EXAMENSARBETEN VID AVDELNINGEN FÖR MATEMATIK, LTH, 2006

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License Plate Recognition
Student: Ida Danielsson, P02 Martina Lundh, P02
Advisor: Kalle Åström, Daniel Elvin, (Axis Communications AB)
In cooperation with: Axis Communications AB
Date finished: 2006-12-15
Abstract: In this thesis an algorithm is implemented to detect and recognize license plates on vehicles. The main purpose was to create a whole license plate recognition (LPR) solution, which should be able to find a plate before the vehicle passes the camera.The method uses high density of vertical edges to find regions of interest. Principal component analysis and geometrical transformation are performed to transform the license plate to be horizontal. In addition, items such as frame and controlling-marksare removed during a segmentation part of the license plate. Furthermore, classification is performed in several steps in the algorithm. At last, the characters are recognizedwith an external optical character recognition (OCR) software.Commercial products and previous work are discussed in the report. Moreover,the implemented LPR algorithm has been tested to evaluate the accuracy. The aim to find a license plate in a sequence of images of one car was accomplished with satisfaction. Finally, the LPR algorithm has been implemented on an Axis Communications network camera.

Evaluation of Layer Potentials Close to Their Sources
Student: Rikard Ojala, Pi02
Advisor: Johan Helsing,
Date finished: 2006-10-05
Abstract: Laplace's equation with Dirichlet boundary conditions is fundamental when modelling many physical phenomena. A natural method of solving this problem on different geometries is using integral equation methods, but a problem when using this approachis that the solution close to the boundary is imprecise due to singularities in the discretized kernel. This thesis deals with methods to overcome this difficulty. Methodsare introduced and tested that compute the solution precisely and rapidly in the entiretyof both simply and multiply connected regions. Experiments show that the methods achieve a relative error as low as around 1e-15 on domains with smooth boundaries using relatively few discretization points.

On the Convergence of the American Put Price in the Cox-Ross-Rubenstein model
Student: Johannes Sivén, Pi03
Advisor: Magnus Fontes and Olivier Verdier
Date finished: 2006-10-04
Abstract: We price the American put option in the Cox-Ross-Rubinstein model with N time steps, and derive an equivalent formulation of the pricing problem in terms of a discrete variational inequality. We show that the solution to the discrete inequality converges weakly in L^2 (when N tendsto infinity) towards a weak solution to the continuous variational inequality associated with the same pricing problem in the Black-Scholes model.

Cyrillic Handwriting Recognition using Support Vector Machines
Student: David Danowsky, D00
Advisor: Kalle Åström, Rikard Berthilsson, Jonas Morwing (Zi-Decuma)
In cooperation with: Zi-Decuma
Date finished: 2006-08-25
Abstract: The most natural thing in the world is to write and that is why it is important to develop good handwriting recognition programs to work on mobile telephones and PDAs, so people can continue to write. In this thesis a handwriting recognition engine is developed for the Cyrillic alphabets, mainly Russian but secondary also for Serbian, Ukrainian and Bulgarian. This is done by first collecting a lot of data and using a method, called clustering, to divide the data into different clusters. The mass centers of these clusters are used as templates in the Cyrillic database. The database then needs to be optimized, which is a very time consuming and iterative process. During testing, some similar looking characters often get mixed up in the interpretation. This thesis tries to evaluate the theory of Support Vector Machines to solve these problems.The results from the optimization and the Support Vector Machines are very satisfying and the handwriting recognition engine should be ready to be used on mobile telephones and PDA's, even though some more optimizations can be done for the secondary Cyrillic languages.

Motion Detection and Evaluation
Student: Johan Brissmyr, D01 and Sebastian Wallin, E00
Advisor: Rikard Berthilsson, Håkan Ardö, Daniel Elvin (Axis)
In cooperation with: Axis Communications AB
Date finished: 2006-08-28
Abstract: The market of digital surveillance is just taking off, growing immensely and stealing market shares from the analog counterpart. The transfer to the digital domain opens up many new possibilities with automated recognition of objects, tracking and so on. However these desirable features can never be feasible without one basic operation: proper detection of objects. As the leader in digital surveillance, it is of course of great interest for AXIS toinvestigate the possibilities in this area. This thesis focuses on evaluation of different techniques for performing detection and segmentation of moving objects, both objectively and subjectively. Since the current techniques for doing this have proved not to be fullymatured, subsidiary algorithms for improving results, both prior to and after detection, are also evaluated to some degree. The objective evaluation is done using pixel error measures like false positives and false negatives. To extend these simple metrics a third, distance weighted error measure that penalizes misclassified pixels farther away from the actual object is also tested.

