A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data

By Facundo M'emoli, Guillermo Sapiro. Foundations of Computational Mathematics, 2005

351 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0729fab2d95fed4b3e94ff45d5f0f67f5c3d0e15

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Citations in the corpus

A spectral notion of Gromov–Wasserstein distance and related methods (2011, methodology): “All these properties are desirable, see [8,9,13].”
Learning shape correspondence with anisotropic convolutional neural networks (2016, methodology): “Minimum-distortion methods establish the matching by minimizing some structure distortion, which can include similarity of local features [OMMG10,ASC11,ZBVH09], geodesic [MS05,BBK06,CK15] or diffusion distances [CLL ∗ 05], or a combination thereof [TKR08], or higher-order structures [Z ∗ 10].”
A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching (2010, methodology): “Best results are in bold This corresponds to results previously reported in the literature (Mémoli and Sapiro 2005b; Bronstein et al. 2006b), and reflects the fact that canonical forms can be regarded as an approximation to a distance between metric spaces.”
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].”
Partial Similarity of Objects, or How to Compare a Centaur to a Horse (2009, background): “A particular case complying to this model are articulated shapes , consisting of rigid parts connected by non-rigid joints (Geiger et al. 1998; Jacobs et al. 2000; Elad and Kimmel 2003; Zhang et al. 2004; Ling and Jacobs 2005; Mémoli and Sapiro 2005; Bronstein et al. 2006e).”
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].”
Conformal Wasserstein distances: Comparing surfaces in polynomial time (2011, methodology): “is crucial to ensure that the algorithm can be used eectively in applications. A prominent mathematical approach to dene distances between surfaces that has been proposed for practical applications [10, 11] is the Gromov-Hausdor (GH) distance; it considers the surfaces as special cases of metric spa”
Efficient Globally Optimal 2D-to-3D Deformable Shape Matching (2016, neutral): “Several popular methods try to find a correspondence that minimally distorts intrinsic distances between pairs of corresponding points by approximate solution to the quadratic assignment problem [13, 16, 6, 21, 25].”
3D-CODED: 3D Correspondences by Deep Deformation (2018, background): “, geodesic distances) remains relatively consistent across all poses [29].”
Scale-invariant heat kernel signatures for non-rigid shape recognition (2010, background): “Elad and Kimmel [12] and follow-up works [26] [8] proposed modeling shapes as metric spaces with intrinsic (e.g. geodesic) distances, which are invariant to inelastic deformations .”
One Point Isometric Matching with the Heat Kernel (2010, neutral): “Furthermore, many measures of similarity between shapes are de-ﬁned through the quality of the maps between them [MS05].”
Dense Non-rigid Shape Correspondence Using Random Forests (2014, background): “Nevertheless, while the advances made by works such as [12, 3, 18, 21, 1, 8] have been dramatic, the problem is far from being solved.”
The Gromov–Hausdorff distance between spheres (2021, background): “The Gromov-Hausdorff distance is also a natural choice for expressing the stability of invariants in applied algebraic topology [5, 6, 7] and has also been invoked in applications related to shape matching [3, 23, 24] as a notion of dissimilarity between shapes.”