Supervised Descriptor Learning for Non-Rigid Shape Matching

Corman, Etienne; Ovsjanikov, Maks; Chambolle, Antonin

doi:10.1007/978-3-319-16220-1_20

Cited by 48 publications

(52 citation statements)

References 41 publications

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“…While later approaches extended the use of functional maps to non‐isometric maps (e.g. [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].…”

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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“…A wide range of fundamental shape analysis problems such as classification [BBGO11], segmentation [KHS10], and correspondence [COC14] have been addressed with machine learning techniques (see [XKH*16] for a survey). Due to recent developments and success of deep neural networks, researchers have focused on developing appropriate shape representations suitable for deep learning.…”

Section: Related Workmentioning

confidence: 99%

GWCNN: A Metric Alignment Layer for Deep Shape Analysis

Ezuz

Solomon

Kim

et al. 2017

Computer Graphics Forum

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Deep neural networks provide a promising tool for incorporating semantic information in geometry processing applications. Unlike image and video processing, however, geometry processing requires handling unstructured geometric data, and thus data representation becomes an important challenge in this framework. Existing approaches tackle this challenge by converting point clouds, meshes, or polygon soups into regular representations using, e.g., multi‐view images, volumetric grids or planar parameterizations. In each of these cases, geometric data representation is treated as a fixed pre‐process that is largely disconnected from the machine learning tool. In contrast, we propose to optimize for the geometric representation during the network learning process using a novel metric alignment layer. Our approach maps unstructured geometric data to a regular domain by minimizing the metric distortion of the map using the regularized Gromov–Wasserstein objective. This objective is parameterized by the metric of the target domain and is differentiable; thus, it can be easily incorporated into a deep network framework. Furthermore, the objective aims to align the metrics of the input and output domains, promoting consistent output for similar shapes. We show the effectiveness of our layer within a deep network trained for shape classification, demonstrating state‐of‐the‐art performance for nonrigid shapes.

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“…Functional maps express maps between surfaces through linear operators transporting functions on one surface to functions on another. Beyond the technique proposed in the original paper, many algorithms exist for computing functional maps, e.g., via sparsity [Pokrass et al 2013], joint diagonalization [Kovnatsky et al 2013], consistency [Huang and Guibas 2013], supervised learning [Corman et al 2014], matrix completion [Kovnatsky et al 2015], or estimation from a point-to-point map [Corman et al 2015]. Our goal of using functional maps to characterize local and global geometry builds upon the machinery of shape differences [Rustamov et al 2013]; see §4 for a summary.…”

Section: Related Workmentioning

confidence: 99%

Functional characterization of intrinsic and extrinsic geometry

Corman¹,

Solomon²,

Ben‐Chen³

et al. 2017

TOG

Self Cite

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We propose a novel way to capture and characterize distortion between pairs of shapes by extending the recently proposed framework of shape differences built on functional maps. We modify the original definition of shape differences slightly and prove that, after this change, the discrete metric is fully encoded in two shape difference operators and can be recovered by solving two linear systems of equations. Then, we introduce an extension of the shape difference operators using offset surfaces to capture extrinsic or embedding-dependent distortion, complementing the purely intrinsic nature of the original shape differences. Finally, we demonstrate that a set of four operators is complete, capturing intrinsic and extrinsic structure and fully encoding a shape up to rigid motion in both discrete and continuous settings. We highlight the usefulness of our constructions by showing the complementary nature of our extrinsic shape differences in capturing distortion ignored by previous approaches. We additionally provide examples where we recover local shape structure from the shape difference operators, suggesting shape editing and analysis tools based on manipulating shape differences.

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Supervised Descriptor Learning for Non-Rigid Shape Matching

Cited by 48 publications

References 41 publications

Deblurring and Denoising of Maps between Shapes

Deblurring and Denoising of Maps between Shapes

GWCNN: A Metric Alignment Layer for Deep Shape Analysis

Functional characterization of intrinsic and extrinsic geometry

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