Which Commutative Monoids Have Only Finitely Generated Submonoids?
Student: Christine Jost, Erasmus
Advisor: Jonas Månsson, Patrik Nordbeck
Date finished: 2006-06-12
Abstract: A monoid is a semigroup with unity. It is well known that every submonoid of the commutative monoid can be generated by some finite subset. But this is not true for commutative monoids in general.In this thesis, a necessary and sufficient condition is given that answers the question which commutative monoids just have finitely generated submonoids. It is a simple condition which is formulated in a constructive sense. That is, an algorithm can be given that tells for an arbitrary commutative monoid whether it only has finitely generated submonoids. Also relations to commutative algebras and generalisations to this context are considered.

An Algorithm to Detect Regular Behaviour of Binomial Gröbner Bases
Student: Karl Mårtensson, F02
Advisor: Patrik Nordbeck, Jonas Månsson
Date finished: 2006-06-08
Abstract: The main objective of this thesis is to pose the idea of an algorithm which finds patterns in a few polynomials of an, in general infinite, Gröbner basis in noncommutative algebra, and from these, predicts the complete basis. The algorithm is presented in two versions. Advantages and disadvantages of these versions are examined, and one of the versions is chosen for practical use. A software implementation of the algorithm has been done and a description of how to use it is presented. An introduction to Gröbner bases in noncommutative algebras is given, meaning that the reader does not have to be very familiar with the subject.Since the algorithm uses the ideas of regular languages and automata, an introduction to these relating subjects is also given.

Estimation of the Quality of Hyperlinked Documents using a Series Formulation of PageRank
Student: Fredrik Andersson, F01
Advisor: Sergei Silvestrov Date finished: 2006-05-18
Abstract: The PageRank algorithm is a fundamental tool for determining document quality in large-scale hyperlinked environments such as the World Wide Web. This thesis provides a thorough treatment of citation ranking and PageRank, their application to search engines, and the underlying theory of non-negative matrices. Furthermore, a matrix series formulation of the PageRank problem is presented, and the numerical aspects of this method are examined. The method is found to converge at approximately the same rate as the classic PageRank algorithm, but provides better error measures and gives useful expressions for the PageRank values of link structures containing for example certain absorbing substructures. The numerical computations were carried out using a 300000-node link graph derived from the Lund Institute of Technology public website.

Pulses in surface catalyzed reactions.
Student: Mattias Hagelberg, F00
Advisor: Mario Natiello
Date finished: 2006-03-20
Abstract: The possibility of moving pulses in a surface catalyzed reaction taking place in one dimension is addressed. The reaction is NO + CO that is catalyzed by a ring consisting of Pt(100). Theseconditions can accurately be modeled with three coupled differential equations. In this thesis a method to solve these equations numerically is presented. The behavior of thesesolutions for different sets of initial conditions and physical parameters is examined. For most initial conditions the solutions consist of waves fixed in space. But for a very narrow choice of initial conditions these solutions are in the form of a single or two traveling pulses moving along the ring. These special conditions and the effect on the solutions of small changes of the variables are investigated. Solutions in the form of one single pulse or two pulses are found. In the latter case it appears that these pulses sooner or later will merge into one single pulse only if the pulses initially are close enough.

Topological Analysis of Unstable Periodic Orbits in the Cardiac Rhytm
Student: Johannes Borgman, F99
Advisor: Mario Natiello
Date finished: 2006-03-20
Abstract: The cardiac rhythm is regarded as a prototypical periodic motion. The periodicity and in particular the heartbeat periodicity is the foundation for human beings and other species life processes. Ill states of the heart, so called arrhythmias, can lead to disorders in the periodicity of the cardiac system. The aim of the thesis was to increase the understanding for how these disturbances are signalled in ECG data. The first step was to identify a mathematical environment where the periodicity of the cardiac rhythm can be understood as periodic solutions of a mathematical problem. Next, periodic solutions were identified out of ECG data in this mathematical environment. The topological properties of the periodic solutions were examined using Braid Theory. The braids that have been created from the normal ECGs were then compared with pathological ECGs. The purpose of this master thesis was to investigate the potential for this method to be used as a diagnostic tool of the cardiac rhythm.

