Integral Invariants for Shape Matching

By S. Manay, Daniel Cremers, Byung-Woo Hong, Anthony J. Yezzi Jr., Stefano Soatto. 2006

278 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Geometry and Topology

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Citations in the corpus

Group Equivariant Convolutional Networks (2016, methodology): “Invariance can be achieved by pose normalization using an equivariant detector (Lowe, 2004; Jaderberg et al., 2015) or by averaging a possibly nonlinear function over a group (Reisert, 2008; Skibbe, 2013; Manay et al., 2006; Kondor, 2007).”
Dynamic Graph CNN for Learning on Point Clouds (2018, background): “trinsic descriptors. Extrinsic descriptors usually are derived from the coordinates of the shape in 3D space and includes classical methods like shape context [3], spin images [17], integral features [27], distance-based descriptors [24], point feature histograms [39, 38], and normal histograms [50]”
Geodesic Convolutional Neural Networks on Riemannian Manifolds (2015, background): “Previous work Early works on shape descriptors such as spin images [19], shape distributions [34], and integral volume descriptors [32] were based on extrinsic structures that are invariant under Euclidean transformations.”
Leafsnap: A Computer Vision System for Automatic Plant Species Identification (2012, background): “[14] concatenated integral measures of curvature along the contour of the object into a single feature vector.”
Robust reconstruction of indoor scenes (2015, methodology): “[16] with subsampling based on integral invariants [42, 20].”
Is Rotation a Nuisance in Shape Recognition? (2014, methodology): “Our approach used the curvature scale space and outperformed the state of the art.”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, background): “Such descriptors also include the Integral Invariants [19], the Multiscale Local Signature [14] and the Point-Aware Metric [18].”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “[2], the integral invariants of [3], the eccentricity functions of [4], the shape distributions of [5], the canonical forms of [6], and the Shape-DNA methods in [7].”
Gromov–Wasserstein Distances and the Metric Approach to Object Matching (2011, background): “In [4, 74, 91], similar invariants were proposed where to each point a ∈ A one attaches the histogram or distribution of distances ‖a − a′‖ for all a′ ∈ A.”
Learning class‐specific descriptors for deformable shapes using localized spectral convolutional networks (2015, background): “Descriptors like spin images [JH99], shape distributions [OFCD02], integral volume descriptors [MCH ∗ 06], and multi-scale features [PKG03] are based on extrinsic structure of the shape and therefore invariant under Euclidean transformations, but not under deformations.”