Learning Spectral Descriptors for Deformable Shape Correspondence

By Roee Litman, A. Bronstein. 2014

161 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): “For instance, in computer graphics and vision applications, one can analyze 3D shapes represented as meshes by constructing local geometric descriptors capturing e.g. curvature-like properties [46], [47].”
Learning shape correspondence with anisotropic convolutional neural networks (2016, methodology): “Analogously to equation (8), the anisotropic heat kernel is given by This construction was used in Anisotropic Diffusion Descrip-tors (ADD) [BMR ∗ 16] to generalize the OSD approach using anisotropic heat kernels (considering the diagonal h αθ t ( x , x ) and learning a set of optimal task-speciﬁc s”
FPNN: Field Probing Neural Networks for 3D Data (2016, background): “While 3D data is represented as meshes, neural networks can benefit from intrinsic constructions[17, 18, 1, 2] to learn object invariance to isometries, thus require less training data for handling deformable objects.”
Dense Human Body Correspondences Using Convolutional Networks (2015, background): “A second popular objective is to match selected subsets of points on the two surfaces with similar feature descriptors [35, 48, 26, 5].”
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, methodology): “We compare with state-of-the-art learning-based approaches for deformable shape correspondence, namely optimal spectral descriptors (OSD) [28], geodesic CNNs (GCNN) [29], localized spectral CNNs (LSCNN) [8], and two variants of anisotropic diffusion descriptors (ADD3, mADD3) [10].”
Learning class‐specific descriptors for deformable shapes using localized spectral convolutional networks (2015, methodology): “To make the comparison fair, all the descriptors were Q = 16-dimensional as in [LB14].”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, methodology): “These techniques represent a possible solution to automatically determine the weights of the different shape features on the basis of context (e.g. the shape classes of a database) [Lag10, BB13b, BSF13, TDVC13] or design class-or application-speciﬁc shape descriptors [LB14, MBBV15, BMM*15].”
Geodesic Convolutional Neural Networks on Riemannian Manifolds (2015, methodology): “Arguing that in many cases it is hard to model invariance but rather easy to create examples of similar and dissimilar shapes, Litman and Bronstein [29] showed that HKS and WKS can be considered as particular parametric families of transfer functions applied to the Laplace-Beltrami operator eigenval”
Image Matching from Handcrafted to Deep Features: A Survey (2020, background): “Litman and Bronstein (2014) generalized the spectral descriptors to a generic family and proposed to learn from examples for obtaining optimized descriptors for a specific task.”
Anisotropic Diffusion Descriptors (2016, methodology): “Learning optimal anisotropic kernels can be considered as an extension of the optimal spectral descriptors method of [LB14].”
Geometric deep learning (2016, methodology): “The main idea of [56] is to learn the optimal parameters A by minimizing a task-speciﬁc loss which reduces to a Mahalanobis-type metric learning.”
GRAND: Graph Neural Diffusion (2021, background): “The solution can be represented as a spectral transfer function (Patané, 2016), which can also be learned (Litman & Bronstein, 2013).”