A variational multiphase level set approach to simultaneous segmentation and bias correction

Department of ComputingRefereed conference pape

Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work

Brain MRI Segmentation with Multiphase Minimal Partitioning: A Comparative Study

This paper presents the implementation and quantitative evaluation of a multiphase three-dimensional deformable model in a level set framework for automated segmentation of brain MRIs. The segmentation algorithm performs an optimal partitioning of three-dimensional data based on homogeneity measures that naturally evolves to the extraction of different tissue types in the brain. Random seed initialization was used to minimize the sensitivity of the method to initial conditions while avoiding the need for a priori information. This random initialization ensures robustness of the method with respect to the initialization and the minimization set up. Postprocessing corrections with morphological operators were applied to refine the details of the global segmentation method. A clinical study was performed on a database of 10 adult brain MRI volumes to compare the level set segmentation to three other methods: “idealized” intensity thresholding, fuzzy connectedness, and an expectation maximization classification using hidden Markov random fields. Quantitative evaluation of segmentation accuracy was performed with comparison to manual segmentation computing true positive and false positive volume fractions. A statistical comparison of the segmentation methods was performed through a Wilcoxon analysis of these error rates and results showed very high quality and stability of the multiphase three-dimensional level set method

Stabilised bias field: segmentation with intensity inhomogeneity

Automatic segmentation in the variational framework is a challenging task within the field of imaging sciences. Achieving robustness is a major problem, particularly for images with high levels of intensity inhomogeneity. The two-phase piecewise-constant case of the Mumford-Shah formulation is most suitable for images with simple and homogeneous features where the intensity variation is limited. However, it has been applied to many different types of synthetic and real images after some adjustments to the formulation. Recent work has incorporated bias field estimation to allow for intensity inhomogeneity, with great success in terms of segmentation quality. However, the framework and assumptions involved lead to inconsistencies in the method that can adversely affect results. In this paper we address the task of generalising the piecewise-constant formulation, to approximate minimisers of the original Mumford-Shah formulation. We first review existing methods for treating inhomogeneity, and demonstrate the inconsistencies with the bias field estimation framework. We propose a modified variational model to account for these problems by introducing an additional constraint, and detail how the exact minimiser can be approximated in the context of this new formulation. We extend this concept to selective segmentation with the introduction of a distance selection term. These models are minimised with convex relaxation methods, where the global minimiser can be found for a fixed fitting term. Finally, we present numerical results that demonstrate an improvement to existing methods in terms of reliability and parameter dependence, and results for selective segmentation in the case of intensity inhomogeneity. </jats:p

