SemiOrthogonal

Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation

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This is an unofficial re-implementation of the paper Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation [1] available on arxiv. This paper proposes a modification on the PaDiM [2] method, mainly to replace the random dimension selection with an optimized inverse covariance computation using a semi-orthogonal embedding.

Features

The key features of this implementation are:

• Constant memory footprint - training on more images does not result in more memory required
• Resumable learning - the training step can be stopped and then resumed with inference in-between
• Limited dependencies - apart from PyTorch, Torchvision and Numpy

Installation

git clone https://github.com/Pangoraw/SemiOrthogonal.git

Getting started

MVTec AD

Here are the metrics compared to the one from the paper (with only one run), with WideResNet50 as a backbone and k=300:

Category	Paper (PRO Score)	This implementation (PRO Score)
Carpet	.974	.971
Grid	.941	.972
Leather	.987	.997
Tile	.859	.932
Wood	.906	.969
Bottle	.962	.988
Cable	.915	.963
Capsule	.952	.967
Hazelnut	.970	.985
Metal nut	.930	.976
Pill	.936	.982
Screw	.953	.984
Toothbrush	.957	.985
Transistor	.929	.969
Zipper	.960	.985
Mean	.942	.975

To reproduce the results on the MVTec AD dataset, download the files.

 $ mkdir data

 $ cd data

 $ wget ftp://guest:GU%2E205dldo@ftp.softronics.ch/mvtec_anomaly_detection/mvtec_anomaly_detection.tar.xz

 $ tar -xvf mvtec_anomaly_detection.tar.xz

And run examples/mvtec.py for each MVTec category:

for CATEGORY in bottle cable capsule carpet grid hazelnut leather metal_nut pill screw tile toothbrush transistor wood zipper
do
  echo "Running category $CATEGORY"
  python examples/mvtec.py \
    --data_root data/$CATEGORY/ \
    --backbone wide_resnet50 \
    -k 300
done

Training

You can choose a backbone model between resnet18 and wide_resnet50, and select the k value for the semi-orthogonal matrix size. For custom image size, you can also pass the image size to the constructor (not square images may not work).

from torch.utils.data import DataLoader
from semi_orthogonal import SemiOrthogonal

# i) Initialize
semi_ortho = SemiOrthogonal(k=100, device="cpu", backbone="resnet18", size=(256,256)) 

# ii) Create a dataloader producing image tensors
dataloader = DataLoader(...)

# iii) Consume the data to learn the normal distribution
# Use semi_ortho.train(...)
semi_ortho.train(dataloader)

# Or SemiOrthogonal.train_one_batch(...)
for imgs in dataloader:
	semi_ortho.train_one_batch(imgs)
semi_ortho.finalize_training() # compute the approx of C^-1

Testing

With the same SemiOrthogonal instance as in the Training section:

for new_imgs in test_dataloader:
	distances = semi_ortho.predict(new_imgs)
	# Note: predict only supports one image batches for now ;)
	# distances is a (1, w, h) matrix of the mahalanobis distances
	# Compute metrics or plot the anomaly map...

References

[1] Kim, J.-H., Kim, D.-H., Yi, S., Lee, T., 2021. Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation. arXiv:2105.14737 [cs].

[2] Defard, T., Setkov, A., Loesch, A., Audigier, R., 2020. PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization. arXiv:2011.08785 [cs].

Acknowledgements

This implementation was built on the work of:

• The original Semi Orthogonal paper
• taikiinoue45/mvtec-utils for the metric evaluation code
• My re-implementation of PaDiM