Physics‐ and Statistics‐Guided Normal Subspace Purification for Training‐Free Few‐Shot Industrial Anomaly Detection

ABSTRACT

Few‐shot industrial visual anomaly detection is challenging because only a limited number of normal samples are available. Existing training‐free subspace‐based methods typically construct the normal subspace using principal component analysis (PCA). However, with limited normal samples, covariance estimation can be affected by imaging disturbances and augmentation artifacts, resulting in an inaccurate normal subspace and reduced anomaly detection performance. To address this problem, we propose a physics‐ and statistics‐guided normal subspace purification framework for training‐free few‐shot industrial anomaly detection. The framework consists of two components. First, a physics‐guided specular filtering (SF) strategy is used to suppress feature disturbances caused by specular reflections and illumination variations. Second, a median absolute deviation (MAD)‐based robust PCA (MAD‐RPCA) strategy assigns reliability weights to feature representations according to their statistical consistency, thereby reducing the influence of unreliable observations during covariance estimation. The resulting normal subspace is used for feature reconstruction and anomaly localisation. Experiments on the MVTec AD and VisA datasets show that the proposed framework achieves competitive anomaly detection performance while improving the robustness of normal subspace estimation. The improvements are particularly evident for industrial categories with strong specular reflections, complex illumination conditions and regular geometric structures.