B-spline surfaces are a well-established tool to analytically describe objects. They are commonly used in various fields, e.g., mechanical and aerospace engineering, computer aided design, and computer graphics. Obtaining and using B-spline surface models of real-life objects is an intricate process. Initial virtual representations are usually obtained via scanning technologies in the form of discrete data, e.g., point clouds, surface meshes, or volume images. This data often requires pre-processing to remove noise and artifacts. Even with high quality data, obtaining models of complex or very large structures needs specialized solutions that are viable for the available hardware. Once B-spline models are constructed, their properties can be utilized and combined with application-specific knowledge to provide efficient solutions for practical problems. This thesis contributes to various aspects of the processing pipeline. It addresses pre-processing, creating B-spline models of large and topologically challenging data, and the use of such models within the context of visual surface inspection. Proposed methods improve existing solutions in terms of efficiency, hardware restrictions, and quality of the results. The following contributions are presented: Fast and memory-efficient quantile filter: Quantile filters are widely used operations in image processing. The most common instance is the median filter which is a standard solution to treat noise while preserving the shape of an object. Various implementations of such filters are available offering either high performance or low memory complexity, but not both. This thesis proposes a generalization of two existing algorithms: one that favors speed and one that favors low memory usage. An adaptable hybrid algorithm is introduced. It can be tuned for optimal performance on the available hardware. Results show that it outperforms both state-of-the-art reference methods for most practical filter sizes. Robust B-spline reconstructions of isosurfaces in volume images: The micro-structure of wood-based thermal insulation materials is analyzed to research heat conductivity properties. High-quality scans reveal a complex system of cellulose fibers. B-spline models of individual fibers are highly desirable to conduct simulations. Due to the physical processing of the material, the surfaces of those fibers consist of challenging elements like loose filaments, holes, and tunnels. Standard solutions fail to partition the data into a small number of quadrilateral cells which is required for the B-spline construction step. A novel approach is presented that splits up the data processing into separate topology and geometry pipelines. This robust method is demonstrated by constructing B-spline models with 236 to 676 surfaces from triangulated isosurfaces with 423628 to 1203844 triangles. Local method for smooth B-spline surface approximations: Constructing smooth B-spline models to approximate discrete data is a challenging task. Various standard solutions exist, often imposing restrictions to knot vectors, spline order, or available degrees of freedom for the data approximation. This thesis presents a local approach with less restrictions aiming for approximate \(G^1\)-continuity. Nonlinear terms are added to standard minimization problems. The local design of the algorithm compensates for the higher computational complexity. Results are shown and evaluated for objects of varying complexity. A comparison with an exact \(G^1\)-continuous method shows that the novel method improves approximation accuracy on average by a factor of 10 at the cost of having small discontinuities in normal vectors of less than 1 degree. Model-based viewpoint generation for surface inspection: Within modern and flexible factories, surface inspection of products is still a very rigid process. An automated inspection system requires the definition of viewpoints from which a robot then takes pictures during the inspection process. Setting up such a system is a time-intensive process which is primarily done manually by experts. This work presents a purely virtual approach for the generation of viewpoints. Based on an intuitive definition of analytic feature functionals, a non-uniform sampling with respect to inspection-specific criteria is performed on given B-spline models. This leads to the definition of a low number of viewpoint candidates. Results of applying this method to several test objects with varying parameters indicate that good viewpoints can be obtained through a fast process that can be performed fully automatically or interactively through the use of meaningful parameters.

Lecture notes for the lecture "Cohomology of Groups" SS 2018

Decentralization is the norm of future smart production as it assists in contextual dynamic decision-making and thereby increases the flexibility required to produce highly customized products. When manufacturing business software is operated as a cloud-based solution, it experiences network latency and connectivity issues. To overcome these problems, the production control should be delegated to the manufacturing edge layer and hence, the argument of decentralization is even more applicable to this narrative. Semantic technologies, on the other hand, assist in discerning the meaning, reasoning and drawing inferences from the data. There are several specifications and frameworks to automate the discovery, orchestration and invocation of web services; the prominent are OWL-S and SAWSDL. This thesis adapts these frameworks for OPC UA, and consequently, the proposed semantically enriched OPC UA concept enables the edge layer to create flexible production orchestration plans in a manufacturing scenario controlled by cloud MES.

