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Convolutional autoencoders have emerged as popular methods for unsupervised defect segmentation on image data. Most commonly, this task is performed by thresholding a per-pixel reconstruction error based on an p -distance. This procedure, however, leads to large residuals whenever the reconstruction includes slight localization inaccuracies around edges. It also fails to reveal defective regions that have been visually altered when intensity values stay roughly consistent. We show that these problems prevent these approaches from being applied to complex real-world scenarios and that they cannot be easily avoided by employing more elaborate architectures such as variational or feature matching autoencoders. We propose to use a perceptual loss function based on structural similarity that examines inter-dependencies between local image regions, taking into account luminance, contrast, and structural information, instead of simply comparing single pixel values. It achieves significant performance gains on a challenging real-world dataset of nanofibrous materials and a novel dataset of two woven fabrics over state-of-the-art approaches for unsupervised defect segmentation that use per-pixel reconstruction error metrics.

The detection of anomalous structures in natural image data is of utmost importance for numerous tasks in the field of computer vision. The development of methods for unsupervised anomaly detection requires data on which to train and evaluate new approaches and ideas. We introduce the MVTec anomaly detection dataset containing 5354 high-resolution color images of different object and texture categories. It contains normal, i.e., defect-free images intended for training and images with anomalies intended for testing. The anomalies manifest themselves in the form of over 70 different types of defects such as scratches, dents, contaminations, and various structural changes. In addition, we provide pixel-precise ground truth annotations for all anomalies. We conduct a thorough evaluation of current state-of-the-art unsupervised anomaly detection methods based on deep architectures such as convolutional autoencoders, generative adversarial networks, and feature descriptors using pretrained convolutional neural networks, as well as classical computer vision methods. We highlight the advantages and disadvantages of multiple performance metrics as well as threshold estimation techniques. This benchmark indicates that methods that leverage descriptors of pretrained networks outperform all other approaches and deep-learning-based generative models show considerable room for improvement.

We investigate the spectral and dynamical localization of a quantum system of n particles on R d which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two conditions which ensure spectral and dynamical localization near the bottom of the spectrum of the n-particle system: (i) localization is established in the regime of weak interactions supposing one-particle localization, and (ii) localization is also established under a Lifshitz-tail type condition on the sparsity of the spectrum. In case of polynomially decaying interactions, we provide an upper bound on the number of particles up to which these conditions apply.

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The accuracy of object detectors and trackers is most commonly evaluated by the Intersection over Union (IoU) criterion. To date, most approaches are restricted to axis-aligned or oriented boxes and, as a consequence, many datasets are only labeled with boxes. Nevertheless, axis-aligned or oriented boxes cannot accurately capture an object's shape. To address this, a number of densely segmented datasets has started to emerge in both the object detection and the object tracking communities. However, evaluating the accuracy of object detectors and trackers that are restricted to boxes on densely segmented data is not straightforward. To close this gap, we introduce the relative Intersection over Union (rIoU) accuracy measure. The measure normalizes the IoU with the optimal box for the segmentation to generate an accuracy measure that ranges between 0 and 1 and allows a more precise measurement of accuracies. Furthermore, it enables an efficient and easy way to understand scenes and the strengths and weaknesses of an object detection or tracking approach. We display how the new measure can be efficiently calculated and present an easy-to-use evaluation framework. The framework is tested on the DAVIS and the VOT2016 segmentations and has been made available to the community.

The unsupervised detection and localization of anomalies in natural images is an intriguing and challenging problem. Anomalies manifest themselves in very different ways and an ideal benchmark dataset for this task should contain representative examples for all of them. We find that existing datasets are biased towards local structural anomalies such as scratches, dents, or contaminations. In particular, they lack anomalies in the form of violations of logical constraints, e.g., permissible objects occurring in invalid locations. We contribute a new dataset based on industrial inspection scenarios that evenly covers both types of anomalies. We provide pixel-precise ground truth data for each anomalous region and define a generalized evaluation metric that addresses localization ambiguities that can arise for logical anomalies. Furthermore, we propose a novel algorithm that improves over the state of the art in the joint detection of structural and logical anomalies. It consists of a local and a global network branch. The first one inspects confined regions independent of their spatial locations in the input image and is primarily responsible for the detection of entirely new local structures. The second one learns a globally consistent representation of the training data through a bottleneck that enables the detection of violations of long-range dependencies, a key characteristic of many logical anomalies. We perform extensive evaluations on our new dataset to corroborate our claims.