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

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

Hybrid Active Contour Based on Local and Global Statistics Parameterized by Weight Coefficients for Inhomogeneous Image Segmentation

Image inhomogeneity often occurs in real-world images and may present considerable difficulties during image segmentation. Therefore, this paper presents a new approach for the segmentation of inhomogeneous images. The proposed hybrid active contour model is formulated by combining the statistical information of both the local and global region-based energy fitting models. The inclusion of the local region-based energy fitting model assists in extracting the inhomogeneous intensity regions, whereas the curve evolution over the homogeneous regions is accelerated by including the global region-based model in the proposed method. Both the local and global region-based energy functions in the proposed model drag contours toward the accurate object boundaries with precision. Each of the local and global region-based parts are parameterized with weight coefficients, based on image complexity, to modulate two parts. The proposed hybrid model is strongly capable of detecting region of interests (ROIs) in the presence of complex object boundaries and noise, as its local region-based part comprises bias field. Moreover, the proposed method includes a new bias field (NBF) initialization and eliminates the dependence over the initial contour position. Experimental results on synthetic and real-world images, produced by the proposed model, and comparative analysis with previous state-of-the-art methods confirm its superior performance in terms of both time efficiency and segmentation accuracy

Level set segmentation using non-negative matrix factorization with application to brain MRI

We address the problem of image segmentation using a new deformable model based on the level set method (LSM) and non-negative matrix factorization (NMF). We describe the use of NMF to reduce the dimension of large images from thousands of pixels to a handful of metapixels or regions. In addition, the exact number of regions is discovered using the nuclear norm of the NMF factors. The proposed NMF-LSM characterizes the histogram of the image, calculated over the image blocks, as nonnegative combinations of basic histograms computed using NMF (V ~ W H). The matrix W represents the histograms of the image regions, whereas the matrix H provides the spatial clustering of the regions. NMF-LSM takes into account the bias field present particularly in medical images. We define two local clustering criteria in terms of the NMF factors. The first criterion defines a local intensity clustering property based on the matrix W by computing the average intensity and standard deviation of every region. The second criterion defines a local spatial clustering using the matrix H. The local clustering is then summed over all regions to give a global criterion of image segmentation. In LSM, these criteria define an energy minimized w.r.t. LSFs and the bias field to achieve the segmentation. The proposed method is validated on synthetic binary and gray-scale images, and then applied to real brain MRI images. NMF-LSM provides a general approach for robust region discovery and segmentation in heterogeneous images

A Geometric Flow Approach for Segmentation of Images with Inhomongeneous Intensity and Missing Boundaries

Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often contain both of these issues, making muscle segmentation especially difficult. In this paper we propose a novel intensity correction and a semi-automatic active contour based segmentation approach. The approach uses a geometric flow that incorporates a reproducing kernel Hilbert space (RKHS) edge detector and a geodesic distance penalty term from a set of markers and anti-markers. We test the proposed scheme on MR muscle segmentation and compare with some state of the art methods. To help deal with the intensity inhomogeneity in this particular kind of image, a new approach to estimate the bias field using a fat fraction image, called Prior Bias-Corrected Fuzzy C-means (PBCFCM), is introduced. Numerical experiments show that the proposed scheme leads to significantly better results than compared ones. The average dice values of the proposed method are 92.5%, 85.3%, 85.3% for quadriceps, hamstrings and other muscle groups while other approaches are at least 10% worse.Comment: Presented at CVIT 2023 Conference. Accepted to Journal of Image and Graphic

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