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

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

Vascular Segmentation Algorithms for Generating 3D Atherosclerotic Measurements

Atherosclerosis manifests as plaques within large arteries of the body and remains as a leading cause of mortality and morbidity in the world. Major cardiovascular events may occur in patients without known preexisting symptoms, thus it is important to monitor progression and regression of the plaque burden in the arteries for evaluating patient\u27s response to therapy. In this dissertation, our main focus is quantification of plaque burden from the carotid and femoral arteries, which are major sites for plaque formation, and are straight forward to image noninvasively due to their superficial location. Recently, 3D measurements of plaque burden have shown to be more sensitive to the changes of plaque burden than one-/two-dimensional measurements. However, despite the advancements of 3D noninvasive imaging technology with rapid acquisition capabilities, and the high sensitivity of the 3D plaque measurements of plaque burden, they are still not widely used due to the inordinate amount of time and effort required to delineate artery walls plus plaque boundaries to obtain 3D measurements from the images. Therefore, the objective of this dissertation is developing novel semi-automated segmentation methods to alleviate measurement burden from the observer for segmentation of the outer wall and lumen boundaries from: (1) 3D carotid ultrasound (US) images, (2) 3D carotid black-blood magnetic resonance (MR) images, and (3) 3D femoral black-blood MR images. Segmentation of the carotid lumen and outer wall from 3DUS images is a challenging task due to low image contrast, for which no method has been previously reported. Initially, we developed a 2D slice-wise segmentation algorithm based on the level set method, which was then extended to 3D. The 3D algorithm required fewer user interactions than manual delineation and the 2D method. The algorithm reduced user time by ≈79% (1.72 vs. 8.3 min) compared to manual segmentation for generating 3D-based measurements with high accuracy (Dice similarity coefficient (DSC)\u3e90%). Secondly, we developed a novel 3D multi-region segmentation algorithm, which simultaneously delineates both the carotid lumen and outer wall surfaces from MR images by evolving two coupled surfaces using a convex max-flow-based technique. The algorithm required user interaction only on a single transverse slice of the 3D image for generating 3D surfaces of the lumen and outer wall. The algorithm was parallelized using graphics processing units (GPU) to increase computational speed, thus reducing user time by 93% (0.78 vs. 12 min) compared to manual segmentation. Moreover, the algorithm yielded high accuracy (DSC \u3e 90%) and high precision (intra-observer CV \u3c 5.6% and inter-observer CV \u3c 6.6%). Finally, we developed and validated an algorithm based on convex max-flow formulation to segment the femoral arteries that enforces a tubular shape prior and an inter-surface consistency of the outer wall and lumen to maintain a minimum separation distance between the two surfaces. The algorithm required the observer to choose only about 11 points on its medial axis of the artery to yield the 3D surfaces of the lumen and outer wall, which reduced the operator time by 97% (1.8 vs. 70-80 min) compared to manual segmentation. Furthermore, the proposed algorithm reported DSC greater than 85% and small intra-observer variability (CV ≈ 6.69%). In conclusion, the development of robust semi-automated algorithms for generating 3D measurements of plaque burden may accelerate translation of 3D measurements to clinical trials and subsequently to clinical care

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

Foetal echocardiographic segmentation

Congenital heart disease affects just under one percentage of all live births [1]. Those defects that manifest themselves as changes to the cardiac chamber volumes are the motivation for the research presented in this thesis. Blood volume measurements in vivo require delineation of the cardiac chambers and manual tracing of foetal cardiac chambers is very time consuming and operator dependent. This thesis presents a multi region based level set snake deformable model applied in both 2D and 3D which can automatically adapt to some extent towards ultrasound noise such as attenuation, speckle and partial occlusion artefacts. The algorithm presented is named Mumford Shah Sarti Collision Detection (MSSCD). The level set methods presented in this thesis have an optional shape prior term for constraining the segmentation by a template registered to the image in the presence of shadowing and heavy noise. When applied to real data in the absence of the template the MSSCD algorithm is initialised from seed primitives placed at the centre of each cardiac chamber. The voxel statistics inside the chamber is determined before evolution. The MSSCD stops at open boundaries between two chambers as the two approaching level set fronts meet. This has significance when determining volumes for all cardiac compartments since cardiac indices assume that each chamber is treated in isolation. Comparison of the segmentation results from the implemented snakes including a previous level set method in the foetal cardiac literature show that in both 2D and 3D on both real and synthetic data, the MSSCD formulation is better suited to these types of data. All the algorithms tested in this thesis are within 2mm error to manually traced segmentation of the foetal cardiac datasets. This corresponds to less than 10% of the length of a foetal heart. In addition to comparison with manual tracings all the amorphous deformable model segmentations in this thesis are validated using a physical phantom. The volume estimation of the phantom by the MSSCD segmentation is to within 13% of the physically determined volume

Automatic Segmentation of Cells of Different Types in Fluorescence Microscopy Images

Recognition of different cell compartments, types of cells, and their interactions is a critical aspect of quantitative cell biology. This provides a valuable insight for understanding cellular and subcellular interactions and mechanisms of biological processes, such as cancer cell dissemination, organ development and wound healing. Quantitative analysis of cell images is also the mainstay of numerous clinical diagnostic and grading procedures, for example in cancer, immunological, infectious, heart and lung disease. Computer automation of cellular biological samples quantification requires segmenting different cellular and sub-cellular structures in microscopy images. However, automating this problem has proven to be non-trivial, and requires solving multi-class image segmentation tasks that are challenging owing to the high similarity of objects from different classes and irregularly shaped structures. This thesis focuses on the development and application of probabilistic graphical models to multi-class cell segmentation. Graphical models can improve the segmentation accuracy by their ability to exploit prior knowledge and model inter-class dependencies. Directed acyclic graphs, such as trees have been widely used to model top-down statistical dependencies as a prior for improved image segmentation. However, using trees, a few inter-class constraints can be captured. To overcome this limitation, polytree graphical models are proposed in this thesis that capture label proximity relations more naturally compared to tree-based approaches. Polytrees can effectively impose the prior knowledge on the inclusion of different classes by capturing both same-level and across-level dependencies. A novel recursive mechanism based on two-pass message passing is developed to efficiently calculate closed form posteriors of graph nodes on polytrees. Furthermore, since an accurate and sufficiently large ground truth is not always available for training segmentation algorithms, a weakly supervised framework is developed to employ polytrees for multi-class segmentation that reduces the need for training with the aid of modeling the prior knowledge during segmentation. Generating a hierarchical graph for the superpixels in the image, labels of nodes are inferred through a novel efficient message-passing algorithm and the model parameters are optimized with Expectation Maximization (EM). Results of evaluation on the segmentation of simulated data and multiple publicly available fluorescence microscopy datasets indicate the outperformance of the proposed method compared to state-of-the-art. The proposed method has also been assessed in predicting the possible segmentation error and has been shown to outperform trees. This can pave the way to calculate uncertainty measures on the resulting segmentation and guide subsequent segmentation refinement, which can be useful in the development of an interactive segmentation framework

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