Enhancing Adversarial Robustness with Signed Distance Fields for Harmonizing Geometric Invariance and Texture

Abstract

Deep neural networks demonstrate impressive performance in visual recognition but remain highly vulnerable to imperceptible adversarial attacks. Existing defense strategies such as adversarial training and diffusion-based purification have achieved significant progress but are frequently constrained by high computational cost, information loss, and inference latency. To address these challenges, we propose a Geometric and Texture balancing Purification (GeoTexPuri) framework that enhances adversarial robustness by harmonizing invariant geometric structures with textural features. Specifically, the framework integrates dense geometric guidance into the training phase by transforming discrete image masks into continuous spatial fields via Signed Distance Fields (SDF). This process establishes stable structural anchors that shield the model from local pixel noise. Through a multi-stream training objective, the model learns to internalize purified representations that effectively align semantic textural cues with these underlying geometric invariants. Extensive experiments on ImageNet demonstrate the efficacy of our approach. GeoTexPuri achieves 84.79\% clean accuracy and 83.52\% robust accuracy under the AutoAttack. Crucially, GeoTexPuri functions as a deterministic classifier during inference, requiring only the input image without any auxiliary geometric modules or additional computational costs, thereby ensuring a scalable and efficient solution for real-time applications.