Dennis Mosbach

• 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.