Subspace-Guided Feature Reconstruction for Unsupervised Anomaly Localization

TL;DR

This work tackles unsupervised anomaly localization by leveraging subspace-guided feature reconstruction to adaptively approximate target embeddings from nominal data. By learning low-dimensional subspaces and employing a self-expressive Sparse representation, the method can mimic out-of-bank features while localizing anomalies via reconstruction error. A subspace-based sampling scheme reduces memory overhead and accelerates inference without sacrificing accuracy, achieving state-of-the-art or competitive results on MVTec AD, BTAD, and MTD. The approach offers practical benefits for industrial defect detection, though it relies on a linearity assumption and could be extended with a more expressive unsupervised self-representation network in future work.

Abstract

Unsupervised anomaly localization, which plays a critical role in industrial manufacturing, aims to identify anomalous regions that deviate from normal sample patterns. Most recent methods perform feature matching or reconstruction for the target sample with pre-trained deep neural networks. However, they still struggle to address challenging anomalies because the deep embeddings stored in the memory bank can be less powerful and informative. More specifically, prior methods often overly rely on the finite resources stored in the memory bank, which leads to low robustness to unseen targets. In this paper, we propose a novel subspace-guided feature reconstruction framework to pursue adaptive feature approximation for anomaly localization. It first learns to construct low-dimensional subspaces from the given nominal samples, and then learns to reconstruct the given deep target embedding by linearly combining the subspace basis vectors using the self-expressive model. Our core is that, despite the limited resources in the memory bank, the out-of-bank features can be alternatively ``mimicked'' under the self-expressive mechanism to adaptively model the target. Eventually, the poorly reconstructed feature dimensions indicate anomalies for localization. Moreover, we propose a sampling method that leverages the sparsity of subspaces and allows the feature reconstruction to depend only on a small resource subset, which contributes to less memory overhead. Extensive experiments on three industrial benchmark datasets demonstrate that our approach generally achieves state-of-the-art anomaly localization performance.

Figures (7)

• Figure 1: An example of anomaly localization results from our method on the MVTec AD benchmark dataset. The red boundary in the target image indicates anomalous regions. Each feature map is shown in red color gradients for visualization. Anomaly localization results are shown by orange for anomaly boundaries and blue-red color gradients for anomaly intensity.
• Figure 2: Overview of our approach. Features are extracted from nominal data $\mathcal{D}$ and a test sample $J$ through a pre-trained network $\phi$. To achieve reduced memory expense and computational complexity, features in hierarchy level $l_{\mathrm{ref}}$ are utilized to estimate the subspace in which the nominal data lie. Only a limited number of data, sufficient for recovering this subspace, is sampled and stored in the memory bank $\mathcal{M}_{S}$. By exclusively utilizing the data in $\mathcal{M}_{S}$, the reconstruction methodology based on the self-expressive model is employed to identify anomalous regions in the test sample. The proposed method performs pixel-level anomaly localization by scoring at multiple hierarchies to benefit from deeper features.
• Figure 3: Illustrative example of covering out-of-bank data ($\mathcal{M} \setminus \mathcal{M}_{S}$) from a few data ($\mathcal{M}_{S}$) chosen through subspace-based sampling in a toy dataset: consider a synthetic dataset created by randomly generating data points lying on a single subspace of $\mathbb{R}^{2}$ in the ambient space of $\mathbb{R}^{3}$. The proposed subspace-based sampling strategy selects only very few basis vectors (green). Through a linear combination of these data points, a comprehensive approximation (red) is achieved for the out-of-bank data (blue) that lie in the same underlying subspace (gray plane).
• Figure 4: Qualitative results of our method on three benchmark datasets. For each category, we show a nominal image (normal), the target image (abnormal), the target feature map, the reconstructed feature map, the anomaly map, and the anomaly localization result identified by our method. The boundary in red denotes the ground-truth anomalous regions.
• Figure 5: Comparison of anomaly localization performance of different sampling mechanisms: (a) PRO and (b) inference time per image.