methods rely on clonable labels produced by a deterministic process. These labels are low-cost but their simple and repeatable preparation processes and regular decoding mechanisms are exploitable by counterfeiters. [4,5] Many of the more complex and safer anti-counterfeiting labels (such as high-end RFID labels with large number of logic gates) cannot become standard on some commonly used products due to their high cost. [5,6] Anti-counterfeiting labels with physical unclonable functions (PUF) are a feasible solution to the above shortcomings. Since the introduction of the PUF in 2002, [7] many anticounterfeiting labels with different PUF characteristics have been developed, such as unique bionic fingerprint pattern with random surface topography; [8][9][10] randomly distributed nanoparticle pattern, including flower-like patterns with random pinning points, [11] nanowires coated with fluorescent dyes in random positions, [12] etc. In addition, researchers have prepared many types of PUF anticounterfeiting labels with optical response. For example, Cheng et al. [13] reported a multicolor plasma nanopaper with random Raman intensity distribution, He et al. [14] designed multi-mode structural-color anti-counterfeiting labels composed of randomly arranged nanospheres, and Leem et al. [15] developed edible silk film labels with random light response. To improve the capabilities and speed of unclonable-pattern recognition,

Detecting image anomalies automatically in industrial scenarios can improve economic efficiency, but the scarcity of anomalous samples increases the challenge of the task. Recently, autoencoder has been widely used in image anomaly detection without using anomalous images during training. However, it is hard to determine the proper dimensionality of the latent space, and it often leads to unwanted reconstructions of the anomalous parts. To solve this problem, we propose a novel method based on the autoencoder. In this method, the latent space of the autoencoder is estimated using a discrete probability model. With the estimated probability model, the anomalous components in the latent space can be well excluded and undesirable reconstruction of the anomalous parts can be avoided. Specifically, we first adopt VQ-VAE as the reconstruction model to get a discrete latent space of normal samples. Then, PixelSail, a deep autoregressive model, is used to estimate the probability model of the discrete latent space. In the detection stage, the autoregressive model will determine the parts that deviate from the normal distribution in the input latent space. Then, the deviation code will be resampled from the normal distribution and decoded to yield a restored image, which is closest to the anomaly input. The anomaly is then detected by comparing the difference between the restored image and the anomaly image. Our proposed method is evaluated on the high-resolution industrial inspection image datasets MVTec AD which consist of 15 categories. The results show that the AUROC of the model improves by 15% over autoencoder and also yields competitive performance compared with state-of-the-art methods.

No abstract