EXAMENSARBETEN VID AVDELNINGEN FÖR MATEMATIK, LTH, 2008

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Improvement of Prognostic Tools in Prostate Cancer: Investigation on the Relationship between PSA Concentration in Prostate Tissue and Gleason Score(Förbättringar av prognostiserande verktyg inom prostatacancer: Undersökning om relationen mellan PSA koncentration i prostatavävnad och Gleason-gradering)
Student: Giuseppe Lippolis
Advisors: Kalle Åström, Matematikcentrum; Thomas Lauell, Kerstin Järås, Elektrisk mätteknik; Anders Bjertell, UMAS
Date Finished: 2008-12-15
Abstract: Prostate cancer (Pca) is the most common cancer among males in the western world and a major cause of death. Up to now Prostate-specific antigen (PSA) is the most well known biomarker for this kind of disease. What is carried out in the clinical routine is the measurement of the PSA in the patient's blood which is acknowledged as an indicator of prostate cancer. This methodology however has its own limits as for sensitivity and specificity.

To further understand the cause of increase of PSA value, biopsies from the prostate of the patients with high PSA value are collected. The analysis of the histology and morphology of these tissues lets the expert to classify the aggressiveness of the cancer according to the Gleason score, a scaling system which is graded from 2 to 10 (roughly from a 'normal' prostate or 'highly differentiated' to a 'serious' condition or 'poorly differentiated tumour').

An important aspect in facing the problem is the capacity to predict the possible progression of the disease and the consequences of a specific therapy on patient's life. This represents what is called prognosis. Up to now the established prognostic tools are the pre-treatment PSA blood concentration, the Gleason score and the staging, that this, the widespread of the cancer through the organ and to other body's sites. One objective motivation for this work is trying to improve this prognostic system by using new tools such as PSA and Androgen Receptor concentration in prostate tissue and investigating if there is any sort of relationship between the Gleason score and these biomarkers. A more specific investigated issue is the spread of the biomarkers in the different areas of one prostate tissue sample, that is, Benign glands (non cancerous areas), PIN glands (gland where some mutations start appearing, probably evolving in cancer) and Cancer areas (where cancerous cells are present).

The help of the image analysis in the study of the tissue sections, once they have been acquired and rendered in a digital format, is decisive in the quantification of the biomarkers opportunely marked and therefore visible in the images. The work consists in the drafting of a protocol which implies: labelling the tissue sections for the showing the biomarker, acquiring the digital images through microscope and CCD camera, pre-processing these images, carrying out the measurements on the required features, processing and analysing the extracted information. It has to be pointed out the use of a specific microscopy technique, that is, the Time Resolved Fluorescence imaging (TRFI) to overcome the problems of auto-fluorescence. The issues of noise reduction have been faced (offset, uneven lighting, etc.) and an estimation of the bleaching effect which affects the fluorescence images has been performed. The gathering of the data has been fulfilled through the software Image Pro-Plus and Matlab code. The survey is directed toward the specific cases of Gleason score 5, 7 and 9 patients. The first (qualitative) results seem to state that in the least aggressive tumours (Gleason 5) the PSA concentration decreases from benign to PIN to cancer. The opposite situation occurs in most of the patients that we analysed with Gleason 7.

Real-Time Hand Motion Tracking - Introducing A Camera Guided User Interface for Mobile Devices(Realtidsföljning av handrörelser för kamerastyrda användargränsssnitt för mobila enheter)
Student: Martin Lennartsson, Pi02
Advisor: Magnus Oskarsson
In cooperation with: Martin Kretz, Sony Ericsson
Date Finished: 20008-10-28
Abstract: In a modern mobile phone, several methods of user interface coexist, e.g. keyboard, touch pad and voice. In this thesis work a camera guided user interface is developed where user hand motions are detected by the phone camera, and interpreted in real-time by embedded software. This opens up for a completely new way of intuitive userinteractivity in three dimensions, and lays the ground for augmented reality applications. The challenges in the field of real-time computer vision in a restricted portable device are many, including computational performance and fast changes in environmental conditions. Here, those issues are addressed and investigated throughfully. A prototype application is developed in MatLab, then ported to Java running on a mobile phone. The mobile Java programme is capable of image processing at 3-4 frames per second. Different methods of pixel classification has also been evaluated, where Support Vector Machine and Naïve Bayes results in a hitrate for skin color at 87-97%. Experimental results and user evaluation show promising results, but computational performance is still an issue which will need to be further addressed in the future.

