Deep Positional and Relational Feature Learning for Rotation-Invariant Point Cloud Analysis

Yu, Ruixuan; Wei, Xin; Tombari, Federico; Sun, Jian

doi:10.1007/978-3-030-58607-2_13

Cited by 29 publications

(17 citation statements)

References 33 publications

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“…For the former, we adopt Point-Net [40] and DGCNN [54], which are widely adopted neural networks for geometric data. For rotation-invariant models, we adopt RIConv [63], ClusterNet [8], PR-invNet [61], and RI-GCN [22], which are state-of-the-art rotation-invariant models. Notice that permutation-equivariant models cannot be simply applied here and thus are not compared, as in all previous works.…”

Section: Point Cloud Analysismentioning

confidence: 99%

Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need?

Zhang¹,

Wang²,

Zhang³

et al. 2021

Preprint

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Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

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Section: Point Cloud Analysismentioning

confidence: 99%

Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need?

Zhang¹,

Wang²,

Zhang³

et al. 2021

Preprint

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show abstract

“…Another direction to enhance rotation-robustness is to learn rotation-invariant representations in networks. To achieve this, the rotation-invariant networks are derived by using kernelized convolutions [25,29], PCA normalization [9,10,49] and rotationinvariant position encoding [3,13,50].…”

Section: Related Workmentioning

confidence: 99%

“…Even worse, training with augmented data also introduces adversary effect that hurts the inference performance when test data is not rotated. Many works [3,9,10,13,25,29,49,50] attempted to address this issue through constructing rotation-invariant frameworks and features. Nevertheless, it is shown that rotation invariant features can still suffer evident performance drop when test data is inherently not rotated.…”

Section: Introductionmentioning

confidence: 99%

SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancement

Qiu

Wang

et al. 2022

Lecture Notes in Computer Science

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In this paper, we propose a novel deep architecture tailored for 3D point cloud applications, named as SPE-Net. The embedded "Selective Position Encoding (SPE)" procedure relies on an attention mechanism that can effectively attend to the underlying rotation condition of the input. Such encoded rotation condition then determines which part of the network parameters to be focused on, and is shown to efficiently help reduce the degree of freedom of the optimization during training. This mechanism henceforth can better leverage the rotation augmentations through reduced training difficulties, making SPE-Net robust against rotated data both during training and testing. The new findings in our paper also urge us to rethink the relationship between the extracted rotation information and the actual test accuracy. Intriguingly, we reveal evidences that by locally encoding the rotation information through SPE-Net, the rotation-invariant features are still of critical importance in benefiting the test samples without any actual global rotation. We empirically demonstrate the merits of the SPE-Net and the associated hypothesis on four benchmarks, showing evident improvements on both rotated and unrotated test data over SOTA methods. Source code is available at https://github.com/ZhaofanQiu/SPE-Net.

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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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Deep Positional and Relational Feature Learning for Rotation-Invariant Point Cloud Analysis

Cited by 29 publications

References 33 publications

Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need?

Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need?

SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancement

Frame Averaging for Equivariant Shape Space Learning

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