Cyclic Functional Mapping: Self-supervised Correspondence Between Non-isometric Deformable Shapes

Ginzburg, Dvir; Raviv, Dan

doi:10.1007/978-3-030-58558-7_3

Cited by 36 publications

(32 citation statements)

References 47 publications

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“…Interestingly, recent learning-based methods have also highlighted the importance of both robust discretizationinsensitive conversion [18,8,35,13] and of enforcing correct losses during training using either functional [35] or point-to-point correspondences [18,12,13]. In the latter category, conversion between functional and point-to-point maps is done as a non-learned layer in the network and thus must be correctly and consistently defined.…”

Section: Related Workmentioning

confidence: 99%

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Pai

Ren

Melzi

et al. 2021

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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Section: Related Workmentioning

confidence: 99%

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Pai

Ren

Melzi

et al. 2021

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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“…The key idea of this framework is to encode correspondences as small matrices, by using a reduced functional basis, thus greatly simplifying many resulting optimization problems. The functional map pipeline has been further improved in accuracy, efficiency and robustness by many recent works including [3,11,14,17,27,35,36]. There also exist other works [2,24,47] that treat shape correspondence as a dense labeling problem but they typically require a lot of data as the label space is very large.…”

Section: Related Workmentioning

confidence: 99%

Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud

Sharma,

Ovsjanikov

2021

Preprint

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Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch are a major challenge in non-rigid shape matching. In this paper, we propose a novel framework that simultaneously learns both self symmetry as well as a pairwise map between a pair of shapes. Our key idea is to couple a self symmetry map and a pairwise map through a regularization term that provides a joint constraint on both of them, thereby, leading to more accurate maps. We validate our method on several benchmarks where it outperforms many competitive baselines on both tasks.

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“…The goal of this task is to find a point-to-point mapping between a pair of shapes. A prominent approach for mesh-represented shapes is based on functional maps, in which a linear operator is optimized for spectral shape bases alignment [19,23,8,5,7]. One advantage of this technique is the structured correspondence prediction using the learned functional map.…”

Section: Related Workmentioning

confidence: 99%

“…taken a spectral approach by computing the functional mapping between the projected features of the shapes onto their Laplace-Beltrami Operator (LBO) eigenbasis [15,8,23,5]. Functional mapping methods rely on the global geometric shape structure and learn a transformation between the eigendecomposition of source and target shapes, which is then translated to a point-to-point correspondence.…”

Section: Introductionmentioning

confidence: 99%

DPC: Unsupervised Deep Point Correspondence via Cross and Self Construction

Lang,

Ginzburg,

Avidan

et al. 2021

Preprint

Self Cite

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We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to previous techniques and presents better generalization capabilities. Until now, two main approaches have been suggested for the dense correspondence problem. The first is a spectral-based approach that obtains great results on synthetic datasets but requires mesh connectivity of the shapes and long inference processing time while being unstable in real-world scenarios. The second is a spatial approach that uses an encoder-decoder framework to regress an ordered point cloud for the matching alignment from an irregular input. Unfortunately, the decoder brings considerable disadvantages, as it requires a large amount of training data and struggles to generalize well in cross-dataset evaluations. DPC's novelty lies in its lack of a decoder component. Instead, we use latent similarity and the input coordinates themselves to construct the point cloud and determine correspondence, replacing the coordinate regression done by the decoder. Extensive experiments show that our construction scheme leads to a performance boost in comparison to recent state-of-the-art correspondence methods. Our code is publicly available 1 .

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Cyclic Functional Mapping: Self-supervised Correspondence Between Non-isometric Deformable Shapes

Cited by 36 publications

References 47 publications

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud

DPC: Unsupervised Deep Point Correspondence via Cross and Self Construction

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