Regularized Pointwise Map Recovery from Functional Correspondence

Rodolà, Emanuele; Moeller, Michael; Cremers, Daniel

doi:10.1111/cgf.13160

Cited by 39 publications

(47 citation statements)

References 42 publications

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“…The latter category has been particularly prominent, especially since methods built on the notion of soft mappings can take advantage of the recent advances in solving optimal transport problems, [Mandad et al 2017;Solomon et al 2015Solomon et al , 2016, or, alternatively, reduce to solving a simple least squares problem in the case of the functional maps framework [Kovnatsky et al 2013;Ovsjanikov et al 2012. At the same time, while computing soft or functional maps can be done efficiently, extracting continuous or bijective pointwise maps is often challenging and error prone [Rodolà et al 2015].…”

Section: Introductionmentioning

confidence: 99%

Continuous and orientation-preserving correspondences via functional maps

et al. 2018

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Fig. 1. Given a pair of shapes, our method produces a point-wise map that is orientation-preserving as well as approximately continuous and bijective. Here we show the maps produced by different methods via texture transfer: BIM [Kim et al. 2011] has a large distortion on the face and the left hand; functional maps with ICP [Ovsjanikov et al. 2012] and PMF with the Gauss kernel [Vestner et al. 2017b] give a map that is flipped left to right; for PMF with the heat kernel [Vestner et al. 2017a], the orientation in the torso region is reversed; The map produced by our method preserves the orientation consistently and has lower overall error when compared to the ground-truth.We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.

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Section: Introductionmentioning

confidence: 99%

Continuous and orientation-preserving correspondences via functional maps

et al. 2018

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“…We then solve the problem above globally by a nearest‐neighbour approach akin to [OBCS*12]. Note that while more sophisticated approaches exist for this step, they either tend to be very slow [RMC17, VLR*17] or do not demonstrate any result with partial shapes [RMC15, EBC17]. Conversely, problem is both scalable and works under missing geometry.…”

Section: Proposed Methodsmentioning

confidence: 99%

FARM: Functional Automatic Registration Method for 3D Human Bodies

Marin

Melzi

Rodolà

et al. 2019

Computer Graphics Forum

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We introduce a new method for non‐rigid registration of 3D human shapes. Our proposed pipeline builds upon a given parametric model of the human, and makes use of the functional map representation for encoding and inferring shape maps throughout the registration process. This combination endows our method with robustness to a large variety of nuisances observed in practical settings, including non‐isometric transformations, downsampling, topological noise and occlusions; further, the pipeline can be applied invariably across different shape representations (e.g. meshes and point clouds), and in the presence of (even dramatic) missing parts such as those arising in real‐world depth sensing applications. We showcase our method on a selection of challenging tasks, demonstrating results in line with, or even surpassing, state‐of‐the‐art methods in the respective areas.

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“…This is popular because it reduces the dimensionality of the problem from the number of vertices to the number of basis functions chosen [OBS*12]. Nevertheless, extracting the correspondence from the low dimensional representation is still a complex problem and often retrieved solutions are noisy or hard to compute [RMC15]. One major problem with purely spectral approaches is that intrinsic symmetries can not be distinguished, [RPWO18] being one of few exceptions.…”

Section: Shape Registration and Matchingmentioning

confidence: 99%

Divergence‐Free Shape Correspondence by Deformation

Eisenberger

Lähner

Cremers

2019

Computer Graphics Forum

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We present a novel approach for solving the correspondence problem between a given pair of input shapes with non‐rigid, nearly isometric pose difference. Our method alternates between calculating a deformation field and a sparse correspondence. The deformation field is constructed with a low rank Fourier basis which allows for a compact representation. Furthermore, we restrict the deformation fields to be divergence‐free which makes our morphings volume preserving. This can be used to extract a correspondence between the inputs by deforming one of them along the deformation field using a second order Runge‐Kutta method and resulting in an alignment of the inputs. The advantages of using our basis are that there is no need to discretize the embedding space and the deformation is volume preserving. The optimization of the deformation field is done efficiently using only a subsampling of the orginal shapes but the correspondence can be extracted for any mesh resolution with close to linear increase in runtime. We show 3D correspondence results on several known data sets and examples of natural intermediate shape sequences that appear as a by‐product of our method.

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Regularized Pointwise Map Recovery from Functional Correspondence

Cited by 39 publications

References 42 publications

Continuous and orientation-preserving correspondences via functional maps

Continuous and orientation-preserving correspondences via functional maps

FARM: Functional Automatic Registration Method for 3D Human Bodies

Divergence‐Free Shape Correspondence by Deformation

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