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Stochastic Network Calculus (SNC) emerged from two branches in the late 90s:
the theory of effective bandwidths and its predecessor the Deterministic Network
Calculus (DNC). As such SNC’s goal is to analyze queueing networks and support
their design and control.
In contrast to queueing theory, which strives for similar goals, SNC uses in-
equalities to circumvent complex situations, such as stochastic dependencies or
non-Poisson arrivals. Leaving the objective to compute exact distributions behind,
SNC derives stochastic performance bounds. Such a bound would, for example,
guarantee a system’s maximal queue length that is violated by a known small prob-
ability only.
This work includes several contributions towards the theory of SNC. They are
sorted into four main contributions:
(1) The first chapters give a self-contained introduction to deterministic net-
work calculus and its two branches of stochastic extensions. The focus lies on the
notion of network operations. They allow to derive the performance bounds and
simplifying complex scenarios.
(2) The author created the first open-source tool to automate the steps of cal-
culating and optimizing MGF-based performance bounds. The tool automatically
calculates end-to-end performance bounds, via a symbolic approach. In a second
step, this solution is numerically optimized. A modular design allows the user to
implement their own functions, like traffic models or analysis methods.
(3) The problem of the initial modeling step is addressed with the development
of a statistical network calculus. In many applications the properties of included
elements are mostly unknown. To that end, assumptions about the underlying
processes are made and backed by measurement-based statistical methods. This
thesis presents a way to integrate possible modeling errors into the bounds of SNC.
As a byproduct a dynamic view on the system is obtained that allows SNC to adapt
to non-stationarities.
(4) Probabilistic bounds are fundamentally different from deterministic bounds:
While deterministic bounds hold for all times of the analyzed system, this is not
true for probabilistic bounds. Stochastic bounds, although still valid for every time
t, only hold for one time instance at once. Sample path bounds are only achieved by
using Boole’s inequality. This thesis presents an alternative method, by adapting
the theory of extreme values.
(5) A long standing problem of SNC is the construction of stochastic bounds
for a window flow controller. The corresponding problem for DNC had been solved
over a decade ago, but remained an open problem for SNC. This thesis presents
two methods for a successful application of SNC to the window flow controller.

Ultraschall ist eines der am häufigsten genutzen, bildgebenden Verfahren in der Kardiologie. Dies ist durch die günstige Erzeugung, die Nicht-Invasivität und die Unschädlichkeit für die Patienten begründet. Nachteilig an den existierenden Geräten ist der Umstand, daß lediglich zwei-dimensionale Bilder generiert werden können. Zusätzlich können diese Bilder aufgrund anatomischer Gegebenheiten nicht aus einer wahlfreien Position akquiriert werden. Dies erschwert die Analyse der Daten und folglich die Diagnose. Mit dieser Arbeit wurden neue, algorithmische Aspekte des vier-dimensionalen, kardiologischen Ultraschalls ausgehend von der Akquisition der Rohdaten, deren Synchronisation und Rekonstruktion bis hin zur Visualisierung bearbeitet. In einem zusätzlichen Kapitel wurde eine neue Technik zur weiteren Aufwertung der Visualisierung, sowie zur visuellen Bearbeitung der Ultraschalldaten entwickelt. Durch die hier entwickelten Verfahren ist es möglich bestimmte Einschränkungen des kardiologischen Ultraschalls aufzuheben oder zumindest zu mildern. Hierunter zählen vor allem die Einschränkung auf zwei-dimensionale Schnittbilder, sowie die eingeschränkte Sichtwahl.

Software is becoming increasingly concurrent: parallelization, decentralization, and reactivity necessitate asynchronous programming in which processes communicate by posting messages/tasks to others’ message/task buffers. Asynchronous programming has been widely used to build fast servers and routers, embedded systems and sensor networks, and is the basis of Web programming using Javascript. Languages such as Erlang and Scala have adopted asynchronous programming as a fundamental concept with which highly scalable and highly reliable distributed systems are built.
Asynchronous programs are challenging to implement correctly: the loose coupling between asynchronously executed tasks makes the control and data dependencies difficult to follow. Even subtle design and programming mistakes on the programs have the capability to introduce erroneous or divergent behaviors. As asynchronous programs are typically written to provide a reliable, high-performance infrastructure, there is a critical need for analysis techniques to guarantee their correctness.
In this dissertation, I provide scalable verification and testing tools to make asyn- chronous programs more reliable. I show that the combination of counter abstraction and partial order reduction is an effective approach for the verification of asynchronous systems by presenting PROVKEEPER and KUAI, two scalable verifiers for two types of asynchronous systems. I also provide a theoretical result that proves a counter-abstraction based algorithm called expand-enlarge-check, is an asymptotically optimal algorithm for the coverability problem of branching vector addition systems as which many asynchronous programs can be modeled. In addition, I present BBS and LLSPLAT, two testing tools for asynchronous programs that efficiently uncover many subtle memory violation bugs.

