26 Anomaly Detection with Variational Autoencoders Additionally, we test the method on lung cancer detection in 3D lung nodules. When comparing to previous methods based on Generative Adversarial Networks (GANs), results show that both GANs and VAEs struggle to perform well on this more challenging task. 3.1 Introduction Defects of 3D-printed products typically take place in the contact area between the foundation of the printer and the surface of the product. It is important to detect such defects in an automated way directly after production, to prevent the propagation of faulty products and reduce the costs associated with manual inspection. As defects typically occur on the surface of a product, an efficient way to facilitate fault detection is to apply machine learning on images of the product surface, for automated visual inspection. Analysing such images poses several challenges however. First of all, the images will have to be sufficiently detailed, i.e. have high enough resolution. This means that inspection methods will have to deal with high-dimensional data. Secondly, defects are typically rare, so there will be more examples of correct surfaces than of defects. Thus we have to be able to deal with a highly imbalanced dataset. Thirdly, to establish some ground truth for the visual inspection outcome, an initial set of examples will have to be labelled whether they are acceptable or contain defects. This typically involves significant manual labour that diminishes the value of automating the process. Deep learning methods, in particular convolutional neural networks, have recently been shown to be one of the most powerful machine learning methods for processing image data. In particular, great success has been achieved with supervised discriminative deep learning methods for classification (Lecun et al., 2015). However, such methods typically need large amounts of labelled training data, which are often not available for our problem scenario, as explained in the aforementioned challenges. In particular, the class of defects is often underrepresented, making it hard for supervised classification methods to reliably classify defects. To deal with this, we frame the fault detection problem not as a binary classification problem, but as an anomaly detection problem (Pimentel et al., 2014), i.e. we treat defects as anomalies or outliers. Given this formulation, we aim to develop a model that estimates the probability density distribution of the expected, non-faulty data. We then wish to detect defects as anomalies or outliers—instances of lower likelihood according to our estimated density model.
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