Padim [anomaly detection: embedded based]

Preface

The blog is from 2020.11CVPR A paper on , At present, the detection and positioning effect is MVTec Dataset ranking 11（papers with code Website ）, This is the deadline for posting .

Source code ：https://github.com/xiahaifeng1995/PaDiM-Anomaly-Detection-Localization-master（ unofficial ）

background

The paper proves that multi-scale features are helpful for information differentiation .

Make the normal image into a reference for testing , These references can be nsphere Center of , Parameters of Gaussian distribution , The whole set of normal embedded vectors .SPADE Use the third one ,PaDiM In the second .

Model principle （ Control code ）

thought ： Through feature extraction, we can get the feature block of each graph , Then, all feature blocks of all graphs are used to form a multi dimension for each pixel Gaussian distribution , Mahalanobis distance as evaluation score . The model does not need training , Only use trained networks to extract features .

A.Embedding extraction

Use resnet After the network extracts features , Form tensor [500,448,56,56], Choose one randomly 100 Dimensions , Form tensor [500,100,56,56].

Patch embedding vector （patch embedding vectors）： The so-called patch , Refers to pixels ; The so-called embedding , It refers to the combination of different features extracted by the network . It's all about encapsulation .

B.Learning of the normality

These pixels of the image are assumed to be multidimensional Gaussian distribution , So the network should work out this distribution , By means of mean and covariance . After processing, there is a multi-dimensional Gaussian distribution at each pixel position .

Tensor reshaping forms [500,100,3136] after , Please all batch The mean value at each pixel position is formed [100,3136]--> Find the formation of the covariance matrix [100,100,3136]

covariance ： The covariance formula here is not only the authentic covariance , Also added a small operation on the diagonal , Make the covariance matrix full rank and reversible . Covariance also correlates the characteristics of different dimensions , Experiments show that this kind of correlated information is helpful to the detection effect .

C.Inference : computation of the anomaly map

The Mahalanobis distance is calculated at each pixel position of the distribution of the test map and the normal map , The highest score in all positions is regarded as the detection score .

Markov distance ： The inverse of the covariance matrix formed by the normal graph is required , Mean and abnormal characteristic diagram .

Detection and location

Convert fractional graph into proportional fractional graph --> The highest score of all proportional scores is passed into rocauc function .

experiment

Comparative experiments ： Use different evaluation indicators , Different data sets MVTec、STC、 Data enhanced MVTec, Different models .

Ablation Experiment ： Choice of different embedding layers , Random dimensionality reduction or principal component analysis dimensionality reduction , Different pre training extraction Networks ResNet18、Wide ResNet-50-2 (WR50)、EfficientNet-B5.

other ： Time contrast , Memory comparison .