Open distributed systems are a class of distributed systems where (i) only partial information about the environment, in which they are running, is present, (ii) new resources may become available at runtime, and (iii) a subsystem may become aware of other subsystems after some interaction. Modeling and implementing such systems correctly is a complex task due to the openness and the dynamicity aspects. One way to ensure that the resulting systems behave correctly is to utilize formal verification.
Formal verification requires an adequate semantic model of the implementation, a specification of the desired behavior, and a reasoning technique. The actor model is a semantic model that captures the challenging aspects of open distributed systems by utilizing actors as universal primitives to represent system entities and allowing them to create new actors and to communicate by sending directed messages as reply to received messages. To enable compositional reasoning, where the reasoning task is reduced to independent verification of the system parts, semantic entities at a higher level of abstraction than actors are needed.
This thesis proposes an automaton model and combines sound reasoning techniques to compositionally verify implementations of open actor systems. Based on I/O automata, the model allows automata to be created dynamically and captures dynamic changes in communication patterns. Each automaton represents either an actor or a group of actors. The specification of the desired behavior is given constructively as an automaton. As the basis for compositionality, we formalize a component notion based on the static structure of the implementation instead of the dynamic entities (the actors) occurring in the system execution. The reasoning proceeds in two stages. The first stage establishes the connection between the automata representing single actors and their implementation description by means of weakest liberal preconditions. The second stage employs this result as the basis for verifying whether a component specification is satisfied. The verification is done by building a simulation relation from the automaton representing the implementation to the component's automaton. Finally, we validate the compositional verification approach through a number of examples by proving correctness of their actor implementations with respect to system specifications.

Optical Character Recognition (OCR) system plays an important role in digitization of data acquired as images from a variety of sources. Although the area is very well explored for Latin languages, some of the languages based on Arabic cursive script are not yet explored. It is due to many factors: Most importantly are the unavailability of proper data sets and complexities posed by cursive scripts. The Pashto language is one of such languages which needs considerable exploration towards OCR. In order to develop such an OCR system, this thesis provides a pioneering study that explores deep learning for the Pashto language in the field of OCR.
The Pashto language is spoken by more than $50$ million people across the world, and it is an active medium both for oral as well as written communication. It is associated with rich literary heritage and contains huge written collection. These written materials present contents of simple to complex nature, and layouts from hand-scribed to printed text. The Pashto language presents mainly two types of complexities (i) generic w.r.t. cursive script, (ii) specific w.r.t. Pashto language. Generic complexities are cursiveness, context dependency, and breaker character anomalies, as well as space anomalies. Pashto specific complexities are variations in shape for a single character and shape similarity for some of the additional Pashto characters. Existing research in the area of Arabic OCR did not lead to an end-to-end solution for the mentioned complexities and therefore could not be generalized to build a sophisticated OCR system for Pashto.
The contribution of this thesis spans in three levels, conceptual level, data level, and practical level. In the conceptual level, we have deeply explored the Pashto language and identified those characters, which are responsible for the challenges mentioned above. In the data level, a comprehensive dataset is introduced containing real images of hand-scribed contents. The dataset is manually transcribed and has the most frequent layout patterns associated with the Pashto language. The practical level contribution provides a bridge, in the form of a complete Pashto OCR system, and connects the outcomes of the conceptual and data levels contributions. The practical contribution comprises of skew detection, text-line segmentation, feature extraction, classification, and post-processing. The OCR module is more strengthened by using deep learning paradigm to recognize Pashto cursive script by the framework of Recursive Neural Networks (RNN). Proposed Pashto text recognition is based on Long Short-Term Memory Network (LSTM) and realizes a character recognition rate of $90.78\%$ on Pashto real hand-scribed images. All these contributions are integrated into an application to provide a flexible and generic End-to-End Pashto OCR system.
The impact of this thesis is not only specific to the Pashto language, but it is also beneficial to other cursive languages like Arabic, Urdu, and Persian e.t.c. The main reason is the Pashto character set, which is a superset of Arabic, Persian, and Urdu languages. Therefore, the conceptual contribution of this thesis provides insight and proposes solutions to almost all generic complexities associated with Arabic, Persian, and Urdu languages. For example, an anomaly caused by breaker characters is deeply analyzed, which is shared among 70 languages, mainly use Arabic script. This thesis presents a solution to this issue and is equally beneficial to almost all Arabic like languages.
The scope of this thesis has two important aspects. First, a social impact, i.e., how a society may benefit from it. The main advantages are to bring the historical and almost vanished document to life and to ensure the opportunities to explore, analyze, translate, share, and understand the contents of Pashto language globally. Second, the advancement and exploration of the technical aspects. Because, this thesis empirically explores the recognition and challenges which are solely related to the Pashto language, both regarding character-set and the materials which present such complexities. Furthermore, the conceptual and practical background of this thesis regarding complexities of Pashto language is very beneficial regarding OCR for other cursive languages.