Segmentation of Leukocyte Clusters Using Level Set-like Active Contours(Segmentering av leukocytkluster med hjälp av level set-liknande aktiva konturer)
Students: Benny Klein and Simon Burgess, Pi04
Advisor: Niels Christian Overgaard
In cooperation with: Adam Morell, Cellavision AB
Date Finished: 2008-10-24
Abstract: In the field of hematology, differential counting is an analysis to determine the distribution of different types of leukocytes in blood smears. An automation of the differential count can be done by image analysis of microscope images of the blood smears. This master thesis deals with the problem of segmenting clustered leukocytes in microscope images, which is important to make an automated differential count reliable, especially in bone marrow smears.

The segmentation method developed is based on level set-like active contours and a probabilistic viewpoint of handling colour images. Variational calculus is used to derive the evolution of active contours from energy functionals, and experimental results lead to further modification of the evolution. The initialization of the active contours is done by producing a rough pre-classification of the image.

Using a test set of 631 clustered leukocytes from peripheral blood images, 97% of the leukocytes were well enough segmented for a classifier to take a correct decision regarding the leukocyte type.

Feature Tracking with Multiple Models(Punktföljning med flera modeller)
Student: Petter Strandmark, Pi-04
Advisor: Irene Gu, Signal processing group, Chalmers
In cooperation with: Chalmers
Date Finished: 2008-10-21
Abstract: This thesis considers the problem of tracking multiple objects in video captured by a non-stationary camera. The SIFT and SURF algorithms for extracting and matching local features are used. For video sequences of low quality, motion estimation using RANSAC fails if the number of correct matches shrinks below the minimum required to estimate the motion model. To handle such video sequences, RANSAC is extended by allowing multiple models of different complexity to be chosen for each random sample. A probability is introduced to measure the suitability of each transformation candidate given the object locations in previous frames. The best suitable transformation is determined by a combination of the number of consensus points, the probability and the complexity of the model. Ways of managing the list of features belonging to an object are also discussed. Experimental results have shown that the proposed estimation method better handles video of low quality and that it is able to track objects with pose changes, occlusions, motion blur and overlap. Moreover, it is demonstrated that the tracker reaches real-time performance in a MATLAB implementation.

Volume Tracking: A Novel Method for Flow Visualization(Volume Tracking: en ny metod för visualisering av flöden)
Student: Johannes Töger
Advisor: Gustaf Söderlind, Matematikcentrum
In cooperation with: Einar Heiberg, Klinsik fysiologi
Date Finished:2008-10-17
Abstract: Cardiovascular disease is the leading cause of death in Europe today, making it a very active field of research. The essential problem is inadequate blood flow, and this means that diagnosis must focus on why blood is not flowing properly, and therapy must focus on reestablishing the flow. However, blood flow in the heart is poorly understood, and present methods focus on secondary parameters. A recent development is the ability to measure the full 3D+T velocity field in the heart using Magnetic Resonance Imaging. This promises a greater understanding of blood flow, but the data sets are huge and of high dimension, and are thus hard to interpret. This leads to a problem of visualization. Earlier attempts have focused on following particles in the flow by integrating the velocity field directly. This easily results in visual clutter, and following a volume of blood is more natural. In this thesis, a new method for visualizing flows using volumes moving with the flow is introduced. The resulting PDE formulation is analyzed theoretically, solved numerically and integrated in existing software for visualization. Lastly, applications in cardiology are investigated.

Automatic Registration of Two-Dimensional Gel Electrophoresis Images (Automatisk registrering av bilder från tvådimensionell gelelektrofores)
Students: Emma Fägerlind och Marianne Sandin, Pi-03
Advisor: Magnus Oskarsson, Matematikcentrum, Mattias Nilsson, Ludesi AB
In cooperation with: Ludesi AB
Date Finished: 2008-09-24
Abstract: Two-dimensional gel electrophoresis images are produced by a widely used technique for the study of proteins. To extract information from the analysis a matching of the resulting protein pattern in the images must be performed. Due to the complexity of these patterns, most current matching techniques employ a semi-automatic approach and require manual input.

Here, algorithms for automatic matching of the images are presented. The algorithms take a surface based approach utilizing multiresolution analysis, combined with different similarity measures. The methods are evaluated with respect to matching quality and robustness to distortions and lastly compared to current state of the art techniques.

