Examensarbeten vid avdelningen for matematik, LTH, 99-01

EXAMENSARBETEN VID AVDELNINGEN FÖR MATEMATIK, LTH, 1999-2001

Tillbaka till huvudsidan
Examensarbeten under 2009
Examensarbeten under 2008
Examensarbeten under 2007
Examensarbeten under 2006
Examensarbeten under 2005
Examensarbeten under 2004
Examensarbeten under 2003
Examensarbeten under 2002
Examensarbeten under 1999-2001
Examensarbeten -1998

Compression of Fingerprint Template Images
Student: Jan Erik Solem, F97
Advisor: Anders Heyden
In cooperation with: Precise Biometrics AB
Date Finished: 01-12-20
Abstract: In a fingerprint verification and identification system, fingerprint characteristics are captured in template images. When these template images are stored on a medium or transmitted over a network it is essential that the templates are as small as possible. The aim of this master's thesis is to find a method for compressing fingerprint template images and to implement this method. The compression should preferably be lossless, or give controllable distortion of the images, in the case of lossy compression.
The final algorithm divides the template image in blocks and uses arithmetic coding to encode the blocks. For the case when some loss is tolerated, a function is added that maps the rare blocks to more frequent blocks if the difference between the block images is small. This increases compression performance and also limits image distortion.

Quality Estimation in Fingerprint Images
Student: Martin Norrefeldt, F95
Advisor: Anders Heyden, Jerker Bergenek (Precise Biometrics AB)
In cooperation with: Precise Biometrics AB
Date Finished: 01-12-20
Abstract Fingerprint matching systems are developed with the aim of being able to identify fingerprints of as broad range of quality as possible. When a failure in matching two fingerprint images from the same finger occurs, it might be a flaw in the match system or due to low quality in the fingerprint images. One of the fingerprint images, or both, might not be of sufficient quality. Therefore, a measure of the system independent quality of fingerprint images is desirable.
Several different methods of quality estimation of processed and unprocessed fingerprint images have been implemented and evaluated. The two methods showing the best results are based on the difference between the original image and the corresponding binary image combined with either local histograms or a test whether the image has uniform intensity. All measurements are local and the images are divided into small blocks that are individually analysed. This standardization has made comparative testing possible.
The results are tested using a system provided by Precise Biometrics AB. This test program has produced matching results for a database and the images that failed in several matches are considered low quality. The object of the quality algorithms have been to find as many of these low quality images in the database as possible. Also important for the performance was making as few misjudgements as possible, i.e. mistaking a properly functioning image for a low quality image. Both methods showed quite good results.

Operator Monotone Functions, Dynamical Systems and Non-commutative Operator Algebras
Student: Tomas Persson, F98
Advisor: Sergei Silvestrov
Date Finished: 01-12-19
Abstract: In this thesis it is shown how pairs of non-commuting linear operators on a Hilbert space can be investigated using dynamical systems. The problem of finding commuting functions of non-commuting operators is considered.
Connection to the theory of operator monotone and operator convex functions is made. Basic notions and facts from the theory of operator monotone and operator convex functions is presented. The theorem of Löwner on integral representation of operator monotone functions is given with two different proofs by Gunnar Sparr and Adam Koranyi.

Hacke, The Robot
Student: Linda-Marie Johansson, E99 and Håkan Ardö, E96
Advisor: Kalle Åström, Henrik Stewenius, Fredrik Kahl, Daniel Elvin (Axis)
In cooperation with: Axis Communications AB
Date Finished: 01-12-19
Abstract: In this thesis, the development of a robot called Hacke is presented. It is a mobile robot, built of Lego, that navigates using stereo vision. The stereo vision is based on two Axis cameras which are pre-calibrated.
The images from the cameras are transformed to get a view of the floor from above. To find obstacles the image made from the difference between the left and the right transformed images is calculated. Since the cameras are calibrated with the floor plane as reference, everything in the picture that not originates from the floor will produce a difference, and should be avoided.
As the robot moves about a floor map is created. Different landmarks of the floor map that have been encountered previously can be recognised to find the present location of the robot.
The robot body is made of Lego and thus its structure can then easily be modified during the development. All signal communication between the robot and the calculating computer are transferred by a radio LAN. The LAN together with battery makes the robot wireless and enables it to freely move around.

The False Rejection Rate in Fingerprint Biometric Verification Systems, Statistical Results and Proposed Improvements
Student: Pablo Cases, F97
Advisor: Anders Heyden
In cooperation with: Precise Biometrics AB
Date Finished: 01-12-06
Abstract: A statistical investigation aims to identify the components of the false rejection rate (FRR) in fingerprint biometric verification systems. The statistics strongly indicate that template ageing does not affect the Precise Biometrics Pattern Matching (PPM) algorithm. It is also statistically proven that the FRR is user-dependent. Sensor size dependence of the FRR is investigated.
Based on the statistical investigation, two algorithms that aim to lower the FRR are conceived, implemented, and evaluated. The first algorithm is based on Dynamic Programming, the second on Morphological operations. The latter algorithm dramatically improves the FRR, specifically in the operational regions of interest to Precise Biometrics.

Structure from Motion approach to Robot Navigation
Student: Johan Pettersson, E97
Advisor: Anders Heyden, Jonas Rahm (NDC)
In cooperation with: NDC, Särö
Date Finished: 01-12-03
Abstract: By grabbing images with a moving camera we can estimate both the cameras movements and the rooms 3D-structure. The purpose of this work is to show that robot navigation is possible with the use of standard computer vision methods and a calibrated camera mounted on a robot.
Algorithms using common computer vision concepts like epipolar geometry, 8-point algorithm, resection and intersection for reconstruction of the 3D-shape in the robots environment and the cameras move-ment between frames have been developed.
The algorithm has been tried, and analyzed on a simulated environment. A real image-sequence with images from a real camera mounted face forward on a robot has also been used for testing.

