3.5 Results 43 model reconstructs anomalous digits quite well. Since this pixel-wise difference between original and reconstruction is directly related to the first term of the ELBO in (3.1), this gives an indication why density estimation appears to work less well with a 32-dimensional latent space. On the other hand, we do note that a 32-dimensional latent space produces sharper, more realistic-looking images. Perfect reconstruction or realistic data generation is however not our main goal in this case, and the blurriness from the 2-dimensional model does not appear to have a negative effect on the anomaly detection performance, as demonstrated by the auROC and auPRC scores. (a) Anomalous digit 0. Latent dimension 2. (b) Anomalous digit 7. Latent dimension 2. (c) Anomalous digit 0. Latent dimension 32. (d) Anomalous digit 7. Latent dimension 32. Figure 3.10: Originals (left), reconstructions (middle), and difference images (right) for anomalous MNIST digits. The difference image consists of the original image, with an overlay of red and blue pixels, representing higher or lower (more white or black) pixel values in the reconstruction. The opacity of the red and blue corresponds to the size of the difference. 3.5.2 3D-Printed Products We evaluate our anomaly framework for each defect type in the 3D-printed products dataset separately, for three different VAE models trained on normal data, with latent dimensions 2, 32 and 64, respectively. The resulting auROC scores are shown in Table 3.5, whereas auPRC scores are shown in Table 3.6. There is no big difference in performance between the architectures with latent dimension 32 or 64, but they clearly outperform the model with a 2-dimensional latent space. This suggests that the 2-dimensional model is too limited to properly learn a density distribution for the normal data.
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