# Learnable Histogram: Statistical Context Features for Deep Neural Networks

arXiv: https://arxiv.org/abs/1804.09398 · HTML: https://mlsanity.com/paper/1804.09398/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2018.

## Built on by (most cited first, 9 of 9)

- [Learning Statistical Texture for Semantic Segmentation](https://mlsanity.com/paper/2103.04133/) (2021)
- [Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders](https://mlsanity.com/paper/2210.16844/) (2022)
- [Deep Unfolding of the DBFB Algorithm with Application to ROI CT Imaging with Limited Angular Density](https://mlsanity.com/paper/2209.13264/) (2022)
- [The Earth Mover's Pinball Loss: Quantiles for Histogram-Valued Regression](https://mlsanity.com/paper/2106.02051/) (2021)
- [Quantification using Permutation-Invariant Networks based on Histograms](https://mlsanity.com/paper/2403.15123/) (2024)
- [Histogram Layers for Synthetic Aperture Sonar Imagery](https://mlsanity.com/paper/2209.03878/) (2022)
- [Affine-Transformation-Invariant Image Classification by Differentiable Arithmetic Distribution Module](https://mlsanity.com/paper/2309.00752/) (2023)
- [Rethinking Image Histogram Matching for Image Classification](https://mlsanity.com/paper/2506.01346/) (2025)
- [Uncertainty Quantification for Deep Learning](https://mlsanity.com/paper/2405.20550/) (2024)

## Abstract (arXiv)

Statistical features, such as histogram, Bag-of-Words (BoW) and Fisher Vector, were commonly used with hand-crafted features in conventional classification methods, but attract less attention since the popularity of deep learning methods. In this paper, we propose a learnable histogram layer, which learns histogram features within deep neural networks in end-to-end training. Such a layer is able to back-propagate (BP) errors, learn optimal bin centers and bin widths, and be jointly optimized with other layers in deep networks during training. Two vision problems, semantic segmentation and object detection, are explored by integrating the learnable histogram layer into deep networks, which show that the proposed layer could be well generalized to different applications. In-depth investigations are conducted to provide insights on the newly introduced layer.