# Rate Distortion Characteristic Modeling for Neural Image Compression

arXiv: https://arxiv.org/abs/2106.12954 · HTML: https://mlsanity.com/paper/2106.12954/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 24 Jun 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Full Resolution Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1608.05148/) (2016)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [Context-adaptive Entropy Model for End-to-end Optimized Image Compression](https://mlsanity.com/paper/1809.10452/) (2018)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Non-local Attention Optimized Deep Image Compression](https://mlsanity.com/paper/1904.09757/) (2019)
- [Learning Convolutional Networks for Content-weighted Image Compression](https://mlsanity.com/paper/1703.10553/) (2017)
- [End-to-end optimization of nonlinear transform codes for perceptual quality](https://mlsanity.com/paper/1607.05006/) (2016)
- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [Learning End-to-End Lossy Image Compression: A Benchmark](https://mlsanity.com/paper/2002.03711/) (2020)
- [Deep Generative Models for Distribution-Preserving Lossy Compression](https://mlsanity.com/paper/1805.11057/) (2018)
- [Soft then Hard: Rethinking the Quantization in Neural Image Compression](https://mlsanity.com/paper/2104.05168/) (2021)
- [Efficient and Effective Context-Based Convolutional Entropy Modeling for Image Compression](https://mlsanity.com/paper/1906.10057/) (2019)
- [A Comprehensive Benchmark for Single Image Compression Artifacts Reduction](https://mlsanity.com/paper/1909.03647/) (2019)
- [An End-to-End Joint Learning Scheme of Image Compression and Quality Enhancement with Improved Entropy Minimization](https://mlsanity.com/paper/1912.12817/) (2019)

## Built on by (most cited first, 6 of 6)

- [QVRF: A Quantization-error-aware Variable Rate Framework for Learned Image Compression](https://mlsanity.com/paper/2303.05744/) (2023)
- [UniPCGC: Towards Practical Point Cloud Geometry Compression via an Efficient Unified Approach](https://mlsanity.com/paper/2503.18541/) (2025)
- [Universal Efficient Variable-rate Neural Image Compression](https://mlsanity.com/paper/2111.11305/) (2021)
- [Adaptive Rate Control for Deep Video Compression with Rate-Distortion Prediction](https://mlsanity.com/paper/2412.18834/) (2024)
- [A Rate-Quality Model for Learned Video Coding](https://mlsanity.com/paper/2505.02720/) (2025)
- [Way to Build Native AI-driven 6G Air Interface: Principles, Roadmap, and Outlook](https://mlsanity.com/paper/2508.15277/) (2025)

## Abstract (arXiv)

End-to-end optimized neural image compression (NIC) has obtained superior lossy compression performance recently. In this paper, we consider the problem of rate-distortion (R-D) characteristic analysis and modeling for NIC. We make efforts to formulate the essential mathematical functions to describe the R-D behavior of NIC using deep networks. Thus arbitrary bit-rate points could be elegantly realized by leveraging such model via a single trained network. We propose a plugin-in module to learn the relationship between the target bit-rate and the binary representation for the latent variable of auto-encoder. The proposed scheme resolves the problem of training distinct models to reach different points in the R-D space. Furthermore, we model the rate and distortion characteristic of NIC as a function of the coding parameter λ respectively. Our experiments show our proposed method is easy to adopt and realizes state-of-the-art continuous bit-rate coding performance, which implies that our approach would benefit the practical deployment of NIC.