Die vorliegende Arbeit beschäftigt sich mit der visuellen Kontrolle raumplanerischer Entwürfe. Grundlage der Überlegungen ist das gegenwärtige Verfahren, der Planungsprozess, das zur Erstellung der Entwürfe führt. Der Entscheidungsweg hin zum endgültigen Ergebnis erfolgt zurzeit noch ohne Rechnerunterstützung. Die in den Planungsprozess Involvierten stützen ihre Entscheidungen bspw. auf Pläne, eigene Erfahrungen und Statistiken und fertigen im Verlauf von Diskussionsrunden verschiedene Entwürfe an. Dieser Ablauf ist komplex, aufgrund der eingehenden Daten und der damit zusammenhängenden Diskussionen, und langwierig da erst nach einigen Iterationsschritten ein Ergebnis vorliegt. Die Arbeit verfolgt das Ziel, die Akteure durch eine Rechnerunterstützung schneller und zielgerichtet zu einer Entscheidungsfindung zu führen. Meine Untersuchung des Anwendungsumfeldes hat ergeben, dass dies nur möglich ist, wenn zum Einen das entstehende System in der Lage ist, die großen, heterogenen Datenmengen zu verarbeiten und andererseits die Visualisierung der Ergebnisse in einer Form erfolgt, die den Akteuren vom bisherigen Planungsprozess her bekannt ist. Die Visualisierung darf dabei keine bewertende Aussage treffen, sondern muss die Informationen der Analyse neutral in einem dem Nutzer bekannten Format abbilden. Als Ansatzpunkt stellt sich der informelle Bereich der Entscheidungsfindung dar. Es werden zwei Lösungswege aus dem Bereich der Clusteringalgorithmen verfolgt, die die großen Datenmengen verarbeiten und analysieren. Als Ergebnis erhalten die Akteure durch das Voronoi-Diagramm direkt einen Entwurf, der die Einschätzungen aller Akteure widerspiegelt und durch ein Übereinanderlegen mit der Karte des Plangebietes dem klassischen Format im Rahmen des Planungsprozesses entspricht. Dadurch wird die Akzeptanz der Rechnerunterstützung bei den Beteiligten des Planungsprozesses gesteigert. Sollte dieser Entwurf noch keine direkte Zustimmung finden, kann über die entwickelte Informationsvisualisierung eine Anzeige und in der Folge eine Anpassung der Eingangsgrößen erfolgen und somit sehr schnell ein neuer Entwurf entwickelt werden. Die Visualisierung übernimmt dabei die Funktion der bisher in Papierform erstellten Pläne im Entscheidungsprozess und bietet damit auch fachfremden Beteiligten eine visuelle Kontrollmöglichkeit der Qualität des Entwurfes. Insgesamt werden mit dem Tool IKone die Akteure in Anlehnung an die standardmäßigen Abläufe und visuellen Darstellungen mittels eines rechnergestützten Systems unterstützt.

