Deep Learning 3D Shape Surfaces Using Geometry Images
Surfaces serve as a natural parametrization to 3D shapes. Learning surfaces using convolutional neural networks (CNNs) is a challenging task. Current paradigms to tackle this challenge are to either adapt the convolutional filters to operate on surfaces,
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Purdue University, West Lafayette, USA {sinha12,ramani}@purdue.edu Beifang University of Nationalities, Yinchuan, China [email protected]
Abstract. Surfaces serve as a natural parametrization to 3D shapes. Learning surfaces using convolutional neural networks (CNNs) is a challenging task. Current paradigms to tackle this challenge are to either adapt the convolutional filters to operate on surfaces, learn spectral descriptors defined by the Laplace-Beltrami operator, or to drop surfaces altogether in lieu of voxelized inputs. Here we adopt an approach of converting the 3D shape into a ‘geometry image’ so that standard CNNs can directly be used to learn 3D shapes. We qualitatively and quantitatively validate that creating geometry images using authalic parametrization on a spherical domain is suitable for robust learning of 3D shape surfaces. This spherically parameterized shape is then projected and cut to convert the original 3D shape into a flat and regular geometry image. We propose a way to implicitly learn the topology and structure of 3D shapes using geometry images encoded with suitable features. We show the efficacy of our approach to learn 3D shape surfaces for classification and retrieval tasks on non-rigid and rigid shape datasets.
Keywords: Deep learning images
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3D Shape
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Surfaces
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CNN
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Geometry
Introduction
The ground-breaking accuracy obtained by convolutional neural networks (CNNs) for image classification [16] marked the advent of deep learning methods for various vision tasks such as video recognition, human and hand pose tracking using 3D sensors, image segmentation and retrieval [9,13,27]. Researchers have tried to adapt the CNN architecture for 3D non-rigid as well as rigid shape analysis. The lack of a unified shape representation has led researchers pursuing deformable and rigid shape analysis using deep learning down different routes. One strategy for learning rigid shapes is to represent a shape as a probability Electronic supplementary material The online version of this chapter (doi:10. 1007/978-3-319-46466-4 14) contains supplementary material, which is available to authorized users. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VI, LNCS 9910, pp. 223–240, 2016. DOI: 10.1007/978-3-319-46466-4 14
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distribution on a 3D voxel grid [20,32]. Other approaches quantify some measure of local or global variation of surface coordinates relative to a fixed frame of reference [26]. These representations based on voxels or surface coordinates are extrinsic to the shape, and can successfully learn shapes for classification or retrieval tasks under rigid transformations (rotations, translations and reflections). However, they will naturally fail to recognize isometric deformation of a shape, say the deformation of a standing person to a sitting person. Invariance to isometry is a necessary property for robust non-rigid shape analysis. This is substantiated by the popularity of the intrinsic shape signatures for 3D deformable shape a
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