Partial Functional Correspondence

Rodolí, E.; Cosmo, Luca; Bronstein, Michael M.; Torsello, Andrea; Cremers, Daniel

doi:10.1111/cgf.12797

Cited by 206 publications

(213 citation statements)

References 34 publications

(58 reference statements)

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“…[KBBV15, PBB*13, RRBW*14, SK14, KBB*13, ERGB16]) and new consistent descriptors have been suggested [COC14, GSTOG16], these methods did not adjust the point‐wise recovery method. Recently, this framework was extended to computing partial correspondence [RCB*16, LRB*16, LRBB17], and to computing correspondences in shape collections [SBC14, HWG14, KGB16]. In addition, functional maps have been used for analysis and visualization of maps [OBCCG13, ROA*13], and image segmentation [WHG13].…”

Section: Related Workmentioning

confidence: 99%

Deblurring and Denoising of Maps between Shapes

Ezuz

Ben‐Chen

2017

Computer Graphics Forum

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Shape correspondence is an important and challenging problem in geometry processing. Generalized map representations, such as functional maps, have been recently suggested as an approach for handling difficult mapping problems, such as partial matching and matching shapes with high genus, within a generic framework. While this idea was shown to be useful in various scenarios, such maps only provide low frequency information on the correspondence. In many applications, such as texture transfer and shape interpolation, a high quality pointwise map that can transport high frequency data between the shapes is required. We name this problem map deblurring and propose a robust method, based on a smoothness assumption, for its solution. Our approach is suitable for non‐isometric shapes, is robust to mesh tessellation and accurately recovers vertex‐to‐point, or precise, maps. Using the same framework we can also handle map denoising, namely improvement of given pointwise maps from various sources. We demonstrate that our approach outperforms the state‐of‐the‐art for both deblurring and denoising of maps on benchmarks of non‐isometric shapes, and show an application to high quality intrinsic symmetry computation.

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Section: Related Workmentioning

confidence: 99%

Deblurring and Denoising of Maps between Shapes

Ezuz

Ben‐Chen

2017

Computer Graphics Forum

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“…For domains with boundary Bohle & Pinkall [BP13] showed that prescribing binormal boundary conditions preserves the self‐adjointness and ellipticity of the extrinsic Dirac operator (see [CPS13, Section 6.3] for a discretization); a similar argument may be possible for the relative Dirac operator. However, the shape of the boundary can cause trouble in spectral geometry processing particularly in the case of partial matching of surface patches [RCB∗17]. Rather than trying to “cut” the meshes so that they all have identical boundary shape, or resorting to potentially fragile re‐discretization ( e.g ., [BSK05]), we substitute standard boundary conditions for an infinite potential well that provides consistent behavior across patches with different boundary shapes or discretizations.…”

Section: Boundary Conditionsmentioning

confidence: 99%

A Dirac Operator for Extrinsic Shape Analysis

Liu

Jacobson

Crane

2017

Computer Graphics Forum

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The eigenfunctions and eigenvalues of the Laplace‐Beltrami operator have proven to be a powerful tool for digital geometry processing, providing a description of geometry that is essentially independent of coordinates or the choice of discretization. However, since Laplace‐Beltrami is purely intrinsic it struggles to capture important phenomena such as extrinsic bending, sharp edges, and fine surface texture. We introduce a new extrinsic differential operator called the relative Dirac operator, leading to a family of operators with a continuous trade‐off between intrinsic and extrinsic features. Previous operators are either fully or partially intrinsic. In contrast, the proposed family spans the entire spectrum: from completely intrinsic (depending only on the metric) to completely extrinsic (depending only on the Gauss map). By adding an infinite potential well to this (or any) operator we can also robustly handle surface patches with irregular boundary. We explore use of these operators for a variety of shape analysis tasks, and study their performance relative to operators previously found in the geometry processing literature.

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“…Another related set of techniques adopts the functional map framework, introduced in [29] and later extended significantly, e.g., in [20,32,35]. These methods work by establishing linear mappings between general real-valued functions and have been used to find related regions on shapes (see [30] for an overview).…”

Section: Generalized Shape Correspondencementioning

confidence: 99%

“…These techniques are better suited to the general shape correspondence problem, as they do not seek precise (e.g., bijective) maps between points, easily accommodating significant sampling, geometric, or even topological changes [35]. Furthermore, those soft maps can also be used as input to more refined point-based correspondence methods, to help improve the robustness and accuracy thereof [10].…”

Section: Introductionmentioning

confidence: 99%

Region-Based Correspondence Between 3D Shapes via Spatially Smooth Biclustering

Denitto

Melzi

Bicego

et al. 2017

2017 IEEE International Conference on Computer Vision (ICCV)

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Region-based correspondence (RBC) is a highly relevant and non-trivial computer vision problem. Given two 3D shapes, RBC seeks segments/regions on these shapes that can be reliably put in correspondence. The problem thus consists both in finding the regions and determining the correspondences between them. This problem statement is similar to that of "biclustering", implying that RBC can be cast as a biclustering problem. Here, we exploit this implication by tackling RBC via a novel biclustering approach, called S 4 B (spatially smooth spike and slab biclustering), which: (i) casts the problem in a probabilistic low-rank matrix factorization perspective; (ii) uses a spike and slab prior to induce sparsity; (iii) is enriched with a spatial smoothness prior, based on geodesic distances, encouraging nearby vertices to belong to the same bicluster. This type of spatial prior cannot be used in classical biclustering techniques. We test the proposed approach on the FAUST dataset, outperforming both state-of-the-art RBC techniques and classical biclustering methods.

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Partial Functional Correspondence

Cited by 206 publications

References 34 publications

Deblurring and Denoising of Maps between Shapes

Deblurring and Denoising of Maps between Shapes

A Dirac Operator for Extrinsic Shape Analysis

Region-Based Correspondence Between 3D Shapes via Spatially Smooth Biclustering

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