Object Recognition Using the L-infinity Norm (Objektigenkänning baserat på oändlighetsnormen)
Student: Erik Ask, F-04
Advisor: Carl Olsson, Fredrik Kahl
Date Finished: 2008-08-29
Abstract: This thesis addresses the problem of object recognition, that is given specifics of an object, the task of recognizing it in images. Using several image pairs as a base, feature points are selected, matched between image pairs and corresponding points are triangulated into 3D models, consisting of image features and locations in space. By matching features stored for a model to features found in training images, hypothetical correspondences are found, where correct matches are considered inliers, and incorrect outliers. If there exists a set of correspondences consistent with a projective transformation, they are considered inliers, and the object is recognized. The task of finding the projection, or camera matrix is known as resectioning. The point correspondences and features are retrieved using Lowe's SIFT method on all color channels, as well as a greyscale version of the images. The inclusion of the three color channels were useful in both creation, and detection of the models. Triangulation and resectioning are solved using optimal methods, based on convex optimization. Treating each reprojection error in an image as a component of a vector, minimizing this vector's L-infinity norm is a quasiconvex optimization problem. It has recently been shown that this allows for effective outlier identification and removal, which is crucial for recognition. The method shows some success. In tests where models were searched for in images, the detection ratio was 67%, where a detection is a correctly recognized instance of an object.

Mathematical Modelling of Traffic Flow at Bottlenecks (Matematisk modellering av trafikflöde vid flaskhalsar)
Student: Cathleen Perlman, F-03
Advisor: Stefan Diehl
Date Finished: 2008-06-18
Abstract: This master's thesis gives a brief overview of mathematical modelling of traffic flow from different perspectives. Focus lies on the fluid flow analogy first derived by Lighthill, Whitham and Richards (LWR) in the 1950's which treats a traffic stream as a compressible one-dimensional fluid.
The LWR theory is applied to bottleneck queueing situations through two different models, utilising two different sets of flow merge rules. The models are compared and contrasted through steady-state solutions and more general queueing situations.
Benefits and drawbacks of the respective models are discussed and some further modifications and/or extensions are suggested.

Rapport
Populärvetenskaplig rapport

Image Based Localisation in Urban Environments (Bildbaserad lokalisering i stadsmiljö)
Student: Louise Funke F-03
Advisor: Klas Josephson, Fredrik Kahl
Date Finished:2008-06-16
Abstract: In this master thesis a method for image-based localisation given a 3D-model of an urban environment is presented. In order to solve the localisation task, a 3D model needs to be constructed. Photos are taken with a calibrated camera of a part of a street from different angles and distances. For the system, the photos are to be matched together in pairs of two, and several 3D-models are built of these pairs. These 3D-models are then concatenated, so they represent one part of a street. The localisation is performed by comparing new images to the model. These photos are also taken with calibrated cameras. Corresponding points between the new image and the model are found using scale invariant discriminate features, called SIFT. The camera location is then determined relative the model. To test the system, the reprojection error is computed for the found correspondences between the image and the model. The results show that the localisation from the 3D-model can be done with good result.

Rapport
Populärvetenskaplig rapport

PDE-Based Filtering in Velocity Encoded Cardiac MRI(Svensk titel: PDE-baserad filtrering av hastighetskodad hjärt-MR)
Student: Anders Brattberg och Ola Öinert, PO2
Advisor: Gunnar Sparr och Erik Bergvall
Date Finished: 2008-04-08
Abstract: Velocity encoded cardiac MRI comes with a lot of noise from the MR Camera, and in order to use this data, this noise needs to be removed. All noise removal methods are more or less good at preserving different structures of an image. We have implemented a filtering method that uses the total variation norm, which has the main advantage, in comparison with other methods, that it is especially good at preserving edges in an image. We looked into several articles, but eventually concluded that the method suggested in an article by Figureido et al., was best suited for our data. Our implemenation is easy to use and doesn't require too much computational power. In the results we can see a clear improvement of the modeled myocardial motion, using our filtered velocity vectors, compared to just using noise distorted unfiltered data. However, since there is no gold standard method for comparison, we can't quantify how well the method has actually worked.


Prototype Based Image Segmentation - A Novel Method to Incorporate a Priori Information in a Level Set Method (Prototypbaserad bildsegmentering - En ny metod att utnyttja a priorikunskap i nivåytesegmentering)
Student: Jane Sjögren, Pi03
Advisor: Kalle Åström,
In cooperation with: Einar Heiberg, Klinisk Fysiologi
Date Finished: 2008-04-02
Abstract: In this master thesis a novel image segmentation method is presented. The method introduces a priori information from a set of few manually segmented image examples to a general segmentation method, the level set method. The a priori information is extracted as an intensity function, which is statistically based upon the example images, an initialization of the segmentation, which is an approximation of the shape, a spatial map, which constrains the segmentation based upon a correction map and a distance map and also parameters for the level set method used for segmentation. The prototype is used for image segmentation with a fast level set method without having to adjust any parameters. The only manual interaction needed is to set landmarks, typically 3 or 4, in the images. The method is validated on different image segmentation problems in MR images, the aorta, left ventricle wall volume, left ventricle blood volume, right ventricle blood volume and pig lungs. The validation shows promising results and that a big advantage of the method is the usage of a spatial map. The strength of the segmentation method is that only a few image examples are required to introduce a priori information that allows to tailor a general purpose segmentation algorithm for specific applications.


