Adversarial attacks have demonstrated remarkable efficacy in altering the output of a learning model by applying a minimal perturbation to the input data. While increasing attention has been placed on the image domain, however, the study of adversarial perturbations for geometric data has been notably lagging behind. In this paper, we show that effective adversarial attacks can be concocted for surfaces embedded in 3D, under weak smoothness assumptions on the perceptibility of the attack. We address the case of deformable 3D shapes in particular, and introduce a general model that is not tailored to any specific surface representation, nor does it assume access to a parametric description of the 3D object. In this context, we consider targeted and untargeted variants of the attack, demonstrating compelling results in either case. We further show how discovering adversarial examples, and then using them for adversarial training, leads to an increase in both robustness and accuracy. Our findings are confirmed empirically over multiple datasets spanning different semantic classes and deformations.

中文翻译：

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通过带限扰动生成对抗性表面

通过对输入数据应用最小扰动，对抗性攻击在改变学习模型的输出方面表现出显着的功效。然而，虽然人们越来越关注图像领域，但对几何数据的对抗性扰动的研究却明显滞后。在本文中，我们表明，在攻击可感知性的弱平滑假设下，可以为嵌入 3D 的表面炮制有效的对抗性攻击。我们特别解决了可变形 3D 形状的情况，并介绍了一个不适合任何特定表面表示的通用模型，也不假设可以访问 3D 对象的参数描述。在这种情况下，我们考虑了有针对性和无针对性的攻击变体，在任何一种情况下都展示了令人信服的结果。我们进一步展示了如何发现对抗性示例，然后将它们用于对抗性训练，从而提高鲁棒性和准确性。我们的发现在跨越不同语义类别和变形的多个数据集上得到了经验证实。