# Momen(e)t: Flavor the Moments in Learning to Classify Shapes

arXiv: https://arxiv.org/abs/1812.07431 · HTML: https://mlsanity.com/paper/1812.07431/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 15 of 15)

- [Regularization Strategy for Point Cloud via Rigidly Mixed Sample](https://mlsanity.com/paper/2102.01929/) (2021)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (2022)
- [MetaPose: Fast 3D Pose from Multiple Views without 3D Supervision](https://mlsanity.com/paper/2108.04869/) (2021)
- [SageMix: Saliency-Guided Mixup for Point Clouds](https://mlsanity.com/paper/2210.06944/) (2022)
- [LACV-Net: Semantic Segmentation of Large-Scale Point Cloud Scene via Local Adaptive and Comprehensive VLAD](https://mlsanity.com/paper/2210.05870/) (2022)
- [PointSCNet: Point Cloud Structure and Correlation Learning Based on Space Filling Curve-Guided Sampling](https://mlsanity.com/paper/2202.10251/) (2022)
- [Improving Shape Awareness and Interpretability in Deep Networks Using Geometric Moments](https://mlsanity.com/paper/2205.11722/) (2022)
- [Advancements in Point Cloud-Based 3D Defect Detection and Classification for Industrial Systems: A Comprehensive Survey](https://mlsanity.com/paper/2402.12923/) (2024)
- [Completing Partial Point Clouds with Outliers by Collaborative Completion and Segmentation](https://mlsanity.com/paper/2203.09772/) (2022)
- [Decodable and Sample Invariant Continuous Object Encoder](https://mlsanity.com/paper/2311.00187/) (2023)
- [S-AT GCN: Spatial-Attention Graph Convolution Network based Feature Enhancement for 3D Object Detection](https://mlsanity.com/paper/2103.08439/) (2021)
- [Depth Refinement for Improved Stereo Reconstruction](https://mlsanity.com/paper/2112.08070/) (2021)
- [VA-GCN: A Vector Attention Graph Convolution Network for learning on Point Clouds](https://mlsanity.com/paper/2106.00227/) (2021)
- [Shrinking unit: a Graph Convolution-Based Unit for CNN-like 3D Point Cloud Feature Extractors](https://mlsanity.com/paper/2209.12770/) (2022)
- [Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design](https://mlsanity.com/paper/2407.07611/) (2024)

## Abstract (arXiv)

A fundamental question in learning to classify 3D shapes is how to treat the data in a way that would allow us to construct efficient and accurate geometric processing and analysis procedures. Here, we restrict ourselves to networks that operate on point clouds. There were several attempts to treat point clouds as non-structured data sets by which a neural network is trained to extract discriminative properties. The idea of using 3D coordinates as class identifiers motivated us to extend this line of thought to that of shape classification by comparing attributes that could easily account for the shape moments. Here, we propose to add polynomial functions of the coordinates allowing the network to account for higher order moments of a given shape. Experiments on two benchmarks show that the suggested network is able to provide state of the art results and at the same token learn more efficiently in terms of memory and computational complexity.