## About

51

Publications

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748

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Introduction

My academic career started in algorithm theory and engineering, especially in computational geometry and topology, with links to CAD/CAM, machine learning and security. Later my focus shifted to artificial intelligence and system architectures for industrial control systems. During my time in industry I worked in a broader sense on smart factory technology.

## Publications

Publications (51)

Industry 4.0 is driven by demands like shorter time-to-market, mass customization of products, and batch size one production. Reinforcement Learning (RL), a machine learning paradigm shown to possess a great potential in improving and surpassing human level performance in numerous complex tasks, allows coping with the mentioned demands. In this pap...

Industry 4.0 factories are complex and data-driven. Data is yielded from many sources, including sensors, PLCs, and other devices, but also from IT, like ERP or CRM systems. We ask how to collect and process this data in a way, such that it includes metadata and can be used for industrial analytics or to derive intelligent support systems. This pap...

The four essential Industry 4.0 design principles information transparency, technical assistance, interconnection and decentralized decisions introduce new requirements to industrial systems. These requirements often bring the challenge of integrating information technology (IT) solutions, which are prevalent on the office floor level of a producti...

Reinforcement Learning (RL) is a powerful machine learning paradigm that has been applied in various fields such as robotics, natural language processing and game playing achieving state-of-the-art results. Targeted to solve sequential decision making problems, it is by design able to learn from experience and therefore adapt to changing dynamic en...

The vision of Industry 4.0 introduces new requirements to Operational Technology (OT) systems. Solutions for these requirements already exist in the Information Technology (IT) world, however, due to the different characteristics of both worlds, these solutions often cannot be directly used in the world of OT. We therefore propose an Industrial Bus...

In this paper, we revisit the application of Genetic Algorithm (GA) to the Traveling Salesperson Problem (TSP) and introduce a family of novel crossover operators that outperform the previous state of the art. The novel crossover operators aim to exploit symmetries in the solution space, which allows us to more effectively preserve well-performing...

Industry 4.0 is driven by demands like shorter time-to-market, mass customization of products, and batch size one production. Reinforcement Learning (RL), a machine learning paradigm shown to possess a great potential in improving and surpassing human level performance in numerous complex tasks, allows coping with the mentioned demands. In this pap...

In this paper we discuss the application of Artificial Intelligence (AI) to the exemplary industrial use case of the two-dimensional commissioning problem in a high-bay storage, which essentially can be phrased as an instance of Traveling Salesperson Problem (TSP). We investigate the mlrose library that provides an TSP optimizer based on various he...

In this work we present an “out-of-the-box” application of Machine Learning (ML) optimizers for an industrial optimization problem. We introduce a piecewise polynomial model (spline) for fitting of Ck-continuous functions, which can be deployed in a cam approximation setting. We then use the gradient descent optimization context provided by the mac...

Artificial intelligence (AI) is a crucial technology of industrial digitalization. Especially in the production industry, a great potential is present in optimizing existing processes, e.g., concerning resource consumption, emission reduction, process and product quality improvements, predictive maintenance, and so on. Some of this potential is add...

In this paper we discuss the application of AI and ML to the exemplary industrial use case of the two-dimensional commissioning problem in a high-bay storage, which essentially can be phrased as an instance of Traveling Salesperson Problem (TSP). We investigate the mlrose library that provides an TSP optimizer based on various heuristic optimizatio...

Topological data analysis (TDA) applies methods of topology in data analysis and found many applications in data science in the recent decade that go well beyond machine learning. TDA builds upon the observation that data often possesses a certain intrinsic shape such as the shape of a point cloud, the shape of a signal or the shape of a geometric...

Given a polygonal shape with holes, we investigate the topology of two types of skeletons (straight skeleton, Voronoi diagram) and the evolution of the inward offsets they induce. It is shown that both skeletons are homotopy equivalent to the shape and an O(n log n) algorithm to compute the persistent homology of the filtration of the inset polygon...

We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.
Using our new framework, we establish, for the first ti...

We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a...

We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alte...

The straight skeleton of a polygon is the geometric graph obtained by tracing
the vertices during a mitered offsetting process. It is known that the straight
skeleton of a simple polygon is a tree, and one can naturally derive directions
on the edges of the tree from the propagation of the shrinking process.
In this paper, we ask the reverse questi...

Topological data analysis offers a rich source of valuable information to
study vision problems. Yet, so far we lack a theoretically sound connection to
popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In
this work, we establish such a connection by designing a multi-scale kernel for
persistence diagrams, a stable summar...

In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.
Using our new framework, we establish, f...

Highlights
•
We study the characteristics of the straight skeleton (SK) of monotone polygons.
•
We devise an algorithm to compute the SK of monotone polygons in O(nlogn) time.
•
This algorithm can also compute the positively weighted SK in O(nlogn) time.

We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditions for input shapes in order to obtain identical stra...

We study the characteristics of straight skeletons of strictly monotone polygonal chains, and use them to devise an algorithm for computing positively weighted straight skeletons of strictly monotone polygons. Our algorithm runs in O(n log n) time and O(n) space.

