Geodesic Convolutional Neural Networks on Riemannian Manifolds

Masci, Jonathan; Boscaini, Davide; Bronstein, Michael M.; Vandergheynst, Pierre

doi:10.1109/iccvw.2015.112

Cited by 640 publications

(589 citation statements)

References 51 publications

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“…Masci et al [2015] build a convolutional network directly on non-Euclidean shape surfaces. Qi et al [2016] discuss ways to improve the performance of both volumetric and multi-view CNNs for shape classification.…”

Section: Statistical Shape Representationsmentioning

confidence: 99%

Deformation-driven shape correspondence via shape recognition

Zhu

Lira

et al. 2017

ACM Trans. Graph.

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Figure 1: We develop GRASS, a Generative Recursive Autoencoder for Shape Structures, which enables structural blending between two 3D shapes. Note the discrete blending of translational symmetries (slats on the chair backs) and rotational symmetries (the swivel legs). GRASS encodes and synthesizes box structures (bottom) and part geometries (top) separately. The blending is performed on fixed-length codes learned by the unsupervised autoencoder, without any form of part correspondences, given or computed. AbstractWe introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which reflects fundamental intra-shape relationships such as adjacency and symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a flat, unlabeled, arbitrary part layout to a compact code. The code effectively captures hierarchical structures of man-made 3D objects of varying structural complexities despite being fixed-dimensional: an associated decoder maps a code back to a full hierarchy. The learned bidirectional mapping is further tuned using an adversarial setup to yield a generative model of plausible structures, from which novel structures can be sampled. Finally, our structure synthesis framework is augmented by a second trained module that produces fine-grained part geometry, conditioned on global and local structural context, leading to a full generative pipeline for 3D shapes. We demonstrate that without supervision, our network learns meaningful structural hierarchies adhering to perceptual grouping principles, produces compact codes which enable applications such as shape classification and partial matching, and supports shape synthesis and interpolation with significant variations in topology and geometry.

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Section: Statistical Shape Representationsmentioning

confidence: 99%

Deformation-driven shape correspondence via shape recognition

Zhu

Lira

et al. 2017

ACM Trans. Graph.

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“…Extending CNNs to unorganized 3D geometric data is an active field of research (e.g. [19]) and beyond the scope of this work. Instead, we take advantage of the fact that 3D faces can be mapped onto 2D depth images for which regular CNN apply.…”

Section: Overviewmentioning

confidence: 99%

Multilinear Autoencoder for 3D Face Model Learning

Abrevaya

Wuhrer

Boyer

2018

2018 IEEE Winter Conference on Applications of Computer Vision (WACV)

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Generative models have proved to be useful tools to represent 3D human faces and their statistical variations. With the increase of 3D scan databases available for training, a growing challenge lies in the ability to learn generative face models that effectively encode shape variations with respect to desired attributes, such as identity and expression, given datasets that can be diverse. This paper addresses this challenge by proposing a framework that learns a generative 3D face model using an autoencoder architecture, allowing hence for weakly supervised training. The main contribution is to combine a convolutional neural network-based encoder with a multilinear model-based decoder, taking therefore advantage of both the convolutional network robustness to corrupted and incomplete data, and of the multilinear model capacity to effectively model and decouple shape variations. Given a set of 3D face scans with annotation labels for the desired attributes, e.g. identities and expressions, our method learns an expressive multilinear model that decouples shape changes due to the different factors. Experimental results demonstrate that the proposed method outperforms recent approaches when learning multilinear face models from incomplete training data, particularly in terms of space decoupling, and that it is capable of learning from an order of magnitude more data than previous methods.

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“…the θ coordinate as done in [BK10,KBLB12]; or by taking the maximum over all the angles as done in [MBBV15]. If formula (10) is used and we consider all the possible rotations θ ∈ [0, 2π), the Laplacian is intrinsic up to the choice of the origin of θ.…”

Section: Anisotropic Diffusion Descriptorsmentioning

confidence: 99%

“…Their work follows the recent trends in the image analysis domain, where hand-crafted descriptors are abandoned in favor of learning approaches [ Contributions. Such kernels capture local directional structures similarly to the geodesic polar coordinates used in the intrinsic shape context [KBLB12] and ShapeNet [MBBV15], however, with several notable advantages. Unlike [ARAC14], we do not use a single anisotropic diffusion kernel in the direction of the principal curvature, but a multitude of kernels at different directions.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Diffusion Descriptors

Boscaini

Masci

Rodolà

et al. 2016

Computer Graphics Forum

135

115

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Spectral methods have recently gained popularity in many domains of computer graphics and geometry processing, especially shape processing, computation of shape descriptors, distances, and correspondence. Spectral geometric structures are intrinsic and thus invariant to isometric deformations, are efficiently computed, and can be constructed on shapes in different representations. A notable drawback of these constructions, however, is that they are isotropic, i.e., insensitive to direction. In this paper, we show how to construct direction-sensitive spectral feature descriptors using anisotropic diffusion on meshes and point clouds. The core of our construction are directed local kernels acting similarly to steerable filters, which are learned in a task-specific manner. Remarkably, while being intrinsic, our descriptors allow to disambiguate reflection symmetries. We show the application of anisotropic descriptors for problems of shape correspondence on meshes and point clouds, achieving results significantly better than state-of-the-art methods.

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Geodesic Convolutional Neural Networks on Riemannian Manifolds

Cited by 640 publications

References 51 publications

Deformation-driven shape correspondence via shape recognition

Deformation-driven shape correspondence via shape recognition

Multilinear Autoencoder for 3D Face Model Learning

Anisotropic Diffusion Descriptors

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