### EXAMENSARBETEN VID AVDELNINGEN FÖR MATEMATIK, LTH, 2002

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2D PrintCode Recognition
Student: Sara Norstedt F98
Advisor: Fredrik Kahl, Drago Boras (Novotek)
In cooperation with: Novotek
Date Finished: 2002-12-19
Abstract: The aim of this master thesis is to develop a fast method for identifying a two-dimensional print code in an image. The identification includes identifying the location and the rotation of both the code and the lines within it. This thesis proposes a solution based on a simple threshold filter scan that segments out the interesting parts of the image. Since some basic facts are known about the image and the code it is not necessary to scan the entire image but only a fraction of it. In this way much time can be saved. The segmentation scan finds points on the different lines within the code. The points are then grouped together to define lines. Experiments show satisfying results in images with a low noise level. All lines are found in a very short time. However if the image is too noisy, some lines may not be detected or false lines may be found.

Curve Reconstruction from multiple projections
Student: Andreas Wernrud F 98
Date Finished: 2002-12-20
Abstract: In this thesis the problem of reconstructing a 3D-curve from a number of its 2D-projections is addressed. In particular the problem of reconstructing using an unorganized set of such projections is solved. To solve this problem it is necessary to find correspondences between curve points in different projections. Due to the aperture problem this must be solved using iteration. In this thesis an algorithm based on the extension of affine shape is used to solve the correspondence problem. Novel methods to finding a start point to this algorithm are presented. The estimate is refined using non-linear least squares optimization, so called bundle adjustment for curves. This is done using a Levenberg-Marquardt type of algorithm. The methods are verified using real data.

Fall Detection in the Elderly Case Using Digital Image Analysis
Student: Fredrik Rosqvist, F98 and Anders Frediksson, F98
Advisor: Anders Heyden, Henrik Benckert (WeSpot)
In cooperation with: WeSpot
Date Finished: 2002-11-21
Abstract: This master thesis presents a fall detection system for the elderly care based on digital image analysis using a visual sensor, called NurseSensor, developed by WeSpot AB.
Unlike other fall detectors this doesn't demand anything from the patient. Other advantages are low costs, easy to install and possibilities to adjust the functionality for the person's own needs.
The fall detection is divided into two main steps; finding the person on the floor and examining the way in which the person ended up on the floor. The first step is further divided into algorithms investigating the percentage share of the body on the floor, the lean of the body and length of the person. The second step includes algorithms examining the velocity and acceleration of the person.
When the first step indicates that the person is on the floor data for a pair of seconds back is saved and analysed in the second step. If this indicates fall the system enters a countdown state, in order to reduce the risk of false alarms, before sending an alarm.
This master thesis has been a pre-study, thus in order to get a product ready to use some work still remain. Though we cherish great hope that this will be a reality in the near future.

Student: Robin Rander, F96
Date Finished: 02-11-11
Abstract: Wavelet bases can be used to approximately solve the radiosity equation. This approach offers a prospect of solving the radiosity problem in a number of operations that is asymptotically linear in the number of patches. The mathematical background for this solution technique is developed and algorithms for solving the radiosity problem using wavelets are presented. Merits and drawbacks of the wavelet approach are discussed. It is concluded that the radiosity transport operator is, contrary to popular belief, not of the Calderon-Zygmund type. This does not, however, imply that wavelets are not attractive for rapidly solving the radiosity problem. The properties that can be expected of a Calderon-Zygmund operator when discretised using wavelets are present away from the shadow boundaries.

3D based face recognition using structured light
Student: Björn Smedman, F 98 and Karl Netzell, F 98
Advisor: Kalle Åström, Fredrik Kahl, Charlotte Svensson, Anders P Eriksson, Daniel Elvin (Axis)
In cooperation with: Axis
Date Finished: 02-11-01
Abstract: The goal of this thesis is to construct a system for face recognition using two cameras and an overhead projector. The set-up makes it possible to extract 3D shapes. The overhead projector is facilitating this by projecting a pattern of parallel lines onto the face. Through a stereo matching algorithm a cloud of 3D points is created, which is turned into a surface model of the face. A distance between two such surfaces is defined and used for recognition. The calculation of the distance involves optimization.

