Sparsity Invariant CNNs

In this paper, we consider convolutional neural networks operating on sparse inputs with an application to depth upsampling from sparse laser scan data. First, we show that traditional convolutional networks perform poorly when applied to sparse data even when the location of missing data is provided to the network. To overcome this problem, we propose a simple yet effective sparse convolution layer which explicitly considers the location of missing data during the convolution operation. We demonstrate the benefits of the proposed network architecture in synthetic and real experiments with respect to various baseline approaches. Compared to dense baselines, the proposed sparse convolution network generalizes well to novel datasets and is invariant to the level of sparsity in the data. For our evaluation, we derive a novel dataset from the KITTI benchmark, comprising 93k depth annotated RGB images. Our dataset allows for training and evaluating depth upsampling and depth prediction techniques in challenging real-world settings and will be made available upon publication

Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection

X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400 x 400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria

Efficient and Accurate Segmentation of Defects in Industrial CT Scans

Industrial computed tomography (CT) is an elementary tool for the non-destructive inspection of cast light-metal or plastic parts. A comprehensive testing not only helps to ensure the stability and durability of a part, it also allows reducing the rejection rate by supporting the optimization of the casting process and to save material (and weight) by producing equivalent but more filigree structures. With a CT scan it is theoretically possible to locate any defect in the part under examination and to exactly determine its shape, which in turn helps to draw conclusions about its harmfulness. However, most of the time the data quality is not good enough to allow segmenting the defects with simple filter-based methods which directly operate on the gray-values—especially when the inspection is expanded to the entire production. In such in-line inspection scenarios the tight cycle times further limit the available time for the acquisition of the CT scan, which renders them noisy and prone to various artifacts. In recent years, dramatic advances in deep learning (and convolutional neural networks in particular) made even the reliable detection of small objects in cluttered scenes possible. These methods are a promising approach to quickly yield a reliable and accurate defect segmentation even in unfavorable CT scans. The huge drawback: a lot of precisely labeled training data is required, which is utterly challenging to obtain—particularly in the case of the detection of tiny defects in huge, highly artifact-afflicted, three-dimensional voxel data sets. Hence, a significant part of this work deals with the acquisition of precisely labeled training data. Firstly, we consider facilitating the manual labeling process: our experts annotate on high-quality CT scans with a high spatial resolution and a high contrast resolution and we then transfer these labels to an aligned ``normal'' CT scan of the same part, which holds all the challenging aspects we expect in production use. Nonetheless, due to the indecisiveness of the labeling experts about what to annotate as defective, the labels remain fuzzy. Thus, we additionally explore different approaches to generate artificial training data, for which a precise ground truth can be computed. We find an accurate labeling to be crucial for a proper training. We evaluate (i) domain randomization which simulates a super-set of reality with simple transformations, (ii) generative models which are trained to produce samples of the real-world data distribution, and (iii) realistic simulations which capture the essential aspects of real CT scans. Here, we develop a fully automated simulation pipeline which provides us with an arbitrary amount of precisely labeled training data. First, we procedurally generate virtual cast parts in which we place reasonable artificial casting defects. Then, we realistically simulate CT scans which include typical CT artifacts like scatter, noise, cupping, and ring artifacts. Finally, we compute a precise ground truth by determining for each voxel the overlap with the defect mesh. To determine whether our realistically simulated CT data is eligible to serve as training data for machine learning methods, we compare the prediction performance of learning-based and non-learning-based defect recognition algorithms on the simulated data and on real CT scans. In an extensive evaluation, we compare our novel deep learning method to a baseline of image processing and traditional machine learning algorithms. This evaluation shows how much defect detection benefits from learning-based approaches. In particular, we compare (i) a filter-based anomaly detection method which finds defect indications by subtracting the original CT data from a generated ``defect-free'' version, (ii) a pixel-classification method which, based on densely extracted hand-designed features, lets a random forest decide about whether an image element is part of a defect or not, and (iii) a novel deep learning method which combines a U-Net-like encoder-decoder-pair of three-dimensional convolutions with an additional refinement step. The encoder-decoder-pair yields a high recall, which allows us to detect even very small defect instances. The refinement step yields a high precision by sorting out the false positive responses. We extensively evaluate these models on our realistically simulated CT scans as well as on real CT scans in terms of their probability of detection, which tells us at which probability a defect of a given size can be found in a CT scan of a given quality, and their intersection over union, which gives us information about how precise our segmentation mask is in general. While the learning-based methods clearly outperform the image processing method, the deep learning method in particular convinces by its inference speed and its prediction performance on challenging CT scans—as they, for example, occur in in-line scenarios. Finally, we further explore the possibilities and the limitations of the combination of our fully automated simulation pipeline and our deep learning model. With the deep learning method yielding reliable results for CT scans of low data quality, we examine by how much we can reduce the scan time while still maintaining proper segmentation results. Then, we take a look on the transferability of the promising results to CT scans of parts of different materials and different manufacturing techniques, including plastic injection molding, iron casting, additive manufacturing, and composed multi-material parts. Each of these tasks comes with its own challenges like an increased artifact-level or different types of defects which occasionally are hard to detect even for the human eye. We tackle these challenges by employing our simulation pipeline to produce virtual counterparts that capture the tricky aspects and fine-tuning the deep learning method on this additional training data. With that we can tailor our approach towards specific tasks, achieving reliable and robust segmentation results even for challenging data. Lastly, we examine if the deep learning method, based on our realistically simulated training data, can be trained to distinguish between different types of defects—the reason why we require a precise segmentation in the first place—and we examine if the deep learning method can detect out-of-distribution data where its predictions become less trustworthy, i.e. an uncertainty estimation

Learning the invisible : a hybrid deep learning-shearlet framework for limited angle computed tomography

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based methodologies such as deep learning. However, in the context of inverse problems, deep neural networks mostly act as black box routines, used for instance for a somewhat unspecified removal of artifacts in classical image reconstructions. In this paper, we will focus on the severely ill-posed inverse problem of limited angle computed tomography, in which entire boundary sections are not captured in the measurements. We will develop a hybrid reconstruction framework that fuses model-based sparse regularization with data-driven deep learning. Our method is reliable in the sense that we only learn the part that can provably not be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to the remaining parts. Such a decomposition into visible and invisible segments is achieved by means of the shearlet transform that allows to resolve wavefront sets in the phase space. Furthermore, this split enables us to assign the clear task of inferring unknown shearlet coefficients to the neural network and thereby offering an interpretation of its performance in the context of limited angle computed tomography. Our numerical experiments show that our algorithm significantly surpasses both pure model- and more data-based reconstruction methods.Peer reviewe

Deep Learning for Inverse Problems (hybrid meeting)

Machine learning and in particular deep learning offer several data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing a solid mathematical theory for analyzing deep neural networks for inverse problems