# On The Classification-Distortion-Perception Tradeoff

arXiv: https://arxiv.org/abs/1904.08816 · HTML: https://mlsanity.com/paper/1904.08816/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2019.

## Built on by (most cited first, 21 of 21)

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- [Lossy Compression for Lossless Prediction](https://mlsanity.com/paper/2106.10800/) (2021)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [Towards Semantic Communications: Deep Learning-Based Image Semantic Coding](https://mlsanity.com/paper/2208.04094/) (2022)
- [Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling](https://mlsanity.com/paper/2307.03992/) (2023)
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- [Conditional Perceptual Quality Preserving Image Compression](https://mlsanity.com/paper/2308.08154/) (2023)
- [Reconciling Stochastic and Deterministic Strategies for Zero-shot Image Restoration using Diffusion Model in Dual](https://mlsanity.com/paper/2503.01288/) (2025)
- [Traversing Distortion-Perception Tradeoff using a Single Score-Based Generative Model](https://mlsanity.com/paper/2503.20297/) (2025)
- [Unified Coding for Both Human Perception and Generalized Machine Analytics with CLIP Supervision](https://mlsanity.com/paper/2501.04579/) (2025)
- [Fidelity Estimation Improves Noisy-Image Classification With Pretrained Networks](https://mlsanity.com/paper/2106.00673/) (2021)
- [A Rate-Distortion-Classification Approach for Lossy Image Compression](https://mlsanity.com/paper/2405.03500/) (2024)
- [Learning degraded image classification with restoration data fidelity](https://mlsanity.com/paper/2101.09606/) (2021)
- [End-to-End Image Compression with Probabilistic Decoding](https://mlsanity.com/paper/2109.14837/) (2021)
- [Unlocking Masked Autoencoders as Loss Function for Image and Video Restoration](https://mlsanity.com/paper/2303.16411/) (2023)
- [The Rate-Distortion-Perception-Classification Tradeoff: Joint Source Coding and Modulation via Inverse-Domain GANs](https://mlsanity.com/paper/2312.14792/) (2023)
- [Universal Representations for Classification-enhanced Lossy Compression](https://mlsanity.com/paper/2504.13191/) (2025)
- [IR-Flow: Bridging Discriminative and Generative Image Restoration via Rectified Flow](https://mlsanity.com/paper/2604.19680/) (2026)
- [Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling](https://mlsanity.com/paper/2605.09833/) (2026)
- [Domain-Adaptive Deep Joint Source-Channel Coding for Image Classification](https://mlsanity.com/paper/2607.28907/) (2026)

## Abstract (arXiv)

Signal degradation is ubiquitous and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal `original' signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension worthy of consideration, namely the semantic quality or the utility for recognition purpose, of the restored signal. In this paper, we extend the previous perception-distortion tradeoff to the case of classification-distortion-perception (CDP) tradeoff, where we introduced the classification error rate of the restored signal in addition to distortion and perceptual difference. Two versions of the CDP tradeoff are considered, one using a predefined classifier and the other dealing with the optimal classifier for the restored signal. For both versions, we can rigorously prove the existence of the CDP tradeoff, i.e. the distortion, perceptual difference, and classification error rate cannot be made all minimal simultaneously. Our findings can be useful especially for computer vision researches where some low-level vision tasks (signal restoration) serve for high-level vision tasks (visual understanding).