# Improving Shape Awareness and Interpretability in Deep Networks Using Geometric Moments

arXiv: https://arxiv.org/abs/2205.11722 · HTML: https://mlsanity.com/paper/2205.11722/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Searching for Efficient Multi-Scale Architectures for Dense Image Prediction](https://mlsanity.com/paper/1809.04184/) (2018)
- [Momen(e)t: Flavor the Moments in Learning to Classify Shapes](https://mlsanity.com/paper/1812.07431/) (2018)
- [Towards Learning Affine-Invariant Representations via Data-Efficient CNNs](https://mlsanity.com/paper/1909.00114/) (2019)
- [Non-Parametric Priors For Generative Adversarial Networks](https://mlsanity.com/paper/1905.07061/) (2019)
- [MomentsNet: a simple learning-free method for binary image recognition](https://mlsanity.com/paper/1702.06767/) (2017)

## Built on by (most cited first, 3 of 3)

- [Deep Geometric Moments Promote Shape Consistency in Text-to-3D Generation](https://mlsanity.com/paper/2408.05938/) (2024)
- [Learning Decomposable and Debiased Representations via Attribute-Centric Information Bottlenecks](https://mlsanity.com/paper/2403.14140/) (2024)
- [Guiding Diffusion with Deep Geometric Moments: Balancing Fidelity and Variation](https://mlsanity.com/paper/2505.12486/) (2025)

## Abstract (arXiv)

Deep networks for image classification often rely more on texture information than object shape. While efforts have been made to make deep-models shape-aware, it is often difficult to make such models simple, interpretable, or rooted in known mathematical definitions of shape. This paper presents a deep-learning model inspired by geometric moments, a classically well understood approach to measure shape-related properties. The proposed method consists of a trainable network for generating coordinate bases and affine parameters for making the features geometrically invariant yet in a task-specific manner. The proposed model improves the final feature's interpretation. We demonstrate the effectiveness of our method on standard image classification datasets. The proposed model achieves higher classification performance compared to the baseline and standard ResNet models while substantially improving interpretability.