Deep Residual Learning for Face Anti-Spoofing: A Mathematical Framework for Optimized Skip Connections

Face anti-spoofing is crucial for protecting biometric authentication systems. Presentation attacks using 3D masks and high-resolution printed images present detection challenges for existing methods. In this paper, we introduce a family of specialized CNN architectures, AttackNet, designed for robust face anti-spoofing with optimized residual connections and activation functions. The study includes the development of four architectures: baseline LivenessNet, AttackNetV1 with concatenation-based skip connections, AttackNetV2.1 with optimized activation functions, and AttackNetV2.2 with efficient addition-based residual learning. Our analysis demonstrates that element-wise addition in skip connections reduces parameters from 8.4 M to 4.2 M while maintaining performance. A comprehensive evaluation was conducted on four benchmark datasets: MSSpoof, 3DMAD, CSMAD, and Replay-Attack. Results show high accuracy (approaching 100%) on the 3DMAD, CSMAD, and Replay-Attack datasets. On the more challenging MSSpoof dataset, AttackNetV1 achieved 99.6% accuracy with an HTER of 0.004, outperforming the baseline LivenessNet (94.35% accuracy, 0.056 HTER). Comparative analysis with state-of-the-art methods confirms the superiority of the proposed approach. AttackNetV2.2 demonstrates an optimal balance between accuracy and computational efficiency, requiring 16.1 MB of memory compared to 32.1 MB for other AttackNet variants. Training time analysis shows twice the speed for AttackNetV2.2 compared to AttackNetV1. Architectural ablation studies highlight the crucial role of residual connections, batch normalization, and suitable dropout rates. Statistical significance testing verifies the reliability of the results (p-value < 0.001). The proposed architectures show excellent generalization ability and practical usefulness for real-world deployment in mobile and embedded systems.