padim

PaDiM: A Patch Distribution Modeling Framework for Anomaly Detection and Localization

This is the implementation of the PaDiM paper.

Model Type: Segmentation

Description

PaDiM is a patch based algorithm. It relies on a pre-trained CNN feature extractor. The image is broken into patches and embeddings are extracted from each patch using different layers of the feature extractors. The activation vectors from different layers are concatenated to get embedding vectors carrying information from different semantic levels and resolutions. This helps encode fine grained and global contexts. However, since the generated embedding vectors may carry redundant information, dimensions are reduced using random selection. A multivariate gaussian distribution is generated for each patch embedding across the entire training batch. Thus, for each patch of the set of training images, we have a different multivariate gaussian distribution. These gaussian distributions are represented as a matrix of gaussian parameters.

During inference, Mahalanobis distance is used to score each patch position of the test image. It uses the inverse of the covariance matrix calculated for the patch during training. The matrix of Mahalanobis distances forms the anomaly map with higher scores indicating anomalous regions.

Architecture

Usage

python tools/train.py --model padim

Benchmark

All results gathered with seed 42.

MVTec AD Dataset

Image-Level AUC

	Avg	Carpet	Grid	Leather	Tile	Wood	Bottle	Cable	Capsule	Hazelnut	Metal Nut	Pill	Screw	Toothbrush	Transistor	Zipper
ResNet-18	0.891	0.945	0.857	0.982	0.950	0.976	0.994	0.844	0.901	0.750	0.961	0.863	0.759	0.889	0.920	0.780
Wide ResNet-50	0.950	0.995	0.942	1.0	0.974	0.993	0.999	0.878	0.927	0.964	0.989	0.939	0.845	0.942	0.976	0.882

Pixel-Level AUC

	Avg	Carpet	Grid	Leather	Tile	Wood	Bottle	Cable	Capsule	Hazelnut	Metal Nut	Pill	Screw	Toothbrush	Transistor	Zipper
ResNet-18	0.968	0.984	0.918	0.994	0.934	0.947	0.983	0.965	0.984	0.978	0.970	0.957	0.978	0.988	0.968	0.979
Wide ResNet-50	0.979	0.991	0.970	0.993	0.955	0.957	0.985	0.970	0.988	0.985	0.982	0.966	0.988	0.991	0.976	0.986

Image F1 Score

	Avg	Carpet	Grid	Leather	Tile	Wood	Bottle	Cable	Capsule	Hazelnut	Metal Nut	Pill	Screw	Toothbrush	Transistor	Zipper
ResNet-18	0.916	0.930	0.893	0.984	0.934	0.952	0.976	0.858	0.960	0.836	0.974	0.932	0.879	0.923	0.796	0.915
Wide ResNet-50	0.951	0.989	0.930	1.0	0.960	0.983	0.992	0.856	0.982	0.937	0.978	0.946	0.895	0.952	0.914	0.947

Sample Results