Face Recognition using 3D information
Student: Janne Karpinnen, E97
Advisor: Kalle Åström, Daniel Elvin (Camera division, Axis Communications AB)
In cooperation with: Axis Communications AB
Date Finished: 01-11-30
Abstract: The goal of this thesis is to build a system performing face recog- nition based on a 3D view that is calculated from two cameras at different positions. Pictures are taken with two cameras in different angles and then a 3D-model is built which can be used for face recognition. Before any pictures are taken, the cameras are fixed at two arbitrary positions, which means the relation between the cameras is the same from that moment and further. When the cameras are fixed, they are calibrated to get hold of the intrinsic and extrinsic camera parameters which are needed for rectification. When the rectification is performed, a depthmap is calculated to be able to build the 3D-model of the face. The next step when the 3D-model is finished is to perform face recogni- tion. The report covers ideas to be used as a basis for face recognition.

Digital Image Analysis for Controlling Automatic Doors in an Embedded Environment
Students: Martin Börjesson, F97 and Jesper Carlgren, F97
Advisors: Anders Heyden och Eva Sjö (WeSpot AB)
In cooperation with: WeSpot AB
Date Finished: 01-11-16
Abstract: This master's thesis constitutes a pre-study examining the possibility to control automatic doors using WeSpot AB:s smart camera.
The advantages using a smart camera is e.g. lower costs, possibility to add extra functionality and a system that is easier to install and maintain.
Specifications describing the desired functionality are presented in terms of zones in front of the door. Existing image analysis algorithms are examined and new suitable algorithms are proposed to meet the specifications. In addition a technique for counting people and determining their directions is developed. The calculations in this technique are of low complexity and can be performed when given time without large memory usage. Hence the interference with the rest of the system is minimized.
Our interpretation of the results is that it's possible to meet the specifications. One main difficulty, shadows, isn't completely solved and needs to be further investigated. We've examined techniques to use color images instead of today's gray-scale images. This approach seems promising. A possible way to achieve a system more robust to shadows is therefor to use a color sensor.

Automatic Roentgen Stereophotogrammetric Analysis
Student: Andreas Olsson, F96
Advisor: Magnus Oskarsson, Kalle Åström, Jonas Tilly (Tilly Medical), Gunnar Flivik (Ortopeden)
In cooperation with: Tilly Medical, Ortopeden
Date Finished: 01-10-26
Abstract: In Roentgen Stereophotogrammetric Analysis, RSA, two radiographs of a patient's knee or hip are simultaneously taken from different angles and the threedimensional positions of artifical markers attached to the bones are calculated. The procedure involves several steps which require user interaction. Some more or less automatic RSA systems exist, and this thesis further investigates the automatization of the RSA procedure.
A method for removing the background from the markers is presented. Using a sigmoid model function, the subpixel locations of the marker centers are then calculated without the need of manually identifying the background. Automatic cage identification follows, together with automatic marker matching based on epipolar geometry. Maximum Likelihood Estimates of the markers' threedimensional coordinates are produced together with estimates of the accuracy of these coordinates.
The marker finding procedure, the accuracy of the measured marker centers and the cage identification procedure are evaluated, showing encouraging results.

Three dimensional modelling by laser-scanner
Student: Johan Edén, E96
Advisor: Gunnar Sparr, Björn Johansson
In cooperation with: Försvarets Forskningsinstitut
Date Finished: 01-08-31
Abstract: Examensarbetet beskriver olika tekniker att utifrån avståndsmätningar med laser skapa tre-dimensionella datormodeller av verkliga objekt som t ex byggnader och fordorn. Närmare undersöks ett system som finns på FOI i Linköping som har använts för att bygga en modell av en helikopter.
Examensarbetet har utförts på matematiska institutionen på lth i sammarbete med FOI (Totalförsvarets Forskningsinstitut) i Linköping. Handledare i Lund har varit Gunnar Sparr och Björn Johansson. Handledare på FOI i Linköping har varit Ulf Söderman och Simon Ahlberg.

Screening for the size of the nuchal translucency using freehand 3-dimensional ultrasound: A feasability study.
Student: Johan Martinsson, E97
Advisor: Gunnar Sparr
In cooperation with: Institut National Polytechnique de Grenoble
Date Finished: 01-08-20
Abstract:
Objectives: This report addresses the generic problem of using freehand Ultrasound for the reco-very of volumetric models. Freehand Ultrasound means that there is no spatial reference on the probe as is the normal case. In our application, very little is known about the spatial position of each image-plane, which is a serious complication to the well explored problem of model-recovery from 3D-data. The interest in the exploitation of Free Hand methods is great, since it will combine the facility of Ultrasound examination with the absence of an expensive locating device. The problem is treated in a general way, examining the conceptual basis and the behaviour of such algorithms, all while aiming at a specific clinical implementation: Screening for the size of the Fetal Nuchal Translucency in the 12th week of pregnancy. The size is a good indicator on the risk for trisomies, heart malfunction and miscarriage. Current methods suffer from either a great uncertainty level or of the intervention being risky.
Results: First test results on synthetic data are promising and indicate the feasibility of a clinical implementation. Convergence occurs within the domain of model and position uncertainty that can be expected in such an environment.

