# Mathematical model of printing-imaging channel for blind detection of fake copy detection patterns

arXiv: https://arxiv.org/abs/2212.07326 · HTML: https://mlsanity.com/paper/2212.07326/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 2 of 2)

- [Clonability of anti-counterfeiting printable graphical codes: a machine learning approach](https://mlsanity.com/paper/1903.07359/) (2019)
- [Mobile authentication of copy detection patterns](https://mlsanity.com/paper/2203.02397/) (2022)

## Built on by (most cited first, 5 of 5)

- [Stochastic Digital Twin for Copy Detection Patterns](https://mlsanity.com/paper/2309.16866/) (2023)
- [Provable Performance Guarantees of Copy Detection Patterns](https://mlsanity.com/paper/2409.17649/) (2024)
- [Diffusion-Based Authentication of Copy Detection Patterns: A Multimodal Framework with Printer Signature Conditioning](https://mlsanity.com/paper/2603.08998/) (2026)
- [Predictive Quality Assessment for Mobile Secure Graphics](https://mlsanity.com/paper/2509.20028/) (2025)
- [Diffusion-Based Multi-Class Normality for OOD Detection: An Application to CDP Authentication](https://mlsanity.com/paper/2607.00609/) (2026)

## Abstract (arXiv)

Nowadays, copy detection patterns (CDP) appear as a very promising anti-counterfeiting technology for physical object protection. However, the advent of deep learning as a powerful attacking tool has shown that the general authentication schemes are unable to compete and fail against such attacks. In this paper, we propose a new mathematical model of printing-imaging channel for the authentication of CDP together with a new detection scheme based on it. The results show that even deep learning created copy fakes unknown at the training stage can be reliably authenticated based on the proposed approach and using only digital references of CDP during authentication.