Hyperbolic geometry enhanced feature filtering network for industrial anomaly detection

Abstract

In recent years, Cutting-edge machine learning algorithms and systems in Industry 4.0 enhance quality control and increase production efficiency. The visual perception algorithms have become extensively utilized in surface defect detection, progressively replacing manual inspection methods. As a crucial component of the Industrial Internet of Things (IIoT), this technology is pivotal for ensuring industrial production quality and has garnered significant attention from the military and aerospace sectors. Nonetheless, most existing methods rely on Euclidean space, which constrains their effectiveness in handling non-Euclidean space data. Additionally, challenges such as addressing pre-trained feature redundancy and bias in the pre-training process persist. This paper presents HADNet, a hyperbolic space-based anomaly detection method. Specifically, we begin by mapping the extracted features to hyperbolic space, a non-Euclidean geometric space. This mapping leverages the unique geometric properties of hyperbolic space, particularly the hyperbolic distance metric, to represent the distances between features more effectively. Next, the most relevant features for anomaly detection are selected through the anomaly-aware feature subset selection module, enhancing anomaly detection performance. Finally, we introduce adaptive residuals discrimination, an adaptive analysis technique that discards residuals lacking anomaly information, thereby isolating the most effective regions for anomaly detection. Extensive experiments on four benchmark datasets NEU-Seg, MT-Defect, FSSD-12, and UCF-EL demonstrate the efficacy of HADNet, achieving mIoU scores of 87%, 81.46%, 77.04%, and 59.41% respectively, significantly surpassing the current state-of-the-art methods.

Keywords: Anomaly detection; Deep learning; Hyperbolic space.

Fig. 1

Comparisons between conventional Euclidean space (a) and hyperbolic space (b). Mean intersection over union of anomaly detection methods on NEU-Seg, MT-Defect and FSSD-12 datasets (c).

Fig. 2

Illustrates the hierarchical relationships of metal surface defect images. (a) The entire image serves as the root node, with local regions acting as branch nodes and detailed areas representing deeper branch nodes. (b) The positions of these nodes in hyperbolic space are depicted accordingly.

Fig. 3

The overall architecture of HADNet. The architecture consists of three main modules: Hyperbolic Space Transformation (HST), Anomaly-aware Feature Subset Selection (AFSS), and Adaptive Residuals Discrimination (ARD). The input features are first mapped from Euclidean space to hyperbolic space using HST to enhance the representation of hierarchical relationships. The AFSS module then selects the most relevant features for anomaly detection, reducing redundancy and improving detection accuracy. Finally, the ARD module analyzes the residuals to isolate the most effective regions for anomaly detection and generates anomaly scores.

Fig. 4

Hyperbolic Space Transformation process. The features embedding of Euclidean space is converted to hyperbolic space by exponential mapping . For Poincare’s ball, given a point z, the distance to the hyperplane is expressed as .

Fig. 5

Comparative detection results of HADNet on the NEU-Seg dataset.

Fig. 6

Comparative detection results of HADNet on the MT-Defect dataset.

Fig. 7

Comparative detection results of HADNet on the FSSD-12 dataset.