28 Anomaly Detection with Variational Autoencoders our work, AnoGAN (Schlegl et al., 2017) also uses a deep generative model for anomaly detection, specifically a Generative Adversarial Network (GAN) (Goodfellow et al., 2014). GANs, however, do not explicitly model likelihood and require an iterative procedure (Yeh et al., 2016) that involves backpropagation steps to assess the likelihood of a data instance. This procedure needs to be run again for each data point, making it rather unsuitable for automating visual quality control. Moreover, GANs are notoriously unstable and therefore hard to train. For these reasons, we mostly ignore GAN-based anomaly detection here. A Variational Autoencoder (VAE) (Kingma and Welling, 2013; Rezende et al., 2014) is a deep generative model that models a probability density function, conditioned on learned latent variables. It also features an inference model for the latent space, meaning that it can provide fast estimates of the likelihood of any data point. This makes it more suitable for fast automated probabilistic anomaly detection. Moreover, as opposed to GANs, VAE training is very stable and therefore much easier and more flexible. On the other hand, VAEs when used to generate data from the learned distribution are known to generate blurry images, whereas GANs are known for producing sharp, realistic results. Our main interest however is anomaly detection, so we are less interested in realistic results and more interested in a reliable and regularised density estimation. See Section 2.1 for a more thorough discussion of VAEs. A similar approach to ours is proposed by Lu and Xu (2018), but for the application of anomaly detection on skin disease images. Here we focus on a different application instead, showing the applicability of such methods for visual quality control of 3D-printed surfaces. In particular we highlight the fact that the method can be easily applied to new 3D-printed products of a different type, needing only a relatively small sample of positive examples to retrain the neural network. Furthermore, we investigate the performance of this method for lung cancer detection from 3D images of lung nodules as well. Another similar approach is the AnoVAEGAN (Baur et al., 2018), which uses GAN components combined with a VAE to learn a generative model. However, this still suffers from training difficulties that are typical for GANs. Moreover, their method does not truly estimate likelihood scores, but only uses a reconstruction error for anomaly detection on pixel level. This requires pixel-wise annotations, whereas we only use image-level annotations. 3.3 Anomaly Detection with Generative Models Our method aims to address three common challenges:
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