Endowing Deep 3d Models With Rotation Invariance Based On Principal Component Analysis

Xiao, Zelin; Lin, Hongxin; Li, Renjie; Geng, Lishuai; Chao, Hongyang; Ding, Shengyong

doi:10.1109/icme46284.2020.9102947

Cited by 23 publications

(7 citation statements)

References 9 publications

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“…Other works encode local neighborhoods using some local or global coordinate system to achieve invariance to rotations and translations. [17,57,60] use PCA to define rotation invariance. Equivariance is a desirable property for autoencoders.…”

Section: Related Workmentioning

confidence: 99%

Frame Averaging for Equivariant Shape Space Learning

Atzmon¹,

Nagano²,

Fidler³

et al. 2021

Preprint

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The task of shape space learning involves mapping a train set of shapes to and from a latent representation space with good generalization properties. Often, real-world collections of shapes have symmetries, which can be defined as transformations that do not change the essence of the shape. A natural way to incorporate symmetries in shape space learning is to ask that the mapping to the shape space (encoder) and mapping from the shape space (decoder) are equivariant to the relevant symmetries. In this paper, we present a framework for incorporating equivariance in encoders and decoders by introducing two contributions: (i) adapting the recent Frame Averaging (FA) framework for building generic, efficient, and maximally expressive Equivariant autoencoders; and (ii) constructing autoencoders equivariant to piecewise Euclidean motions applied to different parts of the shape. To the best of our knowledge, this is the first fully piecewise Euclidean equivariant autoencoder construction. Training our framework is simple: it uses standard reconstruction losses, and does not require the introduction of new losses. Our architectures are built of standard (backbone) architectures with the appropriate frame averaging to make them equivariant. Testing our framework on both rigid shapes dataset using implicit neural representations, and articulated shape datasets using mesh-based neural networks show state of the art generalization to unseen test shapes, improving relevant baselines by a large margin. In particular, our method demonstrates significant improvement in generalizing to unseen articulated poses.

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Section: Related Workmentioning

confidence: 99%

Frame Averaging for Equivariant Shape Space Learning

Atzmon¹,

Nagano²,

Fidler³

et al. 2021

Preprint

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“…Following the success of PointNet, deep learning-based 3D point set analysis methods having rotation invariance have been proposed. Xiao et al [26] proposed to align orientation of an entire 3D shape by using Principal Component Analysis prior to input to a DNN. PPF-FoldNet proposed by Deng et al [27] learns rotation invariant local feature for 3D shape matching by autoencoding the pointpair features.…”

Section: B Rotation-invariant 3d Point Set Analysismentioning

confidence: 99%

“…Chen et al [9] applied EdgeConv to a graph whose node is associated with a point-pair feature computed in a local region. Note, however, that these algorithms [26], [27], [8], [9] are not designed for segmentation of 3D point sets.…”

Section: B Rotation-invariant 3d Point Set Analysismentioning

confidence: 99%

Convolution on Rotation-Invariant and Multi-Scale Feature Graph for 3D Point Set Segmentation

Furuya

Ohbuchi

et al. 2020

IEEE Access

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Invariance against rotation of 3D objects is one of the essential properties for 3D shape analysis. Recently proposed algorithms (e.g., [9], [10], [12], [13]) have achieved rotationally invariant 3D point set analysis by using inherently rotation-invariant 3D shape features, i.e., distances and angles among 3D points, as input to Deep Neural Networks (DNNs). The DNNs capture spatial hierarchy and context among the geometric features to produce accurate analytical results. In this paper, we delve further into the DNN-based approach to rotation-invariant and highly accurate 3D point set analysis. In particular, we focus our attention on segmentation of 3D point sets, which is one of the most challenging among 3D point set analysis tasks. We propose a novel DNN for 3D point set segmentation called Rotation-invariant and Multi-scale feature Graph convolutional neural network, or RMGnet. Our RMGnet is more flexible than the previous methods as it accepts as input any handcrafted 3D shape features having rotation invariance. In addition, to accurately segment 3D point sets composed of parts having various sizes, we randomize scales at which handcrafted features are extracted and perform multi-resolution analysis of the features by using the DNN. Experimental evaluation demonstrates high segmentation accuracy as well as rotation invariance of the proposed RMGnet.

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“…Rotation-invariant deep network have already been proposed in the past. Some works focused on globally invariant architectures, either by aligning the whole input point cloud with Principal Component Analysis (PCA) [32], by using naturally invariant distances and angles point representations [25] or by projecting it to spherical representations [6,19,33]. This type of methods is adapted for object models, which have a global orientation, but do not generalize to real scenes where a global orientation is not available, as each particular object has its own orientation.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, various works have proposed 3D deep learning methods that are invariant under global [6,19,25,32,33] and local [4,15,36,37] rotations. Although these methods help the network ability to generalize to unseen rotations, they are still far from reaching the performances of standard deep learning methods in aligned scenarios.…”

Section: Introductionmentioning

confidence: 99%

Rotation-Invariant Point Convolution With Multiple Equivariant Alignments

Thomas¹

2020

Preprint

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Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study the relation between equivariance and invariance in 3D point convolutions. We show that using rotation-equivariant alignments, it is possible to make any convolutional layer rotation-invariant. Furthermore, we improve this simple alignment procedure by using the alignment themselves as features in the convolution, and by combining multiple alignments together. With this core layer, we design rotation-invariant architectures which improve state-of-the-art results in both object classification and semantic segmentation and reduces the gap between rotationinvariant and standard 3D deep learning approaches.

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Endowing Deep 3d Models With Rotation Invariance Based On Principal Component Analysis

Cited by 23 publications

References 9 publications

Frame Averaging for Equivariant Shape Space Learning

Frame Averaging for Equivariant Shape Space Learning

Convolution on Rotation-Invariant and Multi-Scale Feature Graph for 3D Point Set Segmentation

Rotation-Invariant Point Convolution With Multiple Equivariant Alignments

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