Numerical methods for time-periodic parabolic equations
Date Finished: 02-10-09
Abstract: Every day a multitude of time-periodic phenomena occur around us. Consider for instance an oscillating guitar string, a rotating propeller, or the so crucial beating heart. Often these phenomena can be modelled by some set of partial differential equations. In this thesis different strategies for dealing with time-periodic parabolic equations will be examined. Especially, we compare a time-periodic ansatz with time iteration, for the heat equation, Burgers' equation and briefly Navier-Stokes' equations. The ansatz method showed promising results, with one reservation; shortage of computer memory. The commercial program FEMLAB was used as a benchmark for the iterative method, and in comparison the ansatz method more accurately found periodic solutions, with the drawback of large memory usage.

Matching of two-dimensional gel electrophoresis images
Student: Andreas Karlsson, F97
In cooperation with: Ludesi AB
Date Finished: 02-06-20
Abstract: Proteins play a vital part in the cells of all living things. The most common used technique for protein analysis is 2D gel electrophoresis, a separation method resulting in an image of the separation pattern.
A method has been developed in the purpose of matching and comparing such images. A set of corresponding protein spots is created. The method consists of piecewise surface matching coarsely aligning the images followed by pattern matching using affine invariants within each of the aligned areas. For evaluation one of the images is warped according to the corresponding points and subtracted from the other image.
Matching results are good. The pattern matching proves to be powerful and most of the strongly expressed proteins are correctly matched. Known differences are magnified and can after the matching easily be identified. The method is not by any means a complete matching algorithm but serves as a solid base for further development.
The biggest problem is related to the properties of proteins. We want to match as many proteins as possible. But the separation patterns come out unpredictably distorted, which requires the pattern matching to have some amount of tolerance. But on the other hand we want to track every little difference between the samples. Therefore extensive knowledge in proteomics is required for further improvements.

Segmentation of Two-Dimensional Gel Electrophoresis Images
Student: Gustav Wallmark, F97
In cooperation with: Ludesi AB
Date Finished: 02-06-20
Abstract: Since the genome was sequenced, the importance of proteomics has increased enormously. To detect the different protein profiles contained in cells and other media, a two-dimensional gel electrophoresis method is used. It produces real and digital two-dimensional protein charts, which are analyzed. One of the first steps in the analysis is to detect the proteins in the digital chart. This is done with automatic computer-assisted segmentation.
In this master thesis, based on evolving interfaces, a segmentation system is created, implemented and evaluated for the segmentation of two-dimensional gel electrophoresis images. It is shown that with the use of Fast Marching Methods to approximate the evolving interfaces, the segmentation can be swiftly performed with high quality results. One weakness with this implementation is that it is a marker based segmentation. When two protein spots overlap and lay almost on top of each other, it is difficult to find correct markers. Fortunately, occurrences of this kind of extreme overlapping are rare.

Pattern Recognition using Support Vector Machines
Student: Fredrik Gran, F97
Advisor: Kalle Åström, Rikard Berthilsson (Decuma AB)
In cooperation with: Decuma AB
Date Finished: 02-06-14
Abstract: In this thesis the method of Support Vector Machines (SVM) for pattern classification is investigated and evaluated for the purpose of hand writing recognition. The concept of Support Vector Machines relies on an optimal separating hyperplane. This hyperplane could be derived either in the input space or in a more generalized feature space. One advantage of Support Vector Machines lies in the possibillity to use a feature space by defining a non linear dividing surface. This function could be of a very complex nature, enhancing the separability dramatically. Another advantage of Support Vector Machines is that the problem formulation results in a convex optimization problem for which there exists efficient methods to find the global optimum. In this thesis a classifier for binary sets has been developed for particularly difficult letter pairs. A classifier for single stroke characters relying on SVM has also been developed, as well as a technique for reducing the requirements on storage capacity.