In this paper, we fill in a gap in the wavefront-based definition of weighted straight skeletons in the presence of multiple simultaneous, co-located split events. We interpret the need to pair up wavefront edges to restore planarity as a particular matching problem. Our results on a stable roommate problem defined on a directed pseudo-line arrange...

The embedding of a digital watermark in vector data results in a perturbation of the vertices which needs to be constrained in order to maintain geometric prop-erties of the data. In this paper we investigate the problem of computing so-called perturbation regions in which the vertices of a planar straight-line graph may be dislocated while still p...

We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted stra...

In this paper, we investigate the weighted straight skeleton from a geometric, graph-theoretical and combinato-rial point of view. We start with a thorough definition , shed light on an ambiguity issue in the procedural definition, and propose solutions. We investigate the geometry of faces and the roof model and we discuss in which cases the strai...

A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straigh...

Ambient noise and acoustic echo reduction are indispensable signal processing steps in a hands-free audio communication system. Taking the signals from multiple microphones into account can help to more effectively reduce disturbing noise and echo. This paper outlines the design and implementation of a multi-channel noise reduction and echo cancell...

A straight skeleton is a well-known geometric structure , and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon?...

This paper deals with the fast computation of straight skeletons of planar straight-line graphs (PSLGs) at an industrial-strength level. We discuss both the theoretical foundations of our algorithm and the engineering aspects of our implementation Bone. Our investigation starts with an analysis of the triangulation-based algorithm by Aichholzer and...

We study the computation of the straight skeleton of a planar straight-line graph (PSLG) by means of the triangulation-based wavefront propagation proposed by Aichholzer and Aurenhammer in 1998, and provide both theoretical and practical insights. As our main theoretical contribution we explain the algorithmic extensions and modifications of their...

Let G be a cycle-free connected straight-line graph with predefined edge lengths and fixed order of incident edges around each vertex. We address the problem of deciding whether there exists a simple polygon P such that G is the straight skeleton of P. We show that for given G such a polygon P might not exist, and if it exists it might not be uniqu...

We present an efficient algorithm for computing generalized motorcycle graphs, in which motorcycles are allowed to emerge after time zero. Our algorithm applies kinetic triangulations inside of the convex hull of the input, while a plane sweep is used outside of it.

The straight skeleton is a geometric structure which was introduced to the field of computational geometry in the mid-90s. Similar to the generalized Voronoi diagram, it features a rich variety of applications in diverse domains, such as the computation of mitered offset curves, the generation of roof models and terrains, the reconstruction of thre...

Let G be a cycle-free connected straight-line graph with predefined edge lengths and fixed order of incident edges around each vertex. We address the problem of deciding whether there exists a simple polygon P such that G is the straight skeleton of P. We show that for given G such a polygon P might not exist, and if it exists it might not be uniqu...

We study straight skeletons and make both theoretical and practical contributions which support new approaches to the computation of straight skeletons of arbitrary planar straight-line graphs (PSLGs). We start with an adequate extension of the concept of motorcycle graphs to PSLGs, with motorcycles starting at the reflex vertices of a PSLG, which...

In this article, we study stochastic properties of a geometric setting that underpins random motorcycle graphs and use it to motivate a simple but very efficient algorithm for computing motorcycle graphs. An analysis of the mean trace length of n random motorcycles suggests that, on average, a motorcycle crosses only a constant number of cells with...

We investigate how a straight skeleton can be used to approximate a motorcycle graph. We explain how to construct a planar straight-line graph G such that the straight skeleton of G reveals the motorcycle graph of M, for every given finite set M of motorcycles. An application of our construction is a proof of the P- completeness of the construction...

We study the watermarking of 2D vector data and introduce a framework which preserves topological properties of the input. Our framework is based on so-called maximum perturbation regions (MPR) of the input vertices, which is a concept similar to the just-noticeable-difference constraint. The MPRs are computed by means of the Voronoi diagram of the...

We study straight skeletons of polygons and investigate the dependence of the number of flip events of the classical wavefront propagation by Aichholzer and Aurenhammer on the underlying triangulation. We show that their standard algorithm, applied to a polygon with n vertices, has to cope with at least Ω(n 2) flip events. In particular, Ω(n) diago...

We present a simple algorithm for computing straight skeletons of planar straight-line graphs. We exploit the relation between motorcycle graphs and straight skeletons, and introduce a wavefront-propagation al- gorithm that circumvents the expensive search for the next split event. Our algorithm maintains the simplic- ity of the triangulation-based...

We introduce an algorithm for computing Voronoi diagrams of points, straight-line segments and circular arcs in the two-dimensional Euclidean plane. Based on a randomized incremental insertion, we achieve a Voronoi algorithm that runs in expected time O(nlogn) for a total of n points, segments and arcs, if at most a constant number of segments and...

We study the computation of motorcycle graphs and give the first formal definition of the motorcycle graph as a set of constraints rather than as the result of some process. A constructive proof that the constraints can be fulfilled is cast into a simple algorithm for computing motorcycle graphs, with geometric hashing used for speeding up the algo...

Vroni is one of few existing implementations for the stable computation of Voronoi diagrams of line segments. A topology-oriented approach in combination with double-precision floating-point arithmetic makes Vroni also the fastest and most reliable implementation available. Up to now, Voronoi diagram algorithms used in industrial applications proce...