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@Article{aw-16-skmosnp,
Title = {Straight Skeletons and Mitered Offsets of Nonconvex Polytopes},
Author = {Franz Aurenhammer and Gernot Walzl},
Journal = {Discrete \& Computational Geometry},
Year = {2016},
Volume = {56},
Pages = {743--801},
Abstract = {We give a concise definition of mitered offset surfaces for nonconvex polytopes in 3-space, along with a proof ofexistence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in the generic case. Our results extend to the weighted setting, to a larger class of polytope decompositions, and to general dimensions. For (weighted) straight skeletons of an $n$-facet polytope in $d$-space, an upper bound of~$O(n^d)$ on their combinatorial complexity is derived. It relies on a novel layer partition for straight skeletons, and improves the trivial bound by an order of magnitude for~$d \geq 3$.},
Url = {https://link.springer.com/article/10.1007/s00454-016-9811-5}
}
@PhdThesis{walzl-15-phd,
Title = {Straight Skeletons - From Plane to Space},
Author = {Gernot Walzl},
School = {Graz University of Technology},
Year = {2015},
Url = {http://gernot-walzl.at/About/Scientific_Research/Straight_Skeleton/Walzl-Straight_Skeletons.pdf}
}
@InProceedings{aw-14-poss3,
Title = {{Polytope Offsets and Straight Skeletons in 3D}},
Author = {Franz Aurenhammer and Gernot Walzl},
Booktitle = {Proc. 30th Annual Symposium on Computational Geometry SoCG'14},
Year = {2014},
Address = {Kyoto},
Abstract = {This video demonstrates the first complete implementation of an algorithm for constructing all possible straight skeletons of a general nonconvex polytope in three dimensions.},
Url = {http://computational-geometry.org/SoCG-videos/socg14video/Straight_Skel_2.mkv}
}
@InProceedings{aw-13-scss3,
Title = {Structure and computation of straight skeletons in 3-space},
Author = {Franz Aurenhammer and Gernot Walzl},
Booktitle = {Proc. 24th International Symposium on Algorithms and Computation ISAAC'13},
Year = {2013},
Address = {Hong Kong},
Pages = {44--54},
Abstract = {We characterize the self-parallel (mitered) offsets of a general nonconvex polytope Q in 3-space and give a canonical algorithm that constructs a straight skeleton for Q.}
}
@InProceedings{aw-13-tdssbg,
Title = {Three-dimensional straight skeletons from bisector graphs},
Author = {Franz Aurenhammer and Gernot Walzl},
Booktitle = {Proc. 5th International Conference on Analytic Number Theory and Spatial Tessellations},
Year = {2013},
Address = {Kiev, Ukraine},
Abstract = {A straight skeleton of a polygon or of a polytope is a piecewise linear skeletal structure that partitions the underlying object by means of a self-parallel shrinking process. We propose a method for constructing different straight skeletons for a given nonconvex polytope Q in 3-space. The approach is based on so-called bisector graphs on the sphere, and allows for generating straight skeletons with certain optimality properties. The various events that arise during the process of shrinking Q are discussed. We have implemented our method and give some examples of the output.},
Url = {http://www.igi.tugraz.at/auren/psfiles/aw-tdssbg-13.pdf}
}
@MastersThesis{walzl-11,
Title = {{Stochastische Rekonstruktion der 3-dimensionalen Mikrostruktur von Lithium-Ionen-Zellen}},
Author = {Gernot Walzl},
School = {Graz University of Technology},
Year = {2011},
Abstract = {Cross-sectional images are captured from the electrodes of a lithium-ion cell by using electron microscopy. Computer vision is used to identify existing materials in the cross-sectional image. To achieve this, the image is segmented and then the resulting segments are classified. One class is used to detect 2-dimensional geometric shapes using least squares fitting.
The 2-dimensional geometric shapes are analysed statistically. It is assumed that the images are cross-sections of 3-dimensional geometric shapes. In the given problem, there are ellipsoids cut by a plane and shown as ellipses in the cross-sectional image. A statistical analysis of the 2-dimensional geometric shapes is used to determine the most likely parameters of the assumed 3-dimensional geometric shapes.
Using the determined 3-dimensional geometric shapes, a 3-dimensional geometry is reconstructed. Cross-sections of the reconstructed geometry are statistically comparable to the original cross-sectional image. The original cross-sectional image is not included in the reconstruction.
The reconstructed 3-dimensional geometry is stored in an equidistantly sampled volume. The rendering of the total volume on screen is efficient enough to be rotated interactively.
The reconstructed 3-dimensional geometry is used to indirectly determine parameters of a mathematical model of the electrochemistry of a lithium-ion cell.
The implementation is usable by an automatically generated graphical user interface. The user interface is generated at run-time by an analysis of given functions.},
Url = {http://gernot-walzl.at/About/Scientific_Research/Walzl-Geometrie_LiIon.pdf}
}
@TechReport{walzl-10,
Title = {{Implementation of Hereditary Convex Structures}},
Author = {Gernot Walzl},
Institution = {Graz University of Technology},
Year = {2010},
Url = {http://gernot-walzl.at/About/Scientific_Research/Walzl-HCSImpl.pdf},
Note = {Implementation: \url{http://gernot-walzl.at/About/Scientific_Research/hcs-20101013.tar.gz}}
}
@InProceedings{teufl-08-infect,
Title = {{InFeCT - Network Traffic Classification}},
Author = {Peter Teufl and Udo Payer and Michael Amling and Martin Godec and Stefan Ruff and Gerhard Scheikl and Gernot Walzl},
Booktitle = {Seventh International Conference on Networking (ICN 2008)},
Year = {2008},
Month = {04},
Address = {Cancun, Mexico},
Publisher = {IEEE},
Pages = {439--444},
Abstract = {Network traffic policy verification is the analysis of network traffic to determine if the observed traffic is in compliance or violation of the applied policy. An intuitive approach is the use of machine learning techniques based on specific network traffic characteristics. These traffic characteristics are also known as features, which have to be extracted and selected carefully to build robust and accurate learning models. Thus, finding the best possible learning model in combination with extracting the best possible feature-set is a necessary requirement to design accurate traffic classification models. While feature selection can be automated to find the best subset of a given set of features, there are no known mechanisms to solve the problem of feature extraction. Thus, extracting the best possible features has to be done empirically. In this work we present a framework to simplify the empirical model selection and feature extraction process.},
Url = {https://ieeexplore.ieee.org/document/4498201}
}
@TechReport{walzl-08,
Title = {{Klassifizierung mit Self-Organizing Maps}},
Author = {Gernot Walzl},
Institution = {Graz University of Technology},
Year = {2008},
Month = {01},
Url = {http://gernot-walzl.at/About/Scientific_Research/Walzl-SOMClassifier.de.pdf},
Note = {Implementation: \url{http://gernot-walzl.at/About/Scientific_Research/iaik.som-20071108.tar.gz}}
}