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In my research sabbatical I was working on three different topics, namely orthogonal polynomials in geometric modeling, re-parametrized univariate subdivision curves, and reconstruction of 3d-fish-models and other zoological artifacts. In the subsequent Sections, I will describe my particular activity in these different fields. The sections are meant to present an overview of my research activities, leaving out the technical details.
Section 1 is on orthogonal polynomials and other related generating systems for functions systems of smooth function.
In Section 2, I will discuss the application of various re-parametrization schemes for interpolatory subdivision algorithms for the generation of space curves.
The next Section 3 is concerned with my research at the University of Queensland, Brisbane, in collaboration with Dr. Ulrike Siebeck from the School of Biomedical Sciences on fish behavior and reconstruction of 3d-fish models in particular.
In the last Section 4, I will describe what effects this research will have on in my subsequent teaching at the University of Applied Science Konstanz (HTWG).

IGA using subdivision-solids
(2015)

Deep 3D
(2017)

Vortrag

In the reverse engineering process one has to classify parts of point clouds with the correct type of geometric primitive. Features based on different geometric properties like point relations, normals, and curvature information can be used, to train classifiers like Support Vector Machines (SVM). These geometric features are estimated in the local neighborhood of a point of the point cloud. The multitude of different features makes an in-depth comparison necessary. In this work we evaluate 23 features for the classification of geometric primitives in point clouds. Their performance is evaluated on SVMs when used to classify geometric primitives in simulated and real laser scanned point clouds. We also introduce a normalization of point cloud density to improve classification generalization.

Knot placement for curve approximation is a well known and yet open problem in geometric modeling. Selecting knot values that yield good approximations is a challenging task, based largely on heuristics and user experience. More advanced approaches range from parametric averaging to genetic algorithms.
In this paper, we propose to use Support Vector Machines (SVMs) to determine suitable knot vectors for B-spline curve approximation. The SVMs are trained to identify locations in a sequential point cloud where knot placement will improve the approximation error. After the training phase, the SVM can assign, to each point set location, a so-called score. This score is based on geometric and differential geometric features of points. It measures the quality of each location to be used as knots in the subsequent approximation. From these scores, the final knot vector can be constructed exploring the topography of the score-vector without the need for iteration or optimization in the approximation process. Knot vectors computed with our approach outperform state of the art methods and yield tighter approximations.

Deep neural networks have been successfully applied to problems such as image segmentation, image super-resolution, coloration and image inpainting. In this work we propose the use of convolutional neural networks (CNN) for image inpainting of large regions in high-resolution textures. Due to limited computational resources processing high-resolution images with neural networks is still an open problem. Existing methods separate inpainting of global structure and the transfer of details, which leads to blurry results and loss of global coherence in the detail transfer step. Based on advances in texture synthesis using CNNs we propose patch-based image inpainting by a single network topology that is able to optimize for global as well as detail texture statistics. Our method is capable of filling large inpainting regions, oftentimes exceeding quality of comparable methods for images of high-resolution (2048x2048px). For reference patch look-up we propose to use the same summary statistics that are used in the inpainting process.

In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train interdependent deep neural networks to predict parametric values and knots. We show that it is possible to include B-spline curve approximation directly into the neural network architecture. The resulting parametrizations yield tight approximations and are able to outperform state-of-the-art methods.

Creating cages that enclose a 3D-model of some sort is part of many preprocessing pipelines in computational geometry. Creating a cage of preferably lower resolution than the original model is of special interest when performing an operation on the original model might be to costly. The desired operation can be applied to the cage first and then transferred to the enclosed model. With this paper the authors present a short survey of recent and well known methods for cage computation.
The authors would like to give the reader an insight in common methods and their differences.

Digital cameras are subject to physical, electronic and optic effects that result in errors and noise in the image. These effects include for example a temperature dependent dark current, read noise, optical vignetting or different sensitivities of individual pixels. The task of a radiometric calibration is to reduce these errors in the image and thus improve the quality of the overall application. In this work we present an algorithm for radiometric calibration based on Gaussian processes. Gaussian processes are a regression method widely used in machine learning that is particularly useful in our context. Then Gaussian process regression is used to learn a temperature and exposure time dependent mapping from observed gray-scale values to true light intensities for each pixel. Regression models based on the characteristics of single pixels suffer from excessively high runtime and thus are unsuitable for many practical applications. In contrast, a single regression model for an entire image with high spatial resolution leads to a low quality radiometric calibration, which also limits its practical use. The proposed algorithm is predicated on a partitioning of the pixels such that each pixel partition can be represented by one single regression model without quality loss. Partitioning is done by extracting features from the characteristic of each pixel and using them for lexicographic sorting. Splitting the sorted data into partitions with equal size yields the final partitions, each of which is represented by the partition centers. An individual Gaussian process regression and model selection is done for each partition. Calibration is performed by interpolating the gray-scale value of each pixel with the regression model of the respective partition. The experimental comparison of the proposed approach to classical flat field calibration shows a consistently higher reconstruction quality for the same overall number of calibration frames.

Reconstruction of hand-held laser scanner data is used in industry primarily for reverse engineering. Traditionally, scanning and reconstruction are separate steps. The operator of the laser scanner has no feedback from the reconstruction results. On-line reconstruction of the CAD geometry allows for such an immediate feedback.
We propose a method for on-line segmentation and reconstruction of CAD geometry from a stream of point data based on means that are updated on-line. These means are combined to define complex local geometric properties, e.g., to radii and center points of spherical regions. Using means of local scores, planar, cylindrical, and spherical segments are detected and extended robustly with region growing. For the on-line computation of the means we use so-called accumulated means. They allow for on-line insertion and removal of values and merging of means. Our results show that this approach can be performed on-line and is robust to noise. We demonstrate that our method reconstructs spherical, cylindrical, and planar segments on real scan data containing typical errors caused by hand-held laser scanners.

We present a 3d-laser-scan simulation in virtual
reality for creating synthetic scans of CAD models. Consisting of
the virtual reality head-mounted display Oculus Rift and the
motion controller Razer Hydra our system can be used like
common hand-held 3d laser scanners. It supports scanning of
triangular meshes as well as b-spline tensor product surfaces
based on high performance ray-casting algorithms. While point
clouds of known scanning simulations are missing the man-made
structure, our approach overcomes this problem by imitating
real scanning scenarios. Calculation speed, interactivity and the
resulting realistic point clouds are the beneﬁts of this system.

Classification of point clouds by different types of geometric primitives is an essential part in the reconstruction process of CAD geometry. We use support vector machines (SVM) to label patches in point clouds with the class labels tori, ellipsoids, spheres, cones, cylinders or planes. For the classification features based on different geometric properties like point normals, angles, and principal curvatures are used. These geometric features are estimated in the local neighborhood of a point of the point cloud. Computing these geometric features for a random subset of the point cloud yields a feature distribution. Different features are combined for achieving best classification results. To minimize the time consuming training phase of SVMs, the geometric features are first evaluated using linear discriminant analysis (LDA).
LDA and SVM are machine learning approaches that require an initial training phase to allow for a subsequent automatic classification of a new data set. For the training phase point clouds are generated using a simulation of a laser scanning device. Additional noise based on an laser scanner error model is added to the point clouds. The resulting LDA and SVM classifiers are then used to classify geometric primitives in simulated and real laser scanned point clouds.
Compared to other approaches, where all known features are used for classification, we explicitly compare novel against known geometric features to prove their effectiveness.