Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching

By A. Bronstein, Michael M. Bronstein, Ron Kimmel. 2006

615 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Geometric Deep Learning: Going beyond Euclidean data (2016, background): “[102], [103], [104], [105], [106]) have been devoted to designing local and global features e.”
Computational Optimal Transport (2018, methodology): “This distance is also tightly connected with the Gromov-Hausdorff distance [Gromov, 2001] between metric spaces, which have been used for shape matching Mémoli [2007], Bronstein et al. [2010].”
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, background): “Shape correspondence is an active area of research in computer vision, graphics, and pattern recognition, with a variety of both classical and recent methods [11, 23, 13].”
Deformable Shape Completion with Graph Convolutional Autoencoders (2017, background): “king directly on the embedding features. Thus, in our work we build upon [56] as a basic building block for convolution operations. Partial shape correspondences. Dense non-rigid shape correspondence [23,12,32,45,9] is a fundamental challenge as it is an enabler for many high level tasks like pose o”
Model Composition from Interchangeable Components (2007, background): “Others compute complete point-to-point correspondences [2, 14, 8].”
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.”
Blended intrinsic maps (2011, methodology): “• GMDS* - we use the method of [Bronstein et al. 2006] for surface matching.”
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013, methodology): “[37] use generalized multidimensional scaling to embed one mesh in another for partial matching, Bronstein et al.”
Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “The matching problem, although nontrivial, can significantly be simplified if the embedding manifold is known [57].”
Image Matching from Handcrafted to Deep Features: A Survey (2020, methodology): “This formulation was developed by Bronstein et al. (2006), who introduced a highly nonconvex and non-differentiable objective and generalized multidimensional scaling technique for optimization.”
Conformal Wasserstein distances: Comparing surfaces in polynomial time (2011, background): “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”