# Mesh Watermark Removal Attack and Mitigation: A Novel Perspective of Function Space

arXiv: https://arxiv.org/abs/2311.12059 · HTML: https://mlsanity.com/paper/2311.12059/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 18 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Evading Watermark based Detection of AI-Generated Content](https://mlsanity.com/paper/2305.03807/) (2023)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [Convolutional Generation of Textured 3D Meshes](https://mlsanity.com/paper/2006.07660/) (2020)
- [Deep 3D Mesh Watermarking with Self-Adaptive Robustness](https://mlsanity.com/paper/2109.07202/) (2021)
- [Rethinking Mesh Watermark: Towards Highly Robust and Adaptable Deep 3D Mesh Watermarking](https://mlsanity.com/paper/2307.11628/) (2023)

## Built on by (most cited first, 3 of 3)

- [GS-Hider: Hiding Messages into 3D Gaussian Splatting](https://mlsanity.com/paper/2405.15118/) (2024)
- [NGS-Marker: Robust Native Watermarking for 3D Gaussian Splatting](https://mlsanity.com/paper/2608.17447/) (2026)
- [Geometry-Preserving Blind Watermarking for Raw 3D Point Clouds](https://mlsanity.com/paper/2609.32222/) (2026)

## Abstract (arXiv)

Mesh watermark embeds secret messages in 3D meshes and decodes the message from watermarked meshes for ownership verification. Current watermarking methods directly hide secret messages in vertex and face sets of meshes. However, mesh is a discrete representation that uses vertex and face sets to describe a continuous signal, which can be discretized in other discrete representations with different vertex and face sets. This raises the question of whether the watermark can still be verified on the different discrete representations of the watermarked mesh. We conduct this research in an attack-then-defense manner by proposing a novel function space mesh watermark removal attack FuncEvade and then mitigating it through function space mesh watermarking FuncMark. In detail, FuncEvade generates a different discrete representation of a watermarked mesh by extracting it from the signed distance function of the watermarked mesh. We observe that the generated mesh can evade ALL previous watermarking methods. FuncMark mitigates FuncEvade by watermarking signed distance function through message-guided deformation. Such deformation can survive isosurfacing and thus be inherited by the extracted meshes for further watermark decoding. Extensive experiments demonstrate that FuncEvade achieves 100% evasion rate among all previous watermarking methods while achieving only 0.3% evasion rate on FuncMark. Besides, our FuncMark performs similarly on other metrics compared to state-of-the-art mesh watermarking methods.