A semi-automatic method for segmentation and 3D modeling of glioma tumors from brain MRI

This work presents an efficient method for volume rendering of glioma tumors from segmented 2D MRI Datasets with user interactive control, by replacing manual segmentation required in the state of art methods. The most common primary brain tumors are gliomas, evolving from the cerebral supportive cells. For clinical follow-up, the evaluation of the pre- operative tumor volume is essential. Tumor portions were automatically segmented from 2D MR images using morphological filtering techniques. These seg- mented tumor slices were propagated and modeled with the software package. The 3D modeled tumor consists of gray level values of the original image with exact tumor boundary. Axial slices of FLAIR and T2 weighted images were used for extracting tumors. Volumetric assessment of tumor volume with manual segmentation of its outlines is a time-consuming proc- ess and is prone to error. These defects are overcome in this method. Authors verified the performance of our method on several sets of MRI scans. The 3D modeling was also done using segmented 2D slices with the help of a medical software package called 3D DOCTOR for verification purposes. The results were validated with the ground truth models by the Radi- ologist.

Automatic Optic Disc Boundary Extraction from Color Fundus Images

Efficient optic disc segmentation is an important task in automated retinal screening. For the same reason optic disc detection is fundamental for medical references and is important for the retinal image analysis application. The most difficult problem of optic disc extraction is to locate the region of interest. Moreover it is a time consuming task. This paper tries to overcome this barrier by presenting an automated method for optic disc boundary extraction using Fuzzy C Means combined with thresholding. The discs determined by the new method agree relatively well with those determined by the experts. The present method has been validated on a data set of 110 colour fundus images from DRION database, and has obtained promising results. The performance of the system is evaluated using the difference in horizontal and vertical diameters of the obtained disc boundary and that of the ground truth obtained from two expert ophthalmologists. For the 25 test images selected from the 110 colour fundus images, the Pearson correlation of the ground truth diameters with the detected diameters by the new method are 0.946 and 0.958 and, 0.94 and 0.974 respectively. From the scatter plot, it is shown that the ground truth and detected diameters have a high positive correlation. This computerized analysis of optic disc is very useful for the diagnosis of retinal diseases

A Compiler Integrated Assistance for Optimum Data Allocation in Banked Memory Embedded Processors

Bank switching in embedded processors having partitioned memory architecture results in code size as well as run time overhead. An algorithm and its application to assist the compiler in eliminating the redundant bank switching codes introduced and deciding the optimum data allocation to banked memory is presented in this work. A relation matrix formed for the memory bank state transition corresponding to each bank selection instruction is used for the detection of redundant codes. Data allocation to memory is done by considering all possible permutation of memory banks and combination of data. The compiler output corresponding to each data mapping scheme is subjected to a static machine code analysis which identifies the one with minimum number of bank switching codes. Even though the method is compiler independent, the algorithm utilizes certain architectural features of the target processor. A prototype based on PIC 16F87X microcontrollers is described. This method scales well into larger number of memory blocks and other architectures so that high performance compilers can integrate this technique for efficient code generation. The technique is illustrated with an example

Anisotropic adaptive resolution of boundary layers for heat conduction problems

We deal with the numerical solution of heat conduction problems featuring steep gradients. In order to solve the associated partial differential equation a finite volume technique is used and unstructured grids are employed. A discrete maximum principle for triangulations of a Delaunay type is developed. To capture thin boundary layers incorporating steep gradients an anisotropic mesh adaptation technique is implemented. Computational tests are performed for an academic problem where the exact solution is known as well as for a real world problem of a computer simulation of the thermoregulation of premature infants.

An approximation method using approximate approximations

The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.

Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.

Active regions for colour texture segmentation integrating region and boundary information

In this paper a colour texture segmentation method, which unifies region and boundary information, is proposed. The algorithm uses a coarse detection of the perceptual (colour and texture) edges of the image to adequately place and initialise a set of active regions. Colour texture of regions is modelled by the conjunction of non-parametric techniques of kernel density estimation (which allow to estimate the colour behaviour) and classical co-occurrence matrix based texture features. Therefore, region information is defined and accurate boundary information can be extracted to guide the segmentation process. Regions concurrently compete for the image pixels in order to segment the whole image taking both information sources into account. Furthermore, experimental results are shown which prove the performance of the proposed method

HLA-A Typing in formalin-fixed paraffin embedded tissue samples : towards potential retrospective analysis