Modelling a Paper Fibre Structure
Student: Andreas Ekefjärd, F96
In cooperation with: Stora Enso, Karlstad
Date Finished: 02-06-11
Abstract: Simulation of microstructures is possible today. For research in paper development this enables modelling of the behaviour of paper subjected to external forces. Characteristics such as strength and absorbency can then be analysed through computer simulations.
In this report, using a statistical approach a mathematical model of a paper fibre structure is developed. The report focuses on flocculation, which is a phenomenon resulting in an uneven mass distribution in the paper. Images of paper is used as input data.
To include the flocculation in the model, the point process describing the positions of the fibre centres is modelled as a Poisson process with an intensity described by a varying intensity field. By analysing first- and second-order characteristics of the paper images, a mathematical relation between the characteristics of the images and the intensity field is derived. Suggestions on how to estimate the parameters are given.
The model is tested using data generated by a new method. The results are not completely satisfactory and we believe the model has to be tested on a set of data with more known characteristics.

Non-linear coding and modulation by synchronized chaos
Student: Dragana Arlov, F 97
Advisor: Mario Natiello, Lars Segerlund (Tritium Research AB)
In cooperation with: Tritium Research AB
Date Finished: 02-05-31
Abstract: Ett icke-linjärt system, nämligen ett Lorenzsystem, har undersökts. Lorenz system uppvisar ett kaotiskt fenomen som kallas för säregen attraktor. Då man kopplade samman två säregna attraktorer så fick man en perfekt synkronisering mellan dom. Denna synkronisering har undersökts och har använts för att överföra information mellan en kaotisk sändare och en kaotisk mottagare. Störningskänsligheten och systemkapaciteten har också undersökts.

Hidden Markov Model Based Hand Writing Recognition
Advisor: Sven Spanne, Kalle Åström, Rikard Berthilsson (Decuma AB)
In cooperation with: Decuma AB
Date Finished: 02-05-23
Abstract: Hidden Markov models (HMMs) is a powerful tool for signal processing focusing on statistical properties. Research results presented during the last decade have shown that hidden Markov models works very well in speech recognition and handwriting recognition systems. In this thesis three different applications for handwriting recognition were developed and implemented based on the theory of hidden Markov models. The three applications are; a single character recognition (SCR) engine for Latin letters and Arabic figures, a novel multi character recognition (MCR) system for capital Latin letters and an unconstrained cursive word recognition (CWR) system for non-capital Latin letters.

Recovering Two-Dimensional Projections of the Camera Motion from Images of Unknown Environments
Student: Malin Zippert, F96
Advisor: Gunnar Sparr, Björn Johansson, Per Åstrand (C-Technologies)
In cooperation with: C-Technologies
Date Finished: 02-05-24
Abstract: In this thesis, ways to compute the camera motion from images taken during the movement are explored. Only the 2-d projection of the motion onto the imaging surface is wanted. The method should work for images of different and unknown environments, preferably in real time.
An attempt to retrieve the camera motion using camera models and epipolar geometry is made. However, the need for the solution to work for different environments and hopefully in real time leads to the exploration of alternative approach.
The apparent motion of brightness patterns observed in a time sequence is called the optical flow. This flow is computed using different algorithms and the results are interpreted in the search of the 2-d motion.

Segmentation of Histopathological Tissue Sections using Gradient Vector Flow Snakes
In cooperation with: Cellavision
Date Finished: 02-03-18
Abstract: Histopathology is a diverse field consisting of a wide range of different analyses and it is therefore motivated to investigate semi-automatic methods that might be generally applicable to a group of problems. One such method is a segmentation method called snakes. In this thesis the possibilities of utilizing snakes as a semi-automatic method for segmentation of histopathological sections are investigated and a semi-automatic segmentation tool is created. The implications for a fully automatic system are also analyzed and main problems to which snakes are applicable are identified.
The type of snake investigated is the Gradient Vector Flow snake and the tissue sections studied are Hematoxylin- and Eosin-stained sections from bladder tumors and normal urothelium. Different ways of pre-processing images, based on Otsu's thresholding method and morphological operations, are also investigated. It is found suitable to pre-process in two different fashions depending on how the snake is initialized, and these two methods are presented. The pre-processing aims at calculating an edge map. Instead of just making use of the magnitude of a gradient field, as is common, the proposed methods also take into account the directions of the field. Furthermore insights into the snake's iterative evolution algorithm are presented and based on those a novel implementation of the algorithm, which requires fewer calculations than previously used methods, is proposed.

