Functional Characterization of Deformation Fields

Corman, Etienne; Ovsjanikov, Maks

doi:10.1145/3292480

Cited by 6 publications

(9 citation statements)

References 69 publications

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“…We believe that our approach can serve as an important new tool in the shape analysis and correspondence toolbox. Future work and generalizations include using other inner product metrics to tailor the shape differences for specific applications [CO19], and using better regularization constraints [RPWO19]. Moreover, it might be beneficial to use multiple base shapes, and to learn the shape differences operators from data.…”

Section: Discussionmentioning

confidence: 99%

Robust Shape Collection Matching and Correspondence from Shape Differences

Cohen

Ben‐Chen

2020

Computer Graphics Forum

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We propose a method to automatically match two shape collections with a similar shape space structure, e.g. two characters in similar poses, and compute the inter‐maps between the collections. Given the intra‐maps in each collection, we extract the corresponding shape difference operators, and use them to construct an embedding of the shape space of each collection. We then align the two shape spaces, and use the knowledge gained from the alignment to compute the inter‐maps. Unlike existing approaches for collection alignment, our method is applicable to small and large collections alike, and requires no parameter tuning. Furthermore, unlike most approaches for non‐isometric correspondence, our method uses solely the variation within the collection to extract the inter‐maps, and therefore does not require landmarks, descriptors or any additional input. We demonstrate that we achieve high matching accuracy rates, and compute high quality maps on non‐isometric shapes, which compare favorably with automatic state‐of‐the‐art methods for non‐isometric shape correspondence.

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Section: Discussionmentioning

confidence: 99%

Robust Shape Collection Matching and Correspondence from Shape Differences

Cohen

Ben‐Chen

2020

Computer Graphics Forum

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“…For articulated objects, like human bodies, extrinsic properties are not capable of describing their intrinsic properties, like shapes and symmetric properties. Although suffering from topological noise, isometry-preserving properties are widely used for human-related analysis, e.g., the methods from [80,81,82,83,84,85] are utilized for human shape analysis, and the method from [86] is utilized for human shape recognition. Geometric methods are also isometry-preserving methods.…”

Section: Geometric Method-based Human-related Analysismentioning

confidence: 99%

“…For HSA, the paper reviews the related works on human shape correspondence, human model symmetry analysis, and human shape recognition. For human shape correspondence, the authors in [83] represented a deformation field as a linear operator on real-valued functions on the shape and gave the state-of-the-art performance on human shape correspondence. An exemplary result is illustrated in Figure 25.…”

Section: Performances Of Related Workmentioning

confidence: 99%

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A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

Gong

Zhang

Wang

et al. 2019

Sensors

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Geometric features, such as the topological and manifold properties, are utilized to extract geometric properties. Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision problems. This review presents a literature review on geometric concepts, geometric methods, and their applications in human-related analysis, e.g., human shape analysis, human pose analysis, and human action analysis. This review proposes to categorize geometric methods based on the scope of the geometric properties that are extracted: object-oriented geometric methods, feature-oriented geometric methods, and routine-based geometric methods. Considering the broad applications of deep learning methods, this review also studies geometric deep learning, which has recently become a popular topic of research. Validation datasets are collected, and method performances are collected and compared. Finally, research trends and possible research topics are discussed.

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“…Moreover, our simple Crouzeix-Raviart discretization of the oneform Dirichlet energy containing covariant derivatives from Section 6.2 offers an interesting approach to discretize the vector Dirichlet energy in a wide variety of applications. Potential applications include vector field design [Knöppel et al 2013], parallel transport of vectors [Sharp et al 2018], and many more [Azencot et al 2015;Corman and Ovsjanikov 2019;Liu et al 2016]. Stein et al [2018] (α = 2.5⋅10 -9 ) our Hessian energy (α = 1.8⋅10 -9 )…”

Section: Future Workmentioning

confidence: 99%

A Smoothness Energy without Boundary Distortion for Curved Surfaces

et al. 2020

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Laplacian energy (zero Neumann boundary conditions) planar Hessian energyStein et al. [2018] our Hessian energy Fig. 1. Solving an interpolation problem on an airplane. Using the Laplacian energy with zero Neumann boundary conditions (left) distorts the result near the windows and the cockpit of the plane: the isolines bend so they can be perpendicular to the boundary. The planar Hessian energy of Stein et al. [2018] (center)is unaffected by the holes, but does not account for curvature correctly, leading to unnatural spacing of isolines at the front and back of the fuselage. Our Hessian energy (right) produces a natural-looking result with more regularly spread isolines, unaffected by the boundary.Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking behavior away from the boundary. This leads to an unfortunate trade-off: one can either have natural behavior in the interior, or a distortion-free result at the boundary, but not both. We introduce a generalized Hessian energy for curved surfaces, expressed in terms of the covariant one-form Dirichlet energy, the Gaussian curvature, and the exterior derivative. Energy minimizers solve the Laplace-Beltrami biharmonic equation, correctly accounting for intrinsic curvature, leading to natural-looking isolines. On the boundary, minimizers are as-linear-as-possible, which reduces the distortion of isolines at the boundary. We discretize the covariant one-form Dirichlet energy using Crouzeix-Raviart finite elements, arriving at a discrete formulation of the Hessian energy for applications on curved surfaces. We observe convergence of the discretization in our experiments.

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Functional Characterization of Deformation Fields

Cited by 6 publications

References 69 publications

Robust Shape Collection Matching and Correspondence from Shape Differences

Robust Shape Collection Matching and Correspondence from Shape Differences

A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

A Smoothness Energy without Boundary Distortion for Curved Surfaces

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