Fast and Accurate Intrinsic Symmetry Detection

Nagar, Rajendra; Raman, Shanmuganathan

doi:10.1007/978-3-030-01246-5_26

Cited by 17 publications

(51 citation statements)

References 59 publications

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“…More closely related to ours are recent methods based on advances in shape correspondence, especially the functional maps framework, including [Liu et al 2015;Nagar and Raman 2018;Ren et al 2018;Wang and Huang 2017]. These methods also aim to produce dense correspondences but in most cases require additional information such as detection of extremities [Liu et al 2015] or a priori knowledge of symmetry orbits of a specied landmark of the shape [Wang and Huang 2017].…”

Section: Intrinsic Symmetry Detectionmentioning

confidence: 97%

“…Some previous methods [Jain et al 2007;Mateus et al 2008;Ovsjanikov et al 2008;Rustamov 2007] try to solve the shape matching (or symmetry detection) problem by directly aligning each dimension of the spectral embedding to obtain correspondences. In the functional map language this means forcing the functional maps to be diagonal [Nagar and Raman 2018]. Our method aims to explore block-diagonal functional maps as initializations that we then rene to dense correspondences without imposing diagonality.…”

Section: Shape Matching With Functional Mapsmentioning

confidence: 99%

“…Here we show an example where dierent baselines lead to dierent local minima. Specifically, BIM [Kim et al 2011] obtains a back-to-front map, GroupRep [Wang and Huang 2017] leads to the direct map, IntSymm [Nagar and Raman 2018] leads to a back-to-front and le-to-right map, while ZoomOut [Melzi et al 2019b] that is initialized by OrientRev [Ren et al 2018] obtains a map with mixed symmetry.…”

Section: Introductionmentioning

confidence: 99%

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MapTree

et al. 2020

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In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in most previous approaches. To achieve this, we propose a compact tree structure based on the spectral map representation for encoding and enumerating possible rough initializations, and a novel efficient approach for refining them to dense pointwise maps. This leads to a new method capable of both producing multiple high-quality correspondences across shapes and revealing the symmetry structure of a shape without a priori information. In addition, we demonstrate through extensive experiments that our method is robust and results in more accurate correspondences than state-of-the-art for shape matching and symmetry detection.

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Section: Intrinsic Symmetry Detectionmentioning

confidence: 97%

Section: Shape Matching With Functional Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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MapTree

et al. 2020

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“…Average Error (×10 −3 ) Average Runtime (s) Method \ Dataset FAUST SCAPE FAUST SCAPE BIM [Kim et al 2011] 65.4 133 34.6 41.7 GroupRep [Wang and Huang 2017] 224 347 8.48 16.7 IntSymm [Nagar and Raman 2018] 33.9 60.3 1.35 1.81 OrientRev (Ini) [Ren et al 2018] 68.0 110 0.59 1.07 Ini + BCICP [Ren et al 2018] 29 map computations [Ren et al 2018]. Namely, we compute an initial 10 × 10 functional map by solving an optimization problem with exactly the same parameters as in [Ren et al 2018] and WKS descriptors as input, but instead of orientation-preserving, we promote orientation-reversing maps.…”

Section: Measurementmentioning

confidence: 99%

“…Error summary of symmetry detection. We compare with the recent state-of-the-art methods IntSymm[Nagar and Raman 2018] and GroupRep[Wang and Huang 2017], as well as to the baseline Blended Intrinsic Maps (BIM)[Kim et al 2011] and BCICP.…”

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confidence: 99%

ZoomOut

et al. 2019

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We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.155:2 • Melzi. et al the same or better quality at a fraction of the cost compared to the current top performing methods.(2) We demonstrate how higher-frequency information can be extracted from low-frequency spectral map representations. (3) We introduce a novel variational optimization problem and develop a theoretical justification of our method, shedding light on structural properties of functional maps. RELATED WORKShape matching is a very well-studied area of computer graphics. Below we review the methods most closely related to ours, concentrating on spectral techniques for finding correspondences between non-rigid shapes. We refer the interested readers to recent surveys including [Biasotti et al. 2016;Tam et al. 2013;Van Kaick et al. 2011] for a more in-depth treatment of the area.Point-based Spectral Methods. Early spectral methods for shape correspondence were based on directly optimizing pointwise maps between spectral shape embeddings based on either adjacency or Laplacian matrices of graphs and triangle meshes [Jain and Zhang 2006;Jain et al. 2007;Mateus et al. 2008;Ovsjanikov et al. 2010;Scott and Longuet-Higgins 1991;Umeyama 1988]. Such approaches suffer from the requirement of a good initialization, and rely on restricting assumptions about the type of transformation relating the shapes. An initialization algorithm with optimality guarantees, although limited to few tens of points, was introduced in [Maron et al. 2016] and later extended to deal with intrinsic symmetries in [Dym and Lipman 2017]. Spectral quantities (namely, sequences of Laplacian eigenfunctions) have also been used to define pointwise descriptors, and employed within variants of the quadratic assignment problem in Kimmel 2010, 2011]. These approaches have been recently generalized by spectral generalized multidimensional scaling [Aflalo et al. 2016], which explicitly formulates minimumdistortion shape correspondence in the spectral domain.

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