Handwritten Chinese character recognition
Student: Maria Petersson, F95
Advisor: Kalle Åström, Martin Lindberg (Decuma AB) In cooperation with: Decuma AB
Date finished: 01-06-15
Abstract: Handwriting recognition is used to interpret text that has been input to an electronic device, using hand-writing instead of a keyboard. Due to the increased popularity of hand-held computers, and other portab-le devices such as intelligent pens and mobile phones, handwriting recognition has recently gained more interest. Since the size of technical products is still decreasing, the traditional input method, using a key-board, has become inconvenient. Writing on a pressure-sensitive display with a stick, or using a so called intelligent pen, could instead constitute the input device. This project is about recognizing Chinese charac-ters. Daily, approximately 7000 characters are used in the Chinese writing system. For this project some characters were selected, in order to constitute a prototype database. The characters have then been in-terpreted by the classification system, implemented and described in this master's thesis. Since there are strict time limits for recognition systems, this classification system was developed in order to reduce the time complexity. This was done by implementing a two-level classification system, in which the first level constituted a coarse classification with the intention of reducing the amount of data. The database that makes this two-level classification possible was selected and defined within this project.

Photorealistic 3D-scene reconstruction from images using self-calibration and space carving.
Student: Björn Aspernäs, D96
Advisor: Fredrik Kahl, Kalle Åström
Date Finished: 01-06-12
Abstract: The problem of determining the shape of an existing three-dimensional object, based on multiple images of the object, is a key problem in computer vision. Its applications lie in CAD-systems, automated guidance systems, simulations and many other fields. Even in a situation without any a prori scene-information, it is still possible to obtain a full 3D reconstruction, using only photographs and a few basic assumptions. The entire process of going from photographs to a 3D model is discussed, with an emphasis on the volumetric reconstruction process based on calibrated images. Starting with an introductory discussion on human perception and the physical scene and camera description, this thesis continues into a discussion on computer vision and self-calibration, including feature extraction, the correspondence problem and sparse reconstructions. The major portion of this thesis discusses volumetric dense reconstruction methods in general, and the Space Carving method in particular. The performance of this particular version of Space Carving is demonstrated, and shown to perform well for scenes which do not have complicating lighting effects, e.g. reflections. Examples of situations where the method performs well, as well as examples where it fails are shown. Finally, some interesting pointers to future tests and evaluations are given.

Automatic object recognition from single views.
Student: Martin Sjölin, F96
Advisor: Kalle Åström
Date Finished: 01-06-11

A divergence-free approach to the incompressible Navier-Stokes equations
Student: Shu-Ren Hysing, F96
Advisor: Magnus Fontes
In cooperation with: Comsol AB, Stockholm
Date Finished: 01-06-07
Abstract: Working with the incompressible version of the Navier-Stokes equations poses some difficulties. Of which the most severe is the lack of pressure coupling between the continuity and momentum equations. In the search for solutions to these equations this difficulty may be elegantly handled by using a clever choice of subspace. The requirement that the continuity equation imposes on the velocities is the condition of divergence-freeness. This restriction was used in the construction of basis functions which are exactly divergence-free, after which the finite element method was used in order to evaluate this approach. Whilst the constructed basis is applicable without modification to the incompressible Navier-Stokes equations, the solution of the linearized Stokes equations have been the object of this study. This is due to their simple structure from both mathematical and computational points of view.
The endeavour proved gratifying in the sense that improvements of accuracy were made while using Femlab as a benchmark. Noticeable improvements were visible especially for coarse meshes. The pressure seemed at first elusive but was finally determined with a special Poisson equation.

Prediction of future defects in green boards by measuring specific wood properties with non destructive methods
Student: Peter Lindqvist, F95
Advisor: Gunnar Sparr
In cooperation with: Inst. för träteknik, Luleå Tekniska Högskola
Date Finished: 01-06-01
Abstract: In a sawmill, large quantities of wood are handled. From the time the log arrives to the sawmill, until the wood product leaves it, the wood is passing through several processes. The logs are to be sawn, they have to be stored, dried and so on. All of these processes, of course, require resources in one or the other way. It would be advantageous if pieces, that with big probability would exhibit future defects, could be sorted out in an early stage of the process. By doing this it is possible to minimize the amount of resources needed for wood production. It is believed that some specific properties of the wood product have a correlation with these "future defects". The properties are the shape of the green board, the orientation of the tracheids and the direction of the pattern formed by the annual rings. The formal objective of this thesis is to investigate the possibility to measure these properties with non-destructive methods, especially image processing.

Hidden Markov Model algoritm för markmålföljning av multipla objekt
Student: Robert Artebrant, F97 and Andreas Tyrberg, F96
Advisor: Sven Spanne, Malin Ingerhed (SAAB AB, future products)
In cooperation with: SAAB AB, future products
Date Finished: 01-05-30
Abstract: Many studies have been made addressing the problem of tracking aerodynamic targets moving freely without hard spatial constraints. The problem of tracking ground targets differs in many ways. Terrain structures limit the spatial moving capability of the targets and the terrain has a great influence on the measurement data.
This master's thesis deals with the problem of ground target tracking of multiple objects in a cluttered environment. An algorithm based on Hidden Markov Models (HMM) has been imple-mented and evaluated. Association from measurement to track is done by calculating the most probable measurement from the target state probability distribution at the previous time instant. To reduce the computational burden an association box is used and the scenario is divided into several overlapping subscenarios.
The implemented algorithm handles multiple ground target tracking in a cluttered environment with small error deviations. The HMM tracker shows several advantages to other methods, especially the ability to easily incorporate terrain information for increased performance.

