Master's Thesis
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Statistical shape models learn to capture the most characteristic geometric variations of anatomical structures given samples from their population. Accordingly, shape models have become an essential tool for many medical applications and are used in, for example, shape generation, reconstruction, and classification tasks. However, established statistical shape models require precomputed dense correspondence between shapes, often lack robustness, and ignore the global surface topology. This thesis presents a novel neural flow-based shape model that does not require any precomputed correspondence. The proposed model relies on continuous flows of a neural ordinary differential equation to model shapes as deformations of a template. To increase the expressivity of the neural flow and disentangle global, low-frequency deformations from the generation of local, high- frequency details, we propose to apply a hierarchy of flows. We evaluate the performance of our model on two anatomical structures, liver, and distal femur. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior, as indicated by its generalization ability and specificity. More so, we demonstrate the effectiveness of our shape model on shape reconstruction tasks and find anatomically plausible solutions. Finally, we assess the quality of the emerging shape representation in an unsupervised setting and discriminate healthy from pathological shapes.
AI-based computer vision systems play a crucial role in the environment perception for autonomous driving. Although the development of self-driving systems has been pursued for multiple decades, it is only recently that breakthroughs in Deep Neural Networks (DNNs) have led to their widespread application in perception pipelines, which are getting more and more sophisticated. However, with this rising trend comes the need for a systematic safety analysis to evaluate the DNN's behavior in difficult scenarios as well as to identify the various factors that cause misbehavior in such systems. This work aims to deliver a crucial contribution to the lacking literature on the systematic analysis of Performance Limiting Factors (PLFs) for DNNs by investigating the task of pedestrian detection in urban traffic from a monocular camera mounted on an autonomous vehicle. To investigate the common factors that lead to DNN misbehavior, six commonly used state-of-the-art object detection architectures and three detection tasks are studied using a new large-scale synthetic dataset and a smaller real-world dataset for pedestrian detection. The systematic analysis includes 17 factors from the literature and four novel factors that are introduced as part of this work. Each of the 21 factors is assessed based on its influence on the detection performance and whether it can be considered a Performance Limiting Factor (PLF). In order to support the evaluation of the detection performance, a novel and task-oriented Pedestrian Detection Safety Metric (PDSM) is introduced, which is specifically designed to aid in the identification of individual factors that contribute to DNN failure. This work further introduces a training approach for F1-Score maximization whose purpose is to ensure that the DNNs are assessed at their highest performance. Moreover, a new occlusion estimation model is introduced to replace the missing pedestrian occlusion annotations in the real-world dataset. Based on a qualitative analysis of the correlation graphs that visualize the correlation between the PLFs and the detection performance, this study identified 16 of the initial 21 factors as being PLFs for DNNs out of which the entropy, the occlusion ratio, the boundary edge strength, and the bounding box aspect ratio turned out to be most severely affecting the detection performance. The findings of this study highlight some of the most serious shortcomings of current DNNs and pave the way for future research to address these issues.
We give theorems about asymptotic normality of general additive functionals on patricia tries, derived from results on tries. These theorems are applied to show asymptotic normality of the distribution of random fringe trees in patricia tries. Formulas for asymptotic mean and variance are given. The proportion of fringe trees with π keys is asymptotically, ignoring oscillations, given by (1βπ(π))/(π» +π½)π(πβ1) with the source entropy π», an entropy-like constant π½, that is π» in the binary case, and an exponentially decreasing function π(π). Another application gives asymptotic normality of the independence number and the number of π-protected nodes.