical forms with geodesic distances (Elad and Kimmel 2003), canonical forms with diffusion distances (diffusion maps (Coifman et al. 2005)), and, for reference, Rustamov's GPS embedding (Rustamov 2007).”
Spectral Mesh Processing (2009, methodology): “[Rus07] R. M. Rustamov.”
Deepshape: Deep learned shape descriptor for 3D shape matching and retrieval (2015, methodology): “The high dimensional vector is called GPS.”
Anisotropic Diffusion Descriptors (2016, background): “Examples of such structures include diffusion distances [CL06, LRF10], global point signatures [Rus07], heat-[SOG09,GBAL09] and wave-kernel [ASC11] signatures, heat kernel maps [OMMG10], stable regions [LBB11, RRBC14], functional maps [O ∗ 12,R ∗ 16], and shape difference operators [R ∗ 13].”
Self-supervised Learning of Dense Shape Correspondence (2018, methodology): “This has been an active research goal in shape analysis in the last few years, with examples including GPS [38], heat and wave kernel signatures [41, 6], and the more recent geodesic distance descriptors [40].”
3D deep shape descriptor (2015, methodology): “With recent advancements in 3D acquisition and printing techniques, we have observed an exponential increase in 3D-meshed surface models across a variety of fields, such as engineering, entertainment, and medical imaging [41, 36, 28, 12, 11, 8, 40, 1].”