40-Issue 1

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https://diglib.eg.org/handle/10.2312/2633015

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Browsing 40-Issue 1 by Subject "3D shape matching"

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    Anisotropic Spectral Manifold Wavelet Descriptor
    (© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2021) Li, Qinsong; Hu, Ling; Liu, Shengjun; Yang, Dangfu; Liu, Xinru; Benes, Bedrich and Hauser, Helwig
    In this paper, we present a powerful spectral shape descriptor for shape analysis, named Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). We proposed a novel manifold harmonic signal processing tool termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) first. ASMWT allows to comprehensively analyse signals from multiple wavelet diffusion directions on local manifold regions of the shape with a series of low‐pass and band‐pass frequency filters in each direction. Based on the ASMWT coefficients of a very simple signal, the ASMWD is efficiently constructed as a localizable and discriminative multi‐scale point descriptor. Since the wavelets used in our descriptor are direction‐sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor compact, efficient, and unambiguous under intrinsic symmetry. The extensive experiments demonstrate that our descriptor achieves significantly better performance than the state‐of‐the‐art descriptors and can greatly improve the performance of shape matching methods including both handcrafted and learning‐based methods.
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    ECHO: Extended Convolution Histogram of Orientations for Local Surface Description
    (© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2021) Mitchel, Thomas W.; Rusinkiewicz, Szymon; Chirikjian, Gregory S.; Kazhdan, Michael; Benes, Bedrich and Hauser, Helwig
    This paper presents a novel, highly distinctive and robust local surface feature descriptor. Our descriptor is predicated on a simple observation: instead of describing the points in the vicinity of a feature point relative to a reference frame at the feature point, all points in the region describe the feature point relative to their own frames. Isometry invariance is a byproduct of this construction. Our descriptor is derived relative to the extended convolution – a generalization of the standard convolution that allows the filter to adaptively transform as it passes over the domain. As such, we name our descriptor the Extended Convolution Histogram of Orientations (ECHO). It exhibits superior performance compared to popular surface descriptors in both feature matching and shape correspondence experiments. In particular, the ECHO descriptor is highly stable under near‐isometric deformations and remains distinctive under significant levels of noise, tessellation, complex deformations and the kinds of interference commonly found in real data.
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    Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
    (© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2021) Kirgo, Maxime; Melzi, Simone; Patanè, Giuseppe; Rodolà, Emanuele; Ovsjanikov, Maks; Benes, Bedrich and Hauser, Helwig
    In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.