A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching

By A. Bronstein, Michael M. Bronstein, Ron Kimmel, Mona Mahmoudi, Guillermo Sapiro. International Journal of Computer Vision, 2010

309 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/684121bcfc654330bd94da179a1bbd2ffd577065

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “A second, third and fourth sets of previously proposed ideas that we address with our construction and relate to are those of [20,27,28] and [24].”
Learning Spectral Descriptors for Deformable Shape Correspondence (2014, background): “These distances as well as other diffusion geometric constructs have been show significantly more robust compared to their geodesic counterparts [15], [16].”
Scale-invariant heat kernel signatures for non-rigid shape recognition (2010, methodology): “In [5], shapes were analyzed as metric spaces equipped with diffusion metrics.”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, background): “The heat kernel is intimately related to the diffusion distance between points which has been used intensively for shape analysis recently (cf. e.g. [6]).”
3D deep shape descriptor (2015, background): “Recent efforts on robust 3D shape feature development are mainly based on diffusion [45, 9, 41, 37].”
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].”
Gromov-Wasserstein Learning for Graph Matching and Node Embedding (2019, background): “It can also be viewed as a relaxation of Gromov-Hausdorff distance (Mémoli, 2008; Bronstein et al., 2010) when pairwise distance between entities is defined.”
Shape google: Geometric words and expressions for invariant shape retrieval (2011, methodology): “Finally, another promising direction is the use of multimodal hashing [Bronstein et al. 2010e] to cope with the problem of cross-representation retrieval and different versions of vocabularies.”
Dense Human Body Correspondences Using Convolutional Networks (2015, background): “One popular objective is to measure preservation of pair-wise geodesic [9] or diffusion [8] distances.”
Deepshape: Deep learned shape descriptor for 3D shape matching and retrieval (2015, methodology): “Apart from the earlier shape descriptors, another popular approaches to shape retrieval are diffusion based methods [27, 7, 23].”