On-line Signature Verification using a Multi-judge Strategy
Student: Fredrik Mattisson, F96
Advisor: Kalle Åström
In cooperation with: Decuma AB
Date Finished: 01-05-28
Abstract: Verifying a persons identity has for long been a big problem. The most common way is so long the key, but a key kan be stolen or lost. This gives the biometric methods (i.e. recognition of fingerprints, voice recognition, face recognition etc.) a big advantage. One way, still quite unexplored, is signature verification, although the signature is widley used and accepted.
The big problem of verifying signatures is the great variations that is observed for the same writer, and it has been a matter for experts and courts in judical procedures. This thesis suggests a mathematical view of the problem, how to detect different variations and automatically accept or reject the signature. Different approaches based on both dynamic and static information is tried and evaluated. In the end a signature verification system, based on the evaluated methods, is suggested.

A model for the retinal nerve fiber layer
Student: Oskar Wigelius, F95
Advisor: Gunnar Sparr
In cooperation with: Dept of Ophtalmology, Malmö University Hospital
Date Finished: 01-04-20
Abstract:The purpose of this thesis is to find a mathematical model for the structure of the retinal nerve fiber layer (RNFL). As a first approximation, a solution is found for Poisson's equation -div(c grad u)=rho on the unit disk. The source function rho depends on the ganglion cell density, whereas the RNFL thickness is proportional to abs(grad u). The model is then modified in different ways by letting the diffusivity c depend on u and rho. The new models are evaluated numerically, first by using a finite difference approximation, then by a finite element method. Finally, some other models and possible numerical methods, useful for future investigations, are discussed.

Igenkänning av fingeravtryck med lokal autokorrelation
Student: Johan Almbladh, F95
Advisor: Anders Heyden, Fredrik Kahl
In cooperation with: Precise Biometrics
Date Finished: 01-04-06
Abstract:Recent years' increased use of electronic equipment for communication and transactions has resulted in a growing demand for high security information exchange. With traditional methods, however, this would imply a vast number of different codes and passwords to be remembered. Passwords and codes can be stolen or broken, compromising the safety of the system. Biometrical verification on the other hand, does not suffer from these drawbacks and is therefore an interesting alternative.

This Master's Thesis describes an alternative, correlation based fingerprint verification system, as opposed to the more common, minutiae based approach. As a part of the system, a new enrol algorithm, based on a derived information density measure and using nonlinear optimization is proposed. A matching routine that uses logistic regression to describe a decision surface in the n-dimensional space of various matching results is also investigated, as well as a method of calculating the unknown fingerprint rotation angle prior to matching. Furthermore, a list of possible improvements is suggested for future development.

Recognition of Cursive Handwriting
Student: Jonas Morwing, D95
Advisor: Sven Spanne, Gunnar Sparr
In cooperation with: Decuma AB
Date Finished: 01-03-26
Abstract:Handwriting recognition is a field of rapidly growing interest, scientific as well as industrial. The size of the keyboard is a limiting factor in the ambition to make electronic devices such as mobile phones and pocket PCs even smaller. The keyboard can not be much more compressed and still remain userfriendly. Instead new solutions have to be found. New input devices such as a pressure sensitive screen and a pen or just digitalized pens, will probably play a prominent role on the market of portable advanced electronics in the coming years. Algorithms for handwriting recognition will then be essential. This thesis is a first study of a process for recognition of cursive handwriting, where whole words can be written in one stroke without lifting the pen. The biggest challenge is then to break up this stroke to get the characters separated from each other. Since cursively handwritten text often is more ambiguous than standard handwriting it is also important to use as much information as possible from the input data. Suggestion of how these and other problems in this area could be solved is what this thesis is about.

Computer vision for fridge content determination.
Student: Fredrik Färnström, D95
Advisor: Björn Johansson, Kalle Åström, Rutger Rosen (Electrolux)
In cooperation with: Electrolux AB, Stockholm
Date Finished: 01-02-02
Abstract: The topic of this thesis is a computer vision system for a fridge. A number of cameras are mounted in the fridge. The system then extracts and processes information about the contents of the fridge. As a user manipulates items in the fridge, a motion-detecting system selects key frames from the video streams. Thus, images before and after actions are kept and analyzed. A camera mounted below the shelf is used to obtain an image of the footprints of the objects on it. By analyzing difference images of the footprint, it is possible to determine the type of action that has been performed (insertion, movement, removal). Furthermore, the side view and the footprint are used to estimate the 3D shape of the object within a specific class of object shapes. As long as the true shape lies within or is sufficiently close to this class, this fast and novel method is successful. An alternative method is to use a whole sequence of images from a moving camera to obtain rich shape information for a more general class of objects. Another issue that is briefly discussed is how to evaluate the quality of a 3D model. Together, the estimated shape, the footprint, and the side view are useful features for object recognition, although this issue has not been investigated in this work. Finally, the contents of the fridge are presented as a texture mapped 3D model and a web page. Other visualization possibilities are also discussed. Using inexpensive cameras and standard computer hardware, working prototype systems have been implemented and tested to demonstrate the feasibility of the system.