Spektrala problem för kvantgrafer
Student: Erik Wernersson F-02
Advisor: Pavel Kurasov
Date Finished: 2008-02-08


Arabic Online Handwriting Recognition
Student: Cyrus Bakhtiari-Haftlang, D-03
Advisor: Kalle Åström
Date Finished: 2008-02-08
Abstract: There are more than 400 million Arabic speaking people in the world and twice as many use the Arabic script. Todays consumers have high demand for a natural interaction with their consumer electronics. This is many times made possible thanks to smart handwriting recognition systems. Such recognition products exist for interpretation of Latin based characters and Chinese and Japanese signs. The aim of this thesis was to adapt a handwriting engine to recognize Arabic letters. This was accomplished by gathering writing data from Arabs and using present utilities to process the data by clustering it using divisive hierarchical clustering. Several features were added to the existing recognition engine to eliminate ambiguity between problematic character pairs. The achieved recognition rate of the engine and the Arabic database landed on circa 95 percent. The database from this work could potentially be used in a commercial product in the future.


Archimedean Copulas, l_p -norm Symmetric Distributions and Multivariate Extremes (Arkimediska copula, l_p -norm-symmetriska fördelningar och multivariata extremvärden)
Student: Martin Larsson, Pi04
Advisor: Prof. Paul Embrechts, Dr Johanna Neslehova, ETH, Zürich
In cooperation with: ETH, Zürich
Date Finished: 2008-01-22
Abstract: As a consequence of a celebrated result by A. Sklar, dependence between random variables can be described in isolation from the behavior of the marginal distributions. This leads to the concept of a copula, an object that can be regarded as specifying the dependence structure. In this thesis we look closer at the specific class of Archimedean copulas, which have a very tractable algebraic form.

Recent results by McNeil and Neslehova characterize Archimedean copulas in terms of so-called l_1 -norm symmetric distributions. A special integral transform, the Williamson d-transform, acting on positive random variables plays a crucial role. We show how these results enable us to use univariate extreme value theory to draw conclusions about the multivariate extremal behavior of Archimedean copulas in a transparent fashion. More precisely, the dependence structure of the limiting distributions of multivariate maxima and threshold exceedances are investigated, and are proven to be described by two one-parameter families of Archimedean copulas (the Gumbel and Clayton copulas, respectively). Moreover, we derive expressions for the coefficients of tail dependence of Archimedean copulas in terms of properties of the corresponding l_1 -norm symmetric distributions.

In order to establish the connection between the l_1 -norm symmetric distributions and the corresponding Archimedean copulas, we prove a number of results connecting the asymptotic properties of positive random variables to properties of their Williamson d-transforms.

Generalizations of the l_1 -norm symmetric distributions in the direction of l_p -norm symmetric distributions are also considered. This leads us to look at a family of random variables characterized by the property that their survival function can be expressed as a function of the l_p -norm of its argument. We show that random variables in this family all have Archimedean copulas. We also provide a number of results regarding the possible overlap between the class of l_p -norm symmetric distributions and the class of distributions whose copulas are Archimedean.


Multiresolution Analysis, Wavelets and Covariant Representations of C*-Algebras (Multriresolutioner, wavelets och kovarianta representationer av C*-algebror)
Student: Leo Gumpert Pi02
Advisor: Sergei Silvestrov
Date Finished: 2008-01-22
Abstract: The theory of operator algebras, initiated by von Neumann, Gelfand and others more than 70 years ago, can be described as a study of algebras of bounded linear operators on Hilbert spaces with certain algebraic and topological properties. They can also be characterized by a simple set of axioms, and an operator algebra acting on a concrete Hilbert space can then be regarded as a representation of this abstract algebra.

We will initially study representations of a certain operator algebra occurring in multiresolution wavelet analysis. In connection with this, we will also study how these representations can be dilated, i.e. extended to a larger Hilbert space, and how the scaling map naturally gives rise to covariant representations. Following this, we develop the classical theory of covariant representations in the context of unitary representations of locally compact groups. Finally, we study actions by endomorphisms and transfer operators on C*-algebras, which have connections to non-invertible C*-dynamical systems.


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9 January 2009