An On-Line Recognition System for Handwritten Japanese Characters
Student: Jakob Sternby, F97
Advisor: Fredrik Kahl, Andreas Björklund (C-technologies)
In cooperation with: C-Technologies
Date Finished: 02-02-27
Abstract: Even though Japanese characters at first may appear complex to the uninitiated reader, they all consist of a set of quite simple strokes. 'Simple' here implies that the individual strokes are plausible to portray even for a beginner. All of the strokes display several distinct qualitative features. In this thesis a method for recognizing a character, by exclusively classifying these qualitative features of its composing strokes, is developed. The method consists of two successive decision trees, implemented within this thesis for one of the Japanese phonetic alphabets, hiragana. In most cases characters could be classified by solely using the generated set of stroke-types. In a few cases additional knowledge about the relative sizes and angles between strokes was used to differ between two characters defined by similar sets of stroke-types. The system is invariant to scaling, position and rotation of the input data, suffering only from the limitations of a real computer counting with numbers represented by a fixed word width. It was developed for a C-pen, where the input data is received in a coordinate representation, which is generated for each stroke from calculations of camera movement. Consequently the method is not required to deal with image-related problems.

OCR and barcode reading using a microscope
Student: Daniel Falk, F97
Advisor: Anders Heyden, Martin Almer (Cellavision)
In cooperation with: Cellavision
Date Finished: 02-02-25
Abstract: Slides used in blood smear analysis are labelled with a unique number. This number can be written using either a barcode or characters. The aim of this thesis is to implement both a barcode and a character reader that can decipher this number automatically using a transmission microscope. The demand on the reader is that it is 100% reliable and takes only a couple of seconds to process.
The barcode reader is implemented to decode the standard 'Code 128', but can easily be altered to decode other standards. An image of the barcode is made binary by thresholding after which the widths of the bars and spaces are found by a merging algorithm. The widths are used in the decoding process. The decoding of barcodes proves to be very successful.
The character reader is implemented to read numbers only. Discriminant analysis is used to find a proper threshold value in the segmentation process. A method of sweeping a window over the text, using MSE and projection, is used to segment the characters. The segmentation of the characters works very well. Classification is done with a method called k-nearest neighbour.

Methods for Classification of Gene Expressions
Student: Jens Nilsson, F97
In cooperation with: Klinisk genetik
Date Finished: 02-02-22
Abstract: Recent advances in molecular biology and biotechnology have made it possible to monitor the activity levels of thousands of genes simultaneously. These gene expressions can be measured using microarrays, and then used to diagnose different diseases or to investigate which cellular processes a particular gene is involved in.
This work has two main objectives. First, an overview over existing methods for mathematical analysis of microarray data is given. Second, investigations are made on two microarray data sets, one set of lymphoma samples and one set of breast cancer samples. Here, the Isomap algorithm is compared to multidimensional scaling for the purpose of projecting high-dimensional gene expression data onto two dimensions. Isomap implements a modification of multidimensional scaling in order to capture non-linear dependencies in data. Further, the space of p-norm distance measures is searched for distance measures that best capture biological similarity, as defined by prior diagnosis of the samples. The results show that Isomap gives remarkably better visualizations than multidimensional scaling for the lymphoma data. Diagnostic classes appear as much more discernible in the Isomap visualization. Further, the results show that different p-norm distance measures capture biological similarity to a different degree.

Convoluting Networks applied on White Blood Cells
Student: Erik Alpkvist, F97
Advisor: Anders Heyden, David Gustavsson (Cellavision)
In cooperation with: Cellavision
Date Finished: 02-01-18
Abstract: This thesis investigates the ability of classifying images with convoluting neural networks. A convoluting neural network is a complex neural network architecture where the weights in the network may represent convolution kernels, which are used to extract the information hidden in the images. The use of convoluting neural network may by-pass several time consuming steps in image classification such as segmentation and feature-extraction.
Tests are performed with different convoluting network architectures on images of unsegmented white blood cells. The networks are trained with a special updating method called 'stochastic Levenberg-Marquardt' that combines benefits of both pattern-by-pattern- and batch training. With small adjustments countering the lack of built-in rotation invariance the best network are able to perform a successful classification of the five most common white blood-cells considering the little or none pre-processing of the images.

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