Separation of suspended microparticles in a continuous fluid
Student: Martin Dahlgren, M96
Advisor: Magnus Fontes, Kalle Åström, Henrik Jönsson (Erysave), Thomas Laurell (Elektrisk mätteknik)
In cooperation with: Erysave
Date Finished: 01-01-23
Abstract: The aim of this master's thesis is to get a deeper understanding of the separation of suspended particles in a continuous fluid by ultrasound. We derive a model for describing a moving continuous fluid with a dispersed phase that is exposed to ultrasound and we solve the resulting model equations numerically. The application we have in mind is a filter that separates particles suspended in blood plasma. We use our model to investigate the performance of two different filter geometries and the conclusion is, that the geometry is a very important factor for the filtration grade.

Automated option strategy trading
Student: Martin Larsén, F96
Advisor: Sven Spanne
Date Finished: 01-01-25
Abstract: The markets are changing from open out-cry to fully electronic price matching and trade execution, and the need for more efficient trading systems emerge. Some types of trading are quite mechanical and can therefore be automated, taking advantage of the computional power and the speed of digital communication that modern information technology brings.
The heart of automated trading is to have a sound price dependency structure and handle the risk in a correct way. Different aspects of automated trading were studied using pricerisk theory on (real-time) data from EUREX. Three different programs were implemented with the purposes of

reducing the risk in a derivative portfolio
automatization of the market making process
locking the portfolio payoff function - an upper boundary for hedging

which all show how option strategies can be used for automated trading.
The results indicate that not all of the problems are useful to automate. However the market making seems to work well, and it would be really interesting to test it in a real scenario.

Tomographic reconstruction of flows from Doppler measurements
Student: Fredrik Andersson, F97
Advisor: Sven Spanne, Gunnar Sparr
In cooperation with: Dept of Electrical Measurements, LTH
Date Finished: 00-12-18
Abstract:The mathematical problem of reconstructing vector fields from Doppler measurements has been investigated during the last ten years. Previous results have shown that the rotation part of the field can be reconstructed from such measurements, but the problem of full reconstruction has remained unsolved. The mathematics of full field reconstruction is developed in this master's thesis. A new transform is developed and investigated, which gives rise to new analytic and algebraic relations, which at least theoretically allow reconstruction of the vector field up to known ambiguities, using only algebraic equations. A numerical algorithm for the reconstruction is developed and used for simulations.

Automatic Bone-Marrow Smear Analysis using Angular Grey-Tone Spatial-Dependence Matrices
Student: Martin Hovang, F95
Advisor: Anders Heyden
In cooperation with: Cellavision AB
Date Finished: 00-12-15
Abstract:Today bone marrow samples are examined manually, which is a time consuming task. The manual examination begins with a low-resolution scan of the whole smear. The purpose of the scan is to get a general overview of the smear and to find cells and appropriate areas for further analysis with a high-resolution objective. This work concentrates on how to make the low-resolution pre-scan automatic with the use of image processing.
The steps done are normalization, segmentation, feature extraction and classification. Normalization and segmentation is done with basic image processing, fast but not very accurate. Texture information is extracted with angular grey-tone spatial-dependence matrices. Selected features are then used in the classification. The selection is done with the RELIEF algorithm from 110 features. A nearest-neighbour algorithm is used to identify three different kinds of cell formations. The result looks promising but still needs a lot of work.

Restoration of computerized tomography images with spatially varying point spread functions
Student: Marcus Lundahl, F92
Advisor: Sven Spanne, Gunnar Sparr
In cooperation with: Radiofysik, MAS
Date Finished: 00-12-11
Abstract:Increasing the resolution in computerized tomography images is an important problem. There is a degradation of image quality because of several factors. The finite width of the x-ray beam and the rotation of the scanner while obtaining data are the main reasons. The purpose of this master's thesis is to estimate the space-variant point spread function, PSF, in computerized tomography, CT, and to use this information to improve image quality.
The PSF is estimated by scanning a wire at different locations with the CT. The measured PSF increases in size with the distance from the center of rotation, faster in the radial direction than in the tangential direction. Noise measurements show that the noise is spatially varying.
Different image restoration methods are examined and implemented. Close to the center of rotation, the PSF can be considered space-invariant and the constrained least square restora-tion in the frequency domain works well. For the space-variant case two methods are exami-ned. The constrained adaptive iterative restoration using the conjugate gradient method works well and handles noise better than the other method; restoration in the frequency domain after a coordinate transformation.

Reconstruction of documents from multiple images with applications for OCR
Student: Per Åstrand, F96
Advisor: Karl Åström
In cooperation with: C-technologies
Date Finished: 00-11-29
Abstract: A Method to collect printed text to a computer with a handheld device is investigated. Several overlapping images of the text are taken. The images are tracked by matching the length of the words in subsequent images. To detect the text lines the Hough transform is used and this gives also usable by-products for further steps. The method does not mosaic the images into one large image. Only the relative placement of the images is determined. To decide whether to keep an image or not, the corner points of the image in the real space is calculated by correcting for rotation and perspective effects. The decision is then made using polygon operations to calculate the covered area. When all images are collected optical character recognition is done on all single images. This gives the text in the images and by knowing the placement of the text in relation to each other the text can be string matched. Before the optical character recognition (OCR) can be performed correction for rotation and perspective effects has to be done. A homographic mapping that rectifies the image from the most severe perspective effects is determined from the information extracted in the Hough transform.

