# Affine-Transformation-Invariant Image Classification by Differentiable Arithmetic Distribution Module

arXiv: https://arxiv.org/abs/2309.00752 · HTML: https://mlsanity.com/paper/2309.00752/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [HistoGAN: Controlling Colors of GAN-Generated and Real Images via Color Histograms](https://mlsanity.com/paper/2011.11731/) (2020)
- [Learning Statistical Texture for Semantic Segmentation](https://mlsanity.com/paper/2103.04133/) (2021)
- [Histogram Layers for Texture Analysis](https://mlsanity.com/paper/2001.00215/) (2020)
- [Learnable Histogram: Statistical Context Features for Deep Neural Networks](https://mlsanity.com/paper/1804.09398/) (2018)
- [DeepHist: Differentiable Joint and Color Histogram Layers for Image-to-Image Translation](https://mlsanity.com/paper/2005.03995/) (2020)
- [Learning Temporal Distribution and Spatial Correlation Towards Universal Moving Object Segmentation](https://mlsanity.com/paper/2304.09949/) (2023)
- [Learning Distributions via Monte-Carlo Marginalization](https://mlsanity.com/paper/2308.06352/) (2023)
- [Histogram Layers for Synthetic Aperture Sonar Imagery](https://mlsanity.com/paper/2209.03878/) (2022)
- [See the Difference: Direct Pre-Image Reconstruction and Pose Estimation by Differentiating HOG](https://mlsanity.com/paper/1505.00663/) (2015)

## Built on by (most cited first, 2 of 2)

- [Deep Clustering via Distribution Learning](https://mlsanity.com/paper/2408.03407/) (2024)
- [Image Recognition for Garbage Classification Based on Pixel Distribution Learning](https://mlsanity.com/paper/2409.03913/) (2024)

## Abstract (arXiv)

Although Convolutional Neural Networks (CNNs) have achieved promising results in image classification, they still are vulnerable to affine transformations including rotation, translation, flip and shuffle. The drawback motivates us to design a module which can alleviate the impact from different affine transformations. Thus, in this work, we introduce a more robust substitute by incorporating distribution learning techniques, focusing particularly on learning the spatial distribution information of pixels in images. To rectify the issue of non-differentiability of prior distribution learning methods that rely on traditional histograms, we adopt the Kernel Density Estimation (KDE) to formulate differentiable histograms. On this foundation, we present a novel Differentiable Arithmetic Distribution Module (DADM), which is designed to extract the intrinsic probability distributions from images. The proposed approach is able to enhance the model's robustness to affine transformations without sacrificing its feature extraction capabilities, thus bridging the gap between traditional CNNs and distribution-based learning. We validate the effectiveness of the proposed approach through ablation study and comparative experiments with LeNet.