Active contours for intensity inhomogeneous image segmentation

La “inhomogeneidad” (falta d'homogeneïtat) d'intensitat és un problema ben conegut en la segmentació d'imatges, la qual cosa afecta la precisió dels mètodes de segmentació basats en la intensitat. En aquesta tesi, es proposen mètodes de contorn actiu basat en fronteres i regions per segmentar imatges inhomogènies. En primer lloc, s'ha proposat un mètode de contorn actiu basat en fronteres mitjançant Diferència de Gaussianes (DoG), que ajuda a segmentar l'estructura global de la imatge. En segon lloc, hem proposat un mètode de contorn actiu basat en regions per corregir i segmentar imatges inhomogènies. S'ha utilitzat un nucli de transformació de fase (phase stretch transform - PST) per calcular noves intensitats mitjanes i camps de polarització, que s'empren per definir una imatge ajustada de polarització. En tercer lloc, s'ha proposat un altre mètode de contorn actiu basat en regions utilitzant un funcional d'energia basat en imatges ajustades locals i globals. El camp de polarització s'aproxima amb una distribució Gaussiana i el biaix de les regions no homogènies es corregeix dividint la imatge original pel camp aproximat de polarització. Finalment, s'ha proposat un mètode híbrid de contorns actius multifàsic (quatre fases) per dividir una imatge de RM cerebral en tres regions diferents: matèria blanca (WM), matèria grisa (GM) i líquid cefaloraquidi (CSF). En aquest treball, també s'ha dissenyat un mètode de post-processat (correcció de píxels) per millorar la precisió de les regions WM, GM i CSF segmentades. S'han utilitzat resultats experimentals tant amb imatges sintètiques com amb imatges reals de RM del cervell per a una comparació quantitativa i qualitativa amb mètodes de contorns actius de l'estat de l'art per mostrar els avantatges de les tècniques de segmentació proposades.La “inhomogeneidad” (falta de homogeneidad) de intensidad es un problema bien conocido en la segmentación de imágenes, lo que afecta la precisión de los métodos de segmentación basados en la intensidad. En esta tesis, se proponen métodos de contorno activo basado en bordes y regiones para segmentar imágenes inhomogéneas. En primer lugar, se ha propuesto un método de contorno activo basado en fronteras mediante Diferencia de Gaussianas (DoG), que ayuda a segmentar la estructura global de la imagen. En segundo lugar, hemos propuesto un método de contorno activo basado en regiones para corregir y segmentar imágenes inhomogéneas. Se ha utilizado un núcleo de transformación de fase (phase stretch transform - PST) para calcular nuevas intensidades medias y campos de polarización, que se emplean para definir una imagen ajustada de polarización. En tercer lugar, se ha propuesto otro método de contorno activo basado en regiones utilizando un funcional de energía basado en imágenes ajustadas locales y globales. El campo de polarización se aproxima con una distribución Gaussiana y el sesgo de las regiones no homogéneas se corrige dividiendo la imagen original por el campo aproximado de polarización. Finalmente, se ha propuesto un método híbrido de contornos activos multifásico (cuatro fases) para dividir una imagen de RM cerebral en tres regiones distintas: materia blanca (WM), materia gris (GM) y líquido cefalorraquídeo (CSF). En este trabajo, también se ha diseñado un método de post-procesado (corrección de píxeles) para mejorar la precisión de las regiones WM, GM y CSF segmentadas. Se han utilizado resultados experimentales tanto con imágenes sintéticas como con imágenes reales de RM del cerebro para una comparación cuantitativa y cualitativa con métodos de contornos activos del estado del arte para mostrar las ventajas de las técnicas de segmentación propuestas.Intensity inhomogeneity is a well-known problem in image segmentation, which affects the accuracy of intensity-based segmentation methods. In this thesis, edge-based and region-based active contour methods are proposed to segment intensity inhomogeneous images. Firstly, we have proposed an edge-based active contour method based on the Difference of Gaussians (DoG), which helps to segment the global structure of the image. Secondly, we have proposed a region-based active contour method to both correct and segment intensity inhomogeneous images. A phase stretch transform (PST) kernel has been used to compute new intensity means and bias field, which are employed to define a bias fitted image. Thirdly, another region-based active contour method has been proposed using an energy functional based on local and global fitted images. Bias field is approximated with a Gaussian distribution and the bias of intensity inhomogeneous regions is corrected by dividing the original image by the approximated bias field. Finally, a hybrid region-based multiphase (four-phase) active contours method has been proposed to partition a brain MR image into three distinct regions: white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). In this work, a post-processing (pixel correction) method has also been devised to improve the accuracy of the segmented WM, GM and CSF regions. Experimental results with both synthetic and real brain MR images have been used for a quantitative and qualitative comparison with state-of-the-art active contour methods to show the advantages of the proposed segmentation techniques

Semisupervised Soft Mumford-Shah Model for MRI Brain Image Segmentation

One challenge of unsupervised MRI brain image segmentation is the central gray matter due to the faint contrast with respect to the surrounding white matter. In this paper, the necessity of supervised image segmentation is addressed, and a soft Mumford-Shah model is introduced. Then, a framework of semisupervised image segmentation based on soft Mumford-Shah model is developed. The main contribution of this paper lies in the development a framework of a semisupervised soft image segmentation using both Bayesian principle and the principle of soft image segmentation. The developed framework classifies pixels using a semisupervised and interactive way, where the class of a pixel is not only determined by its features but also determined by its distance from those known regions. The developed semisupervised soft segmentation model turns out to be an extension of the unsupervised soft Mumford-Shah model. The framework is then applied to MRI brain image segmentation. Experimental results demonstrate that the developed framework outperforms the state-of-the-art methods of unsupervised segmentation. The new method can produce segmentation as precise as required