Vehicle Detection and Identification
Student: Paul Lindquist, E97
Advisor: Karl Åström
Date Finished: 00-11-28
Abstract: The purpose of this Master's Thesis is to investigate the state of the art in the license plate recognition field and develop a new system based on existing and novel techniques. License plate recognition (LPR) deals with the problem of automatic detection and recognition of license plates from image sequences. One of the challenges in license plate recognition is to reduce the calculations needed to identify a vehicle, since most systems deals with a data bandwidth ranging from 1Mb/second 100 Mb/second. This Master's Thesis can be divided up into three separate parts, Vehicle Detection, License Plate Locator and License Plate Recognition. These three parts were developed and verified using an ordinary desktop computer with Borland Delphi as the programming tool. The conclusion of this Master's Thesis is that there are some potential of the proposed algorithms. The Vehicle Detection and especially the License Plate Locator had a high rate of success in locating the license plate.

Face Recognition
Student: Markus Thornell, F96 and Johan Malmros, F96
Advisor: Fredrik Kahl, Anders Heyden, Jerker Bergenek (Precise Biometrics AB)
In cooperation with: Precise Biometrics AB
Date Finished:00-11-24
Abstract: The need for automatic personal identification is increasing. Traditional methods like ID-cards or pin codes are, however, subject to some significant drawbacks. They can be lost, stolen or falsified which creates a need of new ways of determining someones identity. The rapid development of new technologies and the cut of expenses are the means that make this possible. Biometry, the use of someones physiological characteristics for identification, is one potential solution. There are, however, a lot of different biometric techniques like fingerprint, iris or voice recognition, all with their specific advantages and disadvantages. In this master's thesis we have studied face recognition which is different from other biometric techniques preliminary because it doesn't require any interaction with the person being recognized. We will discuss the development of face recognition, the strengths and weaknesses and different face recognition approaches. We will present in detail two different methods, eigenfaces and Local Feature Analysis, and present the performance we have obtained by using these. Then we will describe the advantages of combining different biometrics and especially why face recognition should be a part of this multiple system.

Active Contour Methods for the Segmentation of Flame Images
Student: Ferdinand Mühlhäuser, X98/D98
Advisor: Gunnar Sparr, Ronald Rüsch (Univ Kaiserslautern)
In cooperation with: Universität Kaiserslautern
Date Finished: 00-11-16
Abstract: In numerous industrial and non-industrial processes, fire and explosions are involved. In many of these applications it is of very strong, if not vital importance to be able to predict and con-trol the development of the flames. Many approaches have been taken to find suitable simula-tions for the burning process. Most of them involve the Navier Stokes equations which pro-voke numerical instabilities. At the same time the computation becomes extremely time con-suming when refining the resolution of the grid. Because of these problems engineers are searching for a more suitable description of the flames in question. It should supply an accu-rate representation of the flame enabling the engineer to predict the progress to a certain extent and the calculations should not be too time consuming. To this end we have applied an Active Contour approach to the flame front outline in order to reduce the information deduc-ted from the images obtained by taking photographs of interesting regions in turbulent flames by means of the OH-PLIF (OH-Planar Laser Induced Fluorescence) method. Further work might base on preprocessing this outline by correlation algorithms to and out about the development in time. The knowledge gathered by this combination of experimental and mathematical methods could then be reintroduced into the flame model. The work is performed as a collaboration project between the departments of mathematics at LTH and the University of Kaiserslautern, the division of Combustion Physics, LTH, and the Physical Chemistry Group at the University of Bielefeld.

Normalization of Colour Images
Student: Daniel Svanberg, F95
Advisor: Anders Heyden, Per Senmalm (Cellavision AB)
In cooperation with: Cellavision AB
Date Finished: 00-08-30
Abstract:Images, which are subject to automatic processing, need to be fairly homogenous from image to image. This might be hard to achieve due to the effect of environmental factors at the moment when the picture was taken. Another closely related problem is found in embedded image processing units where a slight change of hardware might require extensive changes of the software if the images are colour-distorted in some way. This master thesis deals with those problems at the specific application of analysing white blood cells. As a result a method of normalising images with respect of light fluctuations has been developed. This method has the potential of improving the accuracy of the analysis significantly. Experiments of transforming images taken with different cameras have also been done. The modified images have then been tested in the unchanged analysing system. The result was not perfect but very promising.

Image Processing for Monitoring of Organotypic Brain Slice Culture Activities
Student: Anders Eriksson, E94
Advisor: Gunnar Sparr
In cooperation with: Inst of Microtechnology, University of Neuchatäl, Schweiz, University of Stellenbosch, Sydafrika
Date Finished: 00-08-29

Texture Features for the Classification of Granulocytes
Student: Martin Johansson, D95
Advisor: Anders Heyden
In cooperation with: CellaVision AB
Date Finished: 00-08-25
Abstract:There exists a group of white blood cells called granulocytes, whose main feature is the presence of a number of small granules in the cytoplasm. The aim of this master's thesis is to investigate if the information provided by this granulation, is enough to differentiate between the different kinds of granulocytes. Three different algorithms were developed and implemented, which extract different features related to the granulation. These features where evaluated using a nearest neighbour classification algorithm, to test how much information they contained about which kind of cell they represented. The results are promising. There exists an overlap between the different types of cells, which it will take more features to remove, but the results are good enough to warrant further investigations.