El Antígeno Leucocitario Humano (HLA en inglés) ha sido descrito en muchos casos como factor de pronóstico para cáncer. La característica principal de los genes de HLA, localizados en el cromosoma 6 (6p21.3), son sus numerosos polimorfismos. Los análisis de secuencia de nucleótidos muestran que la variación está restringida predominantemente a los exones que codifican los dominios de unión a péptidos de la proteína. Por lo tanto, el polimorfismo del HLA define el repertorio de péptidos que se unen a los alotipos de HLA y este hecho define la habilidad de un individuo para responder a la exposición a muchos agentes infecciosos durante su vida. La tipificación de HLA se ha convertido en un análisis importante en clínica. Muestras de tejido embebidas en parafina y fijadas con formalina (FFPE en inglés) son recolectadas rutinariamente en oncología. Este procedimiento podría ser utilizado como una buena fuente de ADN, dado que en estudios en el pasado los ensayos de recolección de ADN no eran normalmente llevados a cabo de casi ningún tejido o muestra en procedimientos clínicos regulares. Teniendo en cuenta que el problema más importante con el ADN de muestras FFPE es la fragmentación, nosotros propusimos un nuevo método para la tipificación del alelo HLA-A desde muestras FFPE basado en las secuencias del exón 2, 3 y 4. Nosotros diseñamos un juego de 12 cebadores: cuatro para el exón 2 de HLA-A, tres para el exón 3 de HLA-A y cinco para el exón 4 de HLA-A, cada uno de acuerdo las secuencias flanqueantes de su respectivo exón y la variación en la secuencia entre diferentes alelos. 17 muestran FFPE colectadas en el Hospital Universitario de Karolinska en Estocolmo Suecia fueron sometidas a PCR y los productos fueron secuenciados. Finalmente todas las secuencias obtenidas fueron analizadas y comparadas con la base de datos del IMGT-HLA. Las muestras FFPE habían sido previamente tipificadas para HLA y los resultados fueron comparados con los de este método. De acuerdo con nuestros resultados, las muestras pudieron ser correctamente secuenciadas. Con este procedimiento, podemos concluir que nuestro estudio es el primer método de tipificación basado en secuencia que permite analizar muestras viejas de ADN de las cuales no se tiene otra fuente. Este estudio abre la posibilidad de desarrollar análisis para establecer nuevas relaciones entre HLA y diferentes enfermedades como el cáncer también.

Image segmentation integrating colour, texture and boundary information

La tesis se centra en la Visión por Computador y, más concretamente, en la segmentación de imágenes, la cual es una de las etapas básicas en el análisis de imágenes y consiste en la división de la imagen en un conjunto de regiones visualmente distintas y uniformes considerando su intensidad, color o textura. Se propone una estrategia basada en el uso complementario de la información de región y de frontera durante el proceso de segmentación, integración que permite paliar algunos de los problemas básicos de la segmentación tradicional. La información de frontera permite inicialmente identificar el número de regiones presentes en la imagen y colocar en el interior de cada una de ellas una semilla, con el objetivo de modelar estadísticamente las características de las regiones y definir de esta forma la información de región. Esta información, conjuntamente con la información de frontera, es utilizada en la definición de una función de energía que expresa las propiedades requeridas a la segmentación deseada: uniformidad en el interior de las regiones y contraste con las regiones vecinas en los límites. Un conjunto de regiones activas inician entonces su crecimiento, compitiendo por los píxeles de la imagen, con el objetivo de optimizar la función de energía o, en otras palabras, encontrar la segmentación que mejor se adecua a los requerimientos exprsados en dicha función. Finalmente, todo esta proceso ha sido considerado en una estructura piramidal, lo que nos permite refinar progresivamente el resultado de la segmentación y mejorar su coste computacional. La estrategia ha sido extendida al problema de segmentación de texturas, lo que implica algunas consideraciones básicas como el modelaje de las regiones a partir de un conjunto de características de textura y la extracción de la información de frontera cuando la textura es presente en la imagen. Finalmente, se ha llevado a cabo la extensión a la segmentación de imágenes teniendo en cuenta las propiedades de color y textura. En este sentido, el uso conjunto de técnicas no-paramétricas de estimación de la función de densidad para la descripción del color, y de características textuales basadas en la matriz de co-ocurrencia, ha sido propuesto para modelar adecuadamente y de forma completa las regiones de la imagen. La propuesta ha sido evaluada de forma objetiva y comparada con distintas técnicas de integración utilizando imágenes sintéticas. Además, se han incluido experimentos con imágenes reales con resultados muy positivos.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.