The development of autonomous mobile robots is a major topic of current research. As those robots must be able to react to changing environments and avoid collisions also with moving obstacles, the fulfilment of safety requirements is an important aspect. Behaviour-based systems (BBS) have proven to meet several of the properties required for these kindsof robots, such as reactivity, extensibility and re-usability of individual components. BBS consist of a number of behavioural components that individually realise simple tasks. Their interconnection allows to achieve complex robot behaviour, which implies that correct
connections are crucial. The resulting networks can get very large making them difficult to verify. This dissertation presents a novel concept for the analysis and verification of complex autonomous robot systems controlled by behaviour-based software architectures with special focus on the integration of environmental aspects into the processes.
Several analysis techniques have been investigated and adapted to the special requirements of BBS. These include a structural analysis, which is used to find constraint violations and faults in the network layout. Fault tree analysis is applied to identify root causes of hazards and the relationship of system events. For this, a technique to map the behaviour-based control network to the structure of a fault tree has been developed. Testing and data analysis are used for the detection of failures and their root causes. Here, a new concept that identifies patterns in data recorded during test runs has been introduced.
All of these methods cannot guarantee failure-free and safe robot behaviour and can never prove the absence of failures. Therefore, model checking as formal verification technique that proves a property to be correct for the given system, has been chosen to complement the set of analysis techniques. A novel concept for the integration of environmental influences into the model checking process is proposed. Environmental situations and the sensor processing chain are represented as synchronised automata similar to the modelling of the behavioural network. Tools supporting the whole verification process including the creation of formal queries in its environment have been developed.
During the verification of large behavioural networks, the scalability of the model checking approach appears as a big problem. Several approaches that deal with this problem have been investigated and the selection of slicing and abstraction methods has been justified. A concept for the application of these methods is provided, that reduces the behavioural network to the relevant parts before the actual verification process.
All techniques have been applied to the behaviour-based control system of the autonomous outdoor robot RAVON. Its complex network with more than 400 components allows for demonstrating the soundness of the presented concepts. The set of diﬀerent techniques provides a fundamental basis for a comprehensive analysis and verification of BBS acting in changing environments.

This thesis is concerned with different null-models that are used in network analysis. Whenever it is of interest whether a real-world graph is exceptional regarding a particular measure, graphs from a null-model can be used to compare the real-world graph to. By analyzing an appropriate null-model, a researcher may find whether the results of the measure on the real-world graph is exceptional or not.
Deciding which null-model to use is hard and sometimes the difference between the null-models is not even considered. In this thesis, there are several results presented: First, based on simple global measures, undirected graphs are analyzed. The results for these measures indicates that it is not important which null-model is used, thus, the fastest algorithm of a null-model may be used. Next, local measures are investigated. The fastest algorithm proves to be the most complicated to analyze. The model includes multigraphs which do not meet the conditions of all the measures, thus, the measures themselves have to be altered to take care of multigraphs as well. After careful consideration, the conditions are met and the analysis shows, that the fastest is not always the best.
The same applies for directed graphs, as is shown in the last part. There, another more complex measure on graphs is introduced. I continue testing the applicability of several null-models; in the end, a set of equations proves to be fast and good enough as long as conditions regarding the degree sequence are met.

Analyzing Centrality Indices in Complex Networks: an Approach Using Fuzzy Aggregation Operators
(2018)

The identification of entities that play an important role in a system is one of the fundamental analyses being performed in network studies. This topic is mainly related to centrality indices, which quantify node centrality with respect to several properties in the represented network. The nodes identified in such an analysis are called central nodes. Although centrality indices are very useful for these analyses, there exist several challenges regarding which one fits best
for a network. In addition, if the usage of only one index for determining central
nodes leads to under- or overestimation of the importance of nodes and is
insufficient for finding important nodes, then the question is how multiple indices
can be used in conjunction in such an evaluation. Thus, in this thesis an approach is proposed that includes multiple indices of nodes, each indicating
an aspect of importance, in the respective evaluation and where all the aspects of a node’s centrality are analyzed in an explorative manner. To achieve this
aim, the proposed idea uses fuzzy operators, including a parameter for generating different types of aggregations over multiple indices. In addition, several preprocessing methods for normalization of those values are proposed and discussed. We investigate whether the choice of different decisions regarding the
aggregation of the values changes the ranking of the nodes or not. It is revealed that (1) there are nodes that remain stable among the top-ranking nodes, which
makes them the most central nodes, and there are nodes that remain stable
among the bottom-ranking nodes, which makes them the least central nodes; and (2) there are nodes that show high sensitivity to the choice of normalization
methods and/or aggregations. We explain both cases and the reasons why the nodes’ rankings are stable or sensitive to the corresponding choices in various networks, such as social networks, communication networks, and air transportation networks.

