The wave kernel signature: A quantum mechanical approach to shape analysis

By Mathieu Aubry, Ulrich Schlickewei, Daniel Cremers. 2011

851 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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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.”
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): “Minimum-distortion methods establish the matching by minimizing some structure distortion, which can include similarity of local features [OMMG10,ASC11,ZBVH09], geodesic [MS05,BBK06,CK15] or diffusion distances [CLL ∗ 05], or a combination thereof [TKR08], or higher-order structures [Z ∗ 10].”
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, methodology): “, based on the eigen-decomposition of the Laplacian), demonstrating noticeable improvement upon the classical axiomatic constructions [37, 5].”
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.”
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].”
Learning class‐specific descriptors for deformable shapes using localized spectral convolutional networks (2015, methodology): “We compared the performance of the proposed approach to HKS [SOG09], WKS [ASC11], OSD [LB14], spectral CNN (SCNN) [BZSL14], and ShapeNet (SN1) [MBBV15] using the code and settings provided by the respective authors.”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, methodology): “Recent works proposed a plethora of descriptors such as those based on conformal factor [BCG08], autodiffusion [GBAL09] or the heat kernel signature [SOG09] and its scale-[BK10b] and afﬁne-invariant versions [RBB*11, RK14], and the wave kernel signature [ASC11].”
An Aligned Subtree Kernel for Weighted Graphs (2015, background): “Thus, the CTQW can capture rich topological information in a graph structure (Aubry et al., 2011; Rossi et al., 2013b; Suau et al., 2013).”
Anisotropic Diffusion Descriptors (2016, methodology): “Aubry et al. [ASC11] proposed to deﬁne a shape descriptor by looking at the behavior of a quantum particle on the manifold.”
Intrinsic shape context descriptors for deformable shapes (2012, background): “In [1], another physically-inspired descriptor, the wave kernel signature (WKS) was proposed as a solution to the excessive sensitivity of the HKS to low-frequency information.”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, methodology): “Minimumdistortion methods establish the matching by minimizing some structure distortion, which can include similarity of local features [30, 11, 6, 44], geodesic [27, 10, 12] or diffusion distances [14], or a combination thereof [40].”