[Paper Review] Iterative energy-based projection on a normal data manifold for anomaly localization

David Dehaene, Oriel Frigo+2 more|arXiv (Cornell University)|Feb 10, 2020

Anomaly Detection Techniques and Applications67 citations

TL;DR

The paper introduces an iterative gradient-descent projection of inputs onto a learned normal data manifold, using an energy derived from autoencoder reconstructions, to achieve improved anomaly localization and inpainting. It updates the input in input space (not latent space) and leverages pixel-wise reconstruction error to guide fast convergence.

ABSTRACT

Autoencoder reconstructions are widely used for the task of unsupervised anomaly localization. Indeed, an autoencoder trained on normal data is expected to only be able to reconstruct normal features of the data, allowing the segmentation of anomalous pixels in an image via a simple comparison between the image and its autoencoder reconstruction. In practice however, local defects added to a normal image can deteriorate the whole reconstruction, making this segmentation challenging. To tackle the issue, we propose in this paper a new approach for projecting anomalous data on a autoencoder-learned normal data manifold, by using gradient descent on an energy derived from the autoencoder's loss function. This energy can be augmented with regularization terms that model priors on what constitutes the user-defined optimal projection. By iteratively updating the input of the autoencoder, we bypass the loss of high-frequency information caused by the autoencoder bottleneck. This allows to produce images of higher quality than classic reconstructions. Our method achieves state-of-the-art results on various anomaly localization datasets. It also shows promising results at an inpainting task on the CelebA dataset.

Motivation & Objective

• Motivate unsupervised anomaly localization for industrial inspection where anomalies are rare and labels are scarce.
• Propose a method to project anomalous inputs onto the normal data manifold by optimizing an energy defined from an autoencoder loss.
• Incorporate regularization terms to encode priors on expected anomalies and preserve high-frequency information.
• Demonstrate state-of-the-art anomaly localization on the MVTec dataset and show promising inpainting results on CelebA.

Proposed method

• Train an autoencoder on normal data to learn the normal manifold.
• Define an anomaly detector A(x) based on the autoencoder reconstruction loss with a threshold T.
• Construct an energy E(x) = L_r(x) + lambda * ||x - x0||_1 and perform gradient descent in input space starting from x0 to minimize E(x).
• Use the L1 distance as a surrogate for L0 to regularize the minimal change needed to reach the normal manifold.
• Enhance gradient updates with an adaptive scheme: optional use of Adam and a pixel-wise weighting term (x - f_VAE(x))^2 to speed convergence and preserve high-frequency details.
• Provide stop criteria based on energy convergence or a loss-threshold derived from training data.

Experimental results

Research questions

• RQ1 Can iterative gradient-based projection of an input onto a VAE/autoencoder-learned normal manifold improve anomaly localization compared to standard reconstructions?
• RQ2 Does incorporating a regularization term and high-frequency-preserving gradient updates yield better localization and inpainting quality?
• RQ3 How does the proposed method perform on standard anomaly localization benchmarks (e.g., MVTec) and inpainting tasks (e.g., CelebA)?

Key findings

• The method yields improvements in anomaly segmentation across multiple baselines on the MVTec dataset, with a mean improvement of 9.52% in AUROC.
• Gradient-based iterative reconstruction tends to produce higher-quality localizations by preserving high-frequency image details lost in standard autoencoder reconstructions.
• Using pixel-wise reconstruction error to guide gradient updates speeds convergence and preserves structure, achieving similar performance with fewer iterations.
• The approach also shows promising results for image inpainting on CelebA, improving over baseline VAE reconstructions in the presence of masking/noise.
• Stop criteria based on a reconstruction-loss threshold can efficiently terminate gradient descent, enabling practical application.