Range Determination for Mobile Robots using an Omnidirectional Camera.
Student: Ola Millnert
Advisor: Kalle Åström, Toon Goedeme (K. U. Leuven)
In cooperation with: K. U. Leuven
Date Finished: 2006-03-01
Abstract: This master thesis presents a method to determine distances in a scene using only one omnidirectional camera. The algorithm will be integrated with the navigation system for a robotic wheel chair. In contrast to prior work, our mehtod is able to build absolute scale 3D without the need of a known baseline length, traditionally aqcuired by odometry. Instead we use the ground plane assumption together with the camera system's height to determine the scale factor. Using only one omnidirectional camera our method is proven to be cheaper, more reliable and more compact than the current methods for distance determination. It is cheaper since it only uses one sensor instead of having to rely on laser scanners or other expensive range detectors. It is more realiable since it can determine distances in a 3D space instead of one plane. The experiments conducted here show promising results. The algorithm is indeed capable determine the distances in meters to features and obstacles and is able to located all major obstacles in the scene.

Automated interpretation of cardiac scintigrams
Student: Jens Richter, E96
Advisor: Kalle Åström, Fredrik Kahl, Anders Ericsson, Andreas Järund (Weaidu in Europé AB), Lars Edenbrandt (Weaidu in Europé AB)
In cooperation with: Weaidu in Europé AB
Date finished: 2006-03-01
Abstract: Cardiac scintigram examination is a method to examine the possibility of a present or expected cardiac infarction. The examination is resulted in a three-dimensional data volume where the activity of the cardiac is stored. The interpretation of these three dimensional results does however demand vast experience. A semi automatic system that helps the physician in interpreting these data volumes has been developed by LUTAB. The purpose of this master's thesis was to make an automatic cardiac detection algorithm. The algorithm is then supposed make the semi automatic system, fully automatic. If given the right data, the system in question detects possible diseases and produces very accurate verdicts. The most important issues, in the quest of making it full automatic, were to find the apex and base (bottom and top) in the cardiac. The criteria for the algorithm were, that it had to find these parts even though they may not be visible to the human eye. The final algorithm also displays the cardiac shape and intensity in a three-dimensional image. With the use of statistics it is possible to create a specific cardiac shape with just little information about it. The algorithm will create the shapes with the help of principal component analysis (PCA) and intelligent assumptions. The thesis also describes a method that was developed to gather the statistical information, needed in the main algorithm. This gathering algorithm was written with the main goal to save time in future development, testing and validation. The automatic gathering of information also provides a more precise result than a manual gathering ever could. Both the algorithm that collects the statistical information and the main algorithm are described in such a way, that the reader should be able to create a similar method of his or her own.

Automatic Landmark Detection in Two-Dimensional Gel Electrophoresis Images of Proteins
Student: Elisabeth Edgren, F99
Advisor: Magnus Oskarsson, Andreas Olsson (Ludesi)
In cooperation with: Ludesi
Date finished: 2006-02-07
Abstract: In this master's thesis evaluation of protein spot images is done, with the purpose offinding an algorithm that can automate an existing matching algorithm. Two different algorithms are studied in order to find the most appropriate one to find corresponding points or landmarks in the images. The algorithms investigated are a variant of the RANSAC algorithm, and an algorithm based on Delaunay triangulation.

A New Upper Bound on Rubiks Cube
Student: Silviu Radu, F01
Advisor: Gert Almkvist, Victor Ufnarovski
Date finished: 2006-01-20
Abstract: Rubiks cube is one of the most famous puzzles in the world. Many mathematicians are interested in it because one can associate a group to the cube. Despite its popularity, some of its mysteries remain unsolved. Nobody knows the minimum number of moves required to solve any arbitrary position in this puzzle.The best known upper bound on the number of moves to solve it is 42 due to Michael Reid in 1995. We give here a proof that the cube can actually be solved in 40 moves.The proofs for both bounds use computers. We will also talk about the group structure and other related interesting facts.

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