Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models

Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image-noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating the uncertainty in label assignment is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. On the other hand, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the Active Mean Fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model (CV), in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the icgbench dataset

A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.Comment: 15pages,13figure

Active Contours and Image Segmentation: The Current State Of the Art

Image segmentation is a fundamental task in image analysis responsible for partitioning an image into multiple sub-regions based on a desired feature. Active contours have been widely used as attractive image segmentation methods because they always produce sub-regions with continuous boundaries, while the kernel-based edge detection methods, e.g. Sobel edge detectors, often produce discontinuous boundaries. The use of level set theory has provided more flexibility and convenience in the implementation of active contours. However, traditional edge-based active contour models have been applicable to only relatively simple images whose sub-regions are uniform without internal edges. Here in this paper we attempt to brief the taxonomy and current state of the art in Image segmentation and usage of Active Contours

Anisotropic Mesh Adaptation for Image Segmentation based on Partial Differential Equations

Title from PDF of title page viewed January 12, 2021Dissertation advisor: Xianping LiVitaIncludes bibliographical references (pages 69-85)Thesis (Ph.D.)--Department of Mathematics and Statistics and School of Computing and Engineering. University of Missouri--Kansas City, 2020As the resolution of digital images increases significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this dissertation, we consider image segmentation by solving a partial differential equation (PDE) model based on the Mumford-Shah functional. We first, develop a new anisotropic mesh adaptation (AMA) framework to improve segmentation efficiency and accuracy. In the AMA framework, we incorporate an anisotropic mesh adaptation for image representation and a nite element method for solving the PDE model. Comparing to traditional algorithms solved by the finnite difference method, our AMA framework provides faster and better results without the need for re-sizing the images to lower quality. We also extend the algorithm to segment images with multiple regions. We also improve the well-known Chan-Vese model by developing a locally enhanced Chan-Vese (LECV) model. Our LECV model incorporates a newly define signed pressure force (SPF) function, which is built upon the local image information. The SPF function helps to attract the contour curve to the object boundaries for images with inhomogeneous intensities. The proposed LECV model, together with the AMA segmentation framework can successfully segment the image with or without inhomogeneous intensities. While most other segmentation methods only work on low-resolution images, our LECV model is successfully applied to high-resolution images, with improved efficiency and accuracy.Introduction -- PDE-Based Image Segmentation -- Background and Literature review -- AMA Segmentation Method -- LECV Model for Image Segmentation -- Conclusion and discussio

Medical Image Segmentation Using Phase-Field Method based on GPU Parallel Programming

The use of a Phase Field method for medical image segmentation is proposed in this paper. The Allen-Cahn equation, a mathematical model equation, is used in this method. The Finite Difference method is used for numerical discretization of model equations and semi-algebraic equations integrated over time using the second -order Runge-Kutta method. Numerical algorithms are implemented into computer programming using the serial and parallel C programming language based on GPU CUDA. Based on image segmentation calculations, the Phase Field method has high accuracy. It is indicated by the Jaccard Index and Dice Similarity values that are close to one. The range of Jaccard Index values is 0.859 - 0.952, while the Dice Similarity value range is 0.926 - 0.976. In addition, it is shown that parallel programming with GPU CUDA can accelerate 45.72 times compared to serial programming

THE IMAGE TORQUE OPERATOR FOR MID-LEVEL VISION: THEORY AND EXPERIMENT

A problem central to visual scene understanding and computer vision is to extract semantically meaningful parts of images. A visual scene consists of objects, and the objects and parts of objects are delineated from their surrounding by closed contours. In this thesis a new bottom-up visual operator, called the Torque operator, which captures the concept of closed contours is introduced. Its computation is inspired by the mechanical definition of torque or moment of force, and applied to image edges. It takes as input edges and computes over regions of different size a measure of how well the edges are aligned to form a closed, convex contour. The torque operator is by definition scale independent, and can be seen as an operator of mid-level vision that captures the organizational concept of 'closure' and grouping mechanism of edges. In this thesis, fundamental properties of the torque measure are studied, and experiments are performed to demonstrate and verify that it can be made a useful tool for a variety of applications, including visual attention, segmentation, and boundary edge detection

Geodesic tractography segmentation for directional medical image analysis

Acknowledgements page removed per author's request, 01/06/2014.Geodesic Tractography Segmentation is the two component approach presented in this thesis for the analysis of imagery in oriented domains, with emphasis on the application to diffusion-weighted magnetic resonance imagery (DW-MRI). The computeraided analysis of DW-MRI data presents a new set of problems and opportunities for the application of mathematical and computer vision techniques. The goal is to develop a set of tools that enable clinicians to better understand DW-MRI data and ultimately shed new light on biological processes. This thesis presents a few techniques and tools which may be used to automatically find and segment major neural fiber bundles from DW-MRI data. For each technique, we provide a brief overview of the advantages and limitations of our approach relative to other available approaches.Ph.D.Committee Chair: Tannenbaum, Allen; Committee Member: Barnes, Christopher F.; Committee Member: Niethammer, Marc; Committee Member: Shamma, Jeff; Committee Member: Vela, Patrici