# Topo-ADV: Generating Topology-Driven Imperceptible Adversarial Point Clouds

arXiv: https://arxiv.org/abs/2604.09879 · HTML: https://mlsanity.com/paper/2604.09879/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 30 of 30)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Generating 3D Adversarial Point Clouds](https://mlsanity.com/paper/1809.07016/) (2018)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [PointCloud Saliency Maps](https://mlsanity.com/paper/1812.01687/) (2018)
- [Extending Adversarial Attacks and Defenses to Deep 3D Point Cloud Classifiers](https://mlsanity.com/paper/1901.03006/) (2019)
- [AdvPC: Transferable Adversarial Perturbations on 3D Point Clouds](https://mlsanity.com/paper/1912.00461/) (2019)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)
- [Shape-invariant 3D Adversarial Point Clouds](https://mlsanity.com/paper/2203.04041/) (2022)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [3D Adversarial Attacks Beyond Point Cloud](https://mlsanity.com/paper/2104.12146/) (2021)
- [Isometric 3D Adversarial Examples in the Physical World](https://mlsanity.com/paper/2210.15291/) (2022)
- [Hide in Thicket: Generating Imperceptible and Rational Adversarial Perturbations on 3D Point Clouds](https://mlsanity.com/paper/2403.05247/) (2024)
- [Boosting 3D Adversarial Attacks with Attacking On Frequency](https://mlsanity.com/paper/2201.10937/) (2022)
- [Towards a 3D Transfer-based Black-box Attack via Critical Feature Guidance](https://mlsanity.com/paper/2508.15650/) (2025)

## Abstract (arXiv)

Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D attacks predominantly manipulate geometric properties such as point locations, curvature, or surface structure, implicitly assuming that preserving global shape fidelity preserves semantic content. In this work, we challenge this assumption and introduce the first topology-driven adversarial attack for point cloud deep learning. Our key insight is that the homological structure of a 3D object constitutes a previously unexplored vulnerability surface. We propose Topo-ADV, an end-to-end differentiable framework that incorporates persistent homology as an explicit optimization objective, enabling gradient-based manipulation of topological features during adversarial example generation. By embedding persistence diagrams through differentiable topological representations, our method jointly optimizes (i) a topology divergence loss that alters persistence, (ii) a misclassification objective, and (iii) geometric imperceptibility constraints that preserve visual plausibility. Experiments demonstrate that subtle topology-driven perturbations consistently achieve up to 100% attack success rates on benchmark datasets such as ModelNet40, ShapeNet Part, and ScanObjectNN using PointNet and DGCNN classifiers, while remaining geometrically indistinguishable from the original point clouds, beating state-of-the-art methods on various perceptibility metrics.