Eurographics Symposium on Geometry Processing 2009 a Concise and Provably Informative Multi-scale Signature Based on Heat Diffusion

By Marc Alexa, Michael M. Kazhdan, Jian Sun, M. Ovsjanikov, Leonidas J. Guibas

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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].”
PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space (2017, methodology): “To generate the input intrinsic features, we to extract 100 dimensional WKS, HKS and multiscale Gaussian curvature respectively, leading to a 300 dimensional feature vector for each point.”
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].”
Dynamic Graph CNN for Learning on Point Clouds (2018, background): “are by deﬁnition intrinsic and invariant to isometric deformation. Representatives of this class include spectral descriptors such as global point signatures [37], the heat and wave kernel signatures [48, 2], and variants [8]. Most recently, several approaches wrap machine learning schemes around st”
Learning shape correspondence with anisotropic convolutional neural networks (2016, methodology): “Litman and Bronstein [LB14] learned optimal spectral descriptors that generalize the popular “handcrafted” heat-[SOG09,GBAL09] and wave-kernel signatures [ASC11] and show performance superior to both.”
FPNN: Field Probing Neural Networks for 3D Data (2016, background): “Heat kernel signatures extract shape descriptions by simulating an heat diffusion process on 3D shapes [29, 3].”
Dense Human Body Correspondences Using Convolutional Networks (2015, background): “A recent focus is on spectral shape embedding and induced descriptors [17, 39, 30, 5, 28].”
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, methodology): “, HKS [37] or SHOT [38]) on X and Y are used as the corresponding functions.”
Deformable Shape Completion with Graph Convolutional Autoencoders (2017, background): “In an attempt to ﬁnd dense correspondences between the point cloud extracted from the Kinect sensor and a model of a human, we have noticed that off-the-shelf descriptors such as SHOT [53], HKS [51] and WKS [3], did not transfer well between the partial point cloud and the full mesh domains.”
The Multiscale Laplacian Graph Kernel (2016, background): “cal (and permutation invariant) vertex features. For example, φi(vj) may be the degree of vertex vj, or the value of hβ(vj,vj), where his the diffusion kernel on Gwith length scale parameter β(c.f., (Alexa et al., 2009)). In the chemoinformatics setting, the φi’s might be some way of encoding what t”
LPD-Net: 3D Point Cloud Learning for Large-Scale Place Recognition and Environment Analysis (2018, background): “Handcrafted local features, such as the histogram feature [14], the inner-distance-based descriptor [8] and the heat kernel signatures [21], are widely used for point cloudbased recognition tasks, but they are usually designed for specific applications and have a poor generalization ability.”
Shape‐from‐Operator: Recovering Shapes from Intrinsic Operators (2015, methodology): “Typically, intrinsic descriptors such as heat kernel signature (HKS) [SOG09] or stable regions [LBB11] are used as columns of matrices P , S , making the functional map F intrinsic.”
Graph Representation Learning via Multi-task Knowledge Distillation (2019, methodology): “For more details of the graph representation, we refer the readers to the paper [8] for the DeepGraph model and the paper [13] for the original HKS literature.”
Functional maps (2012, methodology): “We also used the Wave Kernel Signature (WKS) and Heat Kernel Signature descriptors of [Aubry et al. 2011] and [Sun et al. 2009].”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “1 we prove that two (interrelated) invariants: the HKS of [23,36] and the heat trace, are both stable with respect to the metric we construct.”