Shortest route in hierarchichal and partitioned graphs
Student: Fredrik Svensson, D95
Advisor: Kalle Åström
In cooperation with: Itinerary Systems AB
Date Finished: 00-06-16

Extraction of Fixed Length Codes from Fingerprints
Student: Peter Westlund, F95
Advisor: Anders Heyden, Fredrik Kahl
In cooperation with: Precise Biometrics AB
Date Finished: 00-06-08
Abstract: Today's growing electronic society result in an increasing demand for security solutions . Biometrics and fingerprint identification have many advantages over passwords and numerical pin-codes, which have to be remembered. The fingerprint identification systems existing today are based on minutiae extraction or bitmap correlation. Those methods are ok when the problem is to compare two fingerprints. But when we want to search in a database of fingerprints, the existing methods will take too long time. This is one example of when it would be useful to extract a code of fix length from each fingerprint. To compare fingerprints is then simply to calculate the Euclidian distance between the codes. This master thesis describes two methods of extracting a fix length numerical code from fingerprints, one very simple (RidgeCount) and one more complex (FingerCode). An important part in both these algorithms is to find a reference point in the fingerprint. In this thesis two methods ("Core finding mask" and "Energy and Poincaré index") of finding such a reference point are discussed. To evaluate the different code extracting algorithms a general method of evaluating a personal identification code is proposed. The results from this evaluation on a fingerprint database are that FingerCode seems to work quite well while RidgeCount is not recommended.

Digital Image Analysis of Bone Marrow Smears
Student: Sara Roos, F94
Advisor: Anders Heyden, Johan Håkansson (Cellavision AB)
In cooperation with: Cellavision AB
Date Finished: 00-04-13
Abstract: The aim of this master's thesis is to investigate if there exists a fuzzy rule-based system that could be used in a region growing algorithm to segment and separate clustered blood cells on bone marrow slides. Cells like this are very difficult to segment separately. A general model has been built and from that platform different models, rules and parameters have been tested in order to examine the properties and possibilities with the system. It was a difficult task to perfectly separate the clustered cells. Nevertheless the system gave som interesting results. For example the nucleus could easily be segmented. With no doubt more optimal ways can be found to improve the performance of the system. There is almost an endless number of ways to change the system.

Locating Structures in Bone Scintigrams using Active Shape Models
Student: Christian Jacobsen, E93
Advisor: Kalle Åström och Fredrik Kahl
In cooperation with: inst för Klinisk Fysiologi
Date finished: 00-03-20
Abstract: This thesis describes a method of finding structures in bone scinitgram images. The technique used here is called Active Shape Models (ASM). A statistical model is built from a training set consisting of shapes where each shape is defined by a set of points (i.e coordinates). Applying principal component analysis (PCA) on the training set data gives the mean shape and the main axes of the point distribution. PCA gives information of how the location of the points vary and this can be used to generate similar examples to those in the training set. Also modelling the texture variations around each model point is an important part of ASM when searching structures in new images. A description of how ASM is used inorder to locate the chest and the spine in bone scintigram images is presented. The results of the ASM-search are evaluated and discussed.

Lung Segments in Classification of Embolism
Student: Andreas Järund, F93
Advisor: Kalle Åström, Holger Holst (Dept of Clinical Physiology)
In cooperation with: Dept of Clinical Physiology
Date finished: 00-03-10
Abstract: The purpose of this thesis was to examine how Artificial Neural Network (ANN) classification of lung embolism is effected if the ANN inputs are a combination of image information from several ventilation-perfusion lung scintigrams. The images are taken from different angles about the patients torso and represent two dimensional projections of the activity from a radioactive isotope. Method: Static image masks of a set of normal and healthy lungs were created to define segments in six lung scintigrams taken from different angles about the torso. Segments in ventilation and perfusion images where compared to find mismatches and the results were combined to produce a specific feature. Material: The features extracted from 509 examples were used as inputs to train an Artificial Neural Network. Another 104 examples were used to test the Networks performance. Result: A receiver operating curve (ROC) with a total area of 83\% was the best result produced when tested on the test examples. Conclusion: The classification result was slightly increased compared to earlier work. Decomposition into segments are intuitive but are heavily dependent on image pre-processing. Keywords: image processing, pulmonary embolism, Artificial Neural Networks, segmental reference chart, lung scintigram.

Interpolation av plana kurvor för analys av förbränningsbilder
Student: Madelen Andersson, F93
Advisor: Gunnar Sparr, Henrik Malm
In cooperation with: Avd för förbränningsfysik.
Date Finished: 00-06-16

Detection of Auer-Rods in Leukocytes
Student: Joakim Ståhl-Elvander, F94
Advisor: Anders Heyden, Björn Wallin (Cellavision AB)
In cooperation with: Cellavision AB
Date Finished: 00-02-04
Abstract: An algorithm for the detection and segmentation of Auer rods in white blood cells was de veloped and evaluated, using mostly basic segmentation techniques in order to keep the t ime-cost low. It was tested on a limited number of cells with Auer rods, and a reference set of white blood cells without any Auer rods present. The results were promising with a high detection ratio on the cells with Auer rods prese nt, and very few false positives when the algorithm was applied on cells without Auer ro ds. Problems like inconsistency in color and placement of the rods were solved using relatio n properties of the colors and regional segmentation techniques. Some discoveries were made as a side effect of the experiments, in the field of successf ul segmentation of biological entities.