Interconnection networks enable fast data communication between components of a digital system. The selection of an appropriate interconnection network and its architecture plays an important role in the development process of the system. The selection of a bad network architecture may significantly delay the communication between components and decrease the overall system performance. There are various interconnection networks available. Most of them are blocking networks. Blocking means that even though a pair of source and target components may be free, a connection between them might still not be possible due to limited capabilities of the network. Moreover, routing algorithms of blocking networks have to avoid deadlocks and livelocks, which typically does only allow poor real-time guarantees for delivering a message. Nonblocking networks can always manage all requests that are coming from their input components and can therefore deliver all messages in guaranteed time, i.e, with strong real-time guarantees. However, only a few networks are nonblocking and easy to implement. The simplest one is the crossbar network which is a comparably simple circuit with also a simple routing algorithm. However, while its circuit depth of O(log(n)) is optimal, its size increases with O(n^2) and quickly becomes infeasible for large networks. Therefore, the construction of nonblocking networks with a quasipolynomial size O(nlog(n)^a) and polylogarithmic depth O(log(n)^b) turned out as a research problem. Benes [Clos53; Bene65] networks were the first non blocking networks having an optimal size of O(nlog(n)) and an optimal depth of O(log(n)), but their routing algorithms are quite complicated and require circuits of depth O(log(n)^2) [NaSa82]. Other nonblocking interconnection networks are derived from sorting networks. Essentially, there are merge-based (MBS) and radix-based (RBS) sorting networks. MBS and RBS networks can be both implemented in a pipelined fashion which leads to a big advantage for their circuit implementation. While these networks are nonblocking and can implement all n! permutations, they cannot directly handle partial permutations that frequently occur in practice since not every input component communicates at every point of time with an output component. For merge-based sorting networks, there is a well known general solution called the Batcher-Banyan network. However, for the larger class of radix-based sorting networks this does not work, and there is only one solution known for a particular permutation network. In this thesis, new nonblocking radix-based interconnection networks are presented. In particular, for a certain permutation network, three routing algorithms are developed and their circuit implementations are evaluated concerning their size, depth, and power consumption. A special extension of these networks allows them to route also partial permutations. Moreover, three general constructions to convert any binary sorter into a ternary split module were presented which is the key to construct a radix-based interconnection network that can cope with partial permutations. The thesis compares also chip designs of these networks with other radix-based sorting networks as well as with the Batcher-Banyan networks as competitors. As a result, it turns out that the proposed radix-based networks are superior and could form the basis of larger manycore architectures.

The neural networks have been extensively used for tasks based on image sensors. These models have, in the past decade, consistently performed better than other machine learning methods on tasks of computer vision. It is understood that methods for transfer learning from neural networks trained on large datasets can reduce the total data requirement while training new neural network models. These methods tend not to perform well when the data recording sensor or the recording environment is unique from the existing large datasets. The machine learning literature provides various methods for prior-information inclusion in a learning model. Such methods employ methods like designing biases into the data representation vectors, enforcing priors or physical constraints on the models. Including such information into neural networks for the image frames and image-sequence classification is hard because of the very high dimensional neural network mapping function and little information about the relation between the neural network parameters. In this thesis, we introduce methods for evaluating the statistically learned data representation and combining these information descriptors. We have introduced methods for including information into neural networks. In a series of experiments, we have demonstrated methods for adding the existing model or task information to neural networks. This is done by 1) Adding architectural constraints based on the physical shape information of the input data, 2) including weight priors on neural networks by training them to mimic statistical and physical properties of the data (hand shapes), and 3) by including the knowledge about the classes involved in the classification tasks to modify the neural network outputs. These methods are demonstrated, and their positive influence on the hand shape and hand gesture classification tasks are reported. This thesis also proposes methods for combination of statistical and physical models with parametrized learning models and show improved performances with constant data size. Eventually, these proposals are tied together to develop an in-car hand-shape and hand-gesture classifier based on a Time of Flight sensor.