Scale-invariant heat kernel signatures for non-rigid shape recognition

By Michael M. Bronstein, Iasonas Kokkinos. 2010

667 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning

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Citations in the corpus

PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation (2016, background): “Point features often encode certain statistical properties of points and are designed to be invariant to certain transformations, which are typically classified as intrinsic [2, 21, 3] or extrinsic [18, 17, 13, 10, 5].”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “[102], [103], [104], [105], [106]) have been devoted to designing local and global features e.”
Dynamic Graph CNN for Learning on Point Clouds (2018, background): “on. Representatives of this class include spectral descriptors such as global point signatures [Rustamov 2007], the heat and wave kernel signatures [Aubry et al. 2011; Sun et al. 2009], and variants [Bronstein and Kokkinos 2010]. Most recently, several approaches wrap machine learning schemes around”
Distilling Knowledge From Graph Convolutional Networks (2020, methodology): “Deep learning based methods [39, 11, 7, 20, 29, 26] outperform the previous methods that based on hand-crafted feature extractors [1, 3].”
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013, methodology): “Bronstein and Kokkinos [74] use the Fourier transform to avoid scale differences and define a scaleinvariant version of HKS.”
SoftGroup for 3D Instance Segmentation on Point Clouds (2022, methodology): “To process point clouds, early methods [2,3,36,37] extract hand-crafted features based on statistical properties of points.”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, background): “These problems are becoming increasingly important due to the emergence of affordable 3D sensing technology.”
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].”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, background): “• The WKS can easily be made scale-invariant as done in [7] for the heat kernel signature.”
Image Matching from Handcrafted to Deep Features: A Survey (2020, methodology): “The disadvantage of sensitivity to scale of HKSwas addressed by Bronstein and Kokkinos (2010), who used Fourier transform magnitude to extract a scale-invariant quantity from the HKS without the need to perform scale selection.”
Deep Learning Advances in Computer Vision with 3D Data (2017, methodology): “In the work of Bu et al. [2014], two local descriptors, that is, Scale Invariant Heat Kernel Signature (SI-HKS) [Bronstein and Kokkinos 2010] and Average Geodesic Distance (AGD) [Hilaga et al. 2001], were initially extracted from each 3D model and a ﬁnal low-level descriptor was formed by…”
GRAND: Graph Neural Diffusion (2021, methodology): “In computer graphics, solutions of non-Euclidean diffusion equations were studied as heat kernel signature (Sun et al., 2009; Bronstein & Kokkinos, 2010) local shape descriptors related to the Gaussian curvature.”
Intrinsic shape context descriptors for deformable shapes (2012, methodology): “A scale-invariant version of HKS (SIHKS) was developed in [11], and a photometric HKS in [25].”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, methodology): “The scale-invariant HKS (SI-HKS) was proposed by Bronstein et al. [BK10b] to overcome the scale dependence of the standard HKS and inherits its autodiffusion-related structure.”