Feature Detection for Fingerprint Matching
Student: Per Nilsson-Stig, F94
Advisor: Fredrik Kahl och Anders Heyden
In cooperation with: Precise Biometrics AB
Date Finished: 99-12-16

Bildförbättring av tomografiska bilder
Student: Ola Friman, E94
Advisor: Gunnar Sparr
In cooperation with: Inst för datorseende, Linköping
Date finished: 99-11-26

Detektion av ytskador med hjälp av digital bildanalys
Student: Anna Jonasson, D95
Advisor: Anders Heyden, Kent Stråhlen, Torkel Danielsson (Moteco AB)
In cooperation with: Moteco AB
Date Finished: 99-10-21

Classification of fluorescense images of ANA
Student: Lars Ryden, F92
Advisor: Anders Heyden, Per Sennmalm (Cellavision AB)
In cooperation with: CellaVision AB
Date Finished: 99-08-30
Abstract: Autoimmune diseases can appear in almost all the body's organs, and the symptoms can dif fer a lot. Therefore looking for autoimmune antibodies has become a routine analysis. Th ese analyses are made manual in semi-darkness, are time consuming and are associated wit h risks of infections from the blood samples. This report investigates the requirements for an automatization of Anti-Nuclear Antibody analyses, so called ANA-analyses, and tries to describe a couple of useful features for future classification systems. The report covers collecting images from samples, segmen tation of the images and extraction and calculation of the values of features. The segme ntation is mostly based on mathematical morphology and the feature extraction on Markov matrices.

Studies of the Inverse Scattering Problem for the Schrödinger Operator on the Real Line
Student: Reijo Härkönen, F94
Advisor: Gudrun Gudmundsdottir, Anders Melin
Date Finished: 99-05-17
Abstract: The inverse conductivity problem involves determining the (variable) conductivity of a material inside a domain from observations at the boundary. Mathematically, this means determining the potential of a Schrödinger equation inside a domain from the Dirichlet to Neumann map on the boundary. Fimitely many values of the Dirichlet to Neumann map can be observed by imposing different voltages at the boundary, and measuring the resulting current flux. If the problem is radially symmetric, it can be reduced to a one-dimensional problem. The Dirichlet to Neumann map is then represented by the values of a certain function r(k) when k=is and s is a positive integer. The function r is called the (right) reflection coefficient of the potential p(x) of the Schrödinger equation. The potential is uniquely determined by the infinite sequence r(is), s=1,2,..One can show that potentials within certain classes are determined up to an arbitrary degree of accuracy by a finite sequence of r(is), s=1,2,..n, if n is large enough. Here we study the possibility to find a rational function with the same values at is, s=1,2,..n, as the r of an unknown potential. Furthermore, if this rational function satisfies some specific well known conditions, then it is the reflection coefficient of a potential w(x), that can be computed. This w(x) will be a good approximation of the unknown potential if n is large enough.

A Robot Playing Scrabble using Visual Information
Student: Anders Ahlstrand, E93 and Johan Bengtsson, E93
Advisor: Anders Heyden, Bo Bernhardsson, Anders Robertsson (Reglerteknik, LTH)
In cooperation with: Reglerteknik
Date Finished: 99-04-19
Abstract: We have used a robot and a camera to design and implement a system which is able to play the well known game Scrabble. To make this possible we have constructed a robot system and a vision system. The task of the vision system is to finds the position of the cubes that the robot system uses to generate the trajectories. The feedback from the camera is used to correct the trajectory. That fact that the system is able to play Scrabble is not the most important part, the interesting part is that the r obot system uses the camera information in real-time to generate and correct the trajectories. Even if there has been done lot of research to combine a robot system with the sensor information from a camera there still exist few commercial systems on the market. In this thesis we will present two different solutions to the problem which correct and generate the trajectories.

Approximation of the Spectra of Differential Operators by Projection on Finite Dimensional Subspaces
Student: Mattias Nilsson, F92
Advisor: Gudrun Gudmundsdottir, Anders Melin
Date Finished: 99-03-03
Abstract: The spectrum of a linear operator provides substantial information about the operator itself, and hence knowledge about the spectrum is highly desirable. This work aims at approximating the discrete spectra (the eigenvalues) of some differential operators by considering their restrictions to finite dimensional subspaces of the original infinite dimensional function spaces. We restrict ourselves to second order differential operators on functions on the real line, on the form L=-D^2+p, where p=p(x) is a continuous real-valued function. For L acting on functions on a bounded interval of the real line, the subspace used is the span of a finite number of eigenfunctions of the operator -D^2, and when considering all of R, the subspace used is spanned by a set of orthonormal wavelets.

Map Matching with Low Precision Sensors for Vehicle Applications
Student: Henrik Stewenius, F96
Advisor: Kalle Åström, David Svensson (Itenerary Systems AB)
In cooperation with: Itinerary Systems AB
Date Finished: 99-02-15
Abstract: The aim of this work was to build a system that gives the current position of a vehicle in real time. The limitations on the solution was that it had to be effective both in use of CPU-power and in hardware requirements. These requirements are met by a program that recursively evaluates a target function with respect to a map for a large number of different solutions. The most probable position is used a current position. Tests and simulations show that this gives a good precision when the input is odometer and GPS perturbed by Selected Availability and mulipathing effects.

Handskriftsigenkänning med hjälp av proxmity-mått och bigramstatistik
Student: Sten Olsson, F91
Advisor: Gunnar Sparr/Rikard Berthilsson
In cooperation with Ericsson Mobile Communications
Date Finished: 99-02-11
Abstract: Computer devices are constantly getting smaller and more capable. Although it is now possible to make powerful appliances that easily fits into a pocket, traditional input devices, such as keyboards and mice, present a limit to the possible amount of miniaturization. Alternative input methods, such as voice recognition and recognition of hand-written text, are still far from fully developed. In this paper we propose ways of improving a system for recognition of hand-written symbols. The system recognizes symbols, consisting of one or several curves, by using geometrical invariants. The system is extended to recog-nize entire words. The selection of the most likely word candidate is made by including the use of bigram statistics and probability analysis.