This thesis discusses several applications of computational topology to the visualization
of scalar fields. Scalar field data come from different measurements and simulations. The
intrinsic properties of this kind of data, which make the visualization of it to a complicated
task, are the large size and presence of noise. Computational topology is a powerful tool
for automatic feature extraction, which allows the user to interpret the information contained
in the dataset in a more efficient way. Utilizing it one can make the main purpose of
scientific visualization, namely extracting knowledge from data, a more convenient task.
Volume rendering is a class of methods designed for realistic visual representation of 3D
scalar fields. It is used in a wide range of applications with different data size, noise
rate and requirements on interactivity and flexibility. At the moment there is no known
technique which can meet the needs of every application domain, therefore development
of methods solving specific problems is required. One of such algorithms, designed for
rendering of noisy data with high frequencies is presented in the first part of this thesis.
The method works with multidimensional transfer functions and is especially suited for
functions exhibiting sharp features. Compared with known methods the presented algorithm
achieves better visual quality with a faster performance in presence of mentioned
features. An improvement on the method utilizing a topological theory, Morse theory, and
a topological construct, Morse-Smale complex, is also presented in this part of the thesis.
The improvement allows for performance speedup at a little precomputation and memory
cost.
The usage of topological methods for feature extraction on a real world dataset often
results in a very large feature space which easily leads to information overflow. Topology
simplification is designed to reduce the number of features and allow a domain expert
to concentrate on the most important ones. In the terms of Morse theory features are
represented by critical points. An importance measure which is usually used for removing
critical points is called homological persistence. Critical points are cancelled pairwise
according to their homological persistence value. In the presence of outlier-like noise
homological persistence has a clear drawback: the outliers get a high importance value
assigned and therefore are not being removed. In the second part of this thesis a new
importance measure is presented which is especially suited for data with outliers. This
importance measure is called scale space persistence. The algorithm for the computation
of this measure is based on the scale space theory known from the area of computer
vision. The development of a critical point in scale space gives information about its
spacial extent, therefore outliers can be distinguished from other critical points. The usage
of the presented importance measure is demonstrated on a real world application, crater
identification on a surface of Mars.
The third part of this work presents a system for general interactive topology analysis
and exploration. The development of such a system is motivated by the fact that topological
methods are often considered to be complicated and hard to understand, because
application of topology for visualization requires deep understanding of the mathematical
background behind it. A domain expert exploring the data using topology for feature
extraction needs an intuitive way to manipulate the exploration process. The presented
system is based on an intuitive notion of a scene graph, where the user can choose and
place the component blocks to achieve an individual result. This way the domain expert
can extract more knowledge from given data independent on the application domain. The
tool gives the possibility for calculation and simplification of the underlying topological
structure, Morse-Smale complex, and also the visualization of parts of it. The system also
includes a simple generic query language to acquire different structures of the topological
structure at different levels of hierarchy.
The fourth part of this dissertation is concentrated on an application of computational
geometry for quality assessment of a triangulated surface. Quality assessment of a triangulation
is called surface interrogation and is aimed for revealing intrinsic irregularities
of a surface. Curvature and continuity are the properties required to design a visually
pleasing geometric object. For example, a surface of a manufactured body usually should
be convex without bumps of wiggles. Conventional rendering methods hide the regions
of interest because of smoothing or interpolation. Two new methods which are presented
here: curvature estimation using local fitting with B´ezier patches and computation of reflection
lines for visual representation of continuity, are specially designed for assessment
problems. The examples and comparisons presented in this part of the thesis prove the
benefits of the introduced algorithms. The methods are also well suited for concurrent visualization
of the results from simulation and surface interrogation to reveal the possible
intrinsic relationship between them.