In image segmentation, we are often interested in using certain quantities to characterize the object, and perform the classification based on criteria such as mean intensity, gradient magnitude, and responses to certain predefined filters. Unfortunately, in many cases such quantities are not adequate to model complex textured objects. Along a different line of research, the sparse characteristic of natural signals has been recognized and studied in recent years. Therefore, how such sparsity can be utilized, in a non-parametric way, to model the object texture and assist the textural image segmentation process is studied in this paper, and a segmentation scheme based on the sparse representation of the texture information is proposed. More explicitly, the texture is encoded by the dictionaries constructed from the user initialization. Then, an active contour is evolved to optimize the fidelity of the representation provided by the dictionary of the target. In doing so, not only a non-parametric texture modeling technique is provided, but also the sparsity of the representation guarantees the computation efficiency. The experiments are carried out on the publicly available image data sets which contain a large variety of texture images, to analyze the user interaction, performance statistics, and to highlight the algorithm's capability of robustly extracting textured regions from an image.

Extracting anatomical and functional significant structures renders one of the important tasks for both the theoretical study of the medical image analysis, and the clinical and practical community. In the past, much work has been dedicated only to the algorithmic development. Nevertheless, for clinical end users, a well designed algorithm with an interactive software is necessary for an algorithm to be utilized in their daily work. Furthermore, the software would better be open sourced in order to be used and validated by not only the authors but also the entire community. Therefore, the contribution of the present work is twofolds: first, we propose a new robust statistics based conformal metric and the conformal area driven multiple active contour framework, to simultaneously extract multiple targets from MR and CT medical imagery in 3D. Second, an open source graphically interactive 3D segmentation tool based on the aforementioned contour evolution is implemented and is publicly available for end users on multiple platforms. In using this software for the segmentation task, the process is initiated by the user drawn strokes (seeds) in the target region in the image. Then, the local robust statistics are used to describe the object features, and such features are learned adaptively from the seeds under a non-parametric estimation scheme. Subsequently, several active contours evolve simultaneously with their interactions being motivated by the principles of action and reaction-this not only guarantees mutual exclusiveness among the contours, but also no longer relies upon the assumption that the multiple objects fill the entire image domain, which was tacitly or explicitly assumed in many previous works. In doing so, the contours interact and converge to equilibrium at the desired positions of the desired multiple objects. Furthermore, with the aim of not only validating the algorithm and the software, but also demonstrating how the tool is to be used, we provide the reader reproducible experiments that demonstrate the capability of the proposed segmentation tool on several public available data sets.

We describe a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by those previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Using two- and three-fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.

We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output of the algorithm is a small number of template images that represent different modes in a population. This is in contrast with traditional, hypothesis-driven computational anatomy approaches that assume a single template to construct an atlas. We derive the algorithm based on a generative model of an image population as a mixture of deformable template images. We validate and explore our method in four experiments. In the first experiment, we use synthetic data to explore the behavior of the algorithm and inform a design choice on parameter settings. In the second experiment, we demonstrate the utility of having multiple atlases for the application of localizing temporal lobe brain structures in a pool of subjects that contains healthy controls and schizophrenia patients. Next, we employ iCluster to partition a data set of 415 whole brain MR volumes of subjects aged 18 through 96 years into three anatomical subgroups. Our analysis suggests that these subgroups mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the final experiment, we run iCluster on a group of 15 patients with dementia and 15 age-matched healthy controls. The algorithm produces two modes, one of which contains dementia patients only. These results suggest that the algorithm can be used to discover subpopulations that correspond to interesting structural or functional "modes."

This paper introduces and analyzes a linear minimum mean square error (LMMSE) estimator using a Rician noise model and its recursive version (RLMMSE) for the restoration of diffusion weighted images. A method to estimate the noise level based on local estimations of mean or variance is used to automatically parametrize the estimator. The restoration performance is evaluated using quality indexes and compared to alternative estimation schemes. The overall scheme is simple, robust, fast, and improves estimations. Filtering diffusion weighted magnetic resonance imaging (DW-MRI) with the proposed methodology leads to more accurate tensor estimations. Real and synthetic datasets are analyzed.

This paper proposes to use the volumetric Laplace spectrum as a global shape descriptor for medical shape analysis. The approach allows for shape comparisons using minimal shape preprocessing. In particular, no registration, mapping, or remeshing is necessary. All computations can be performed directly on the voxel representations of the shapes. The discriminatory power of the method is tested on a population of female caudate shapes (brain structure) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the volumetric Laplace spectrum are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann spectra. Both, the computations of spectra on 3D voxel data for shape matching as well as the use of the Neumann spectrum for shape analysis are completely new.

We introduce an algorithm for segmenting brain magnetic resonance (MR) images into anatomical compartments such as the major tissue classes and neuro-anatomical structures of the gray matter. The algorithm is guided by prior information represented within a tree structure. The tree mirrors the hierarchy of anatomical structures and the subtrees correspond to limited segmentation problems. The solution to each problem is estimated via a conventional classifier. Our algorithm can be adapted to a wide range of segmentation problems by modifying the tree structure or replacing the classifier. We evaluate the performance of our new segmentation approach by revisiting a previously published statistical group comparison between first-episode schizophrenia patients, first-episode affective psychosis patients, and comparison subjects. The original study is based on 50 MR volumes in which an expert identified the brain tissue classes as well as the superior temporal gyrus, amygdala, and hippocampus. We generate analogous segmentations using our new method and repeat the statistical group comparison. The results of our analysis are similar to the original findings, except for one structure (the left superior temporal gyrus) in which a trend-level statistical significance (p = 0.07) was observed instead of statistical significance.

Poisson's equation, a fundamental partial differential equation in classical physics, has a number of properties that are interesting for shape analysis. In particular, the equipotential sets of the solution graph become smoother as the potential increases. We use the displacement map, the length of the streamlines formed by the gradient field of the solution, to measure the "complexity" (or smoothness) of the equipotential sets, and study its behavior as the potential increases. We believe that this function complexity = f(potential), which we call the shape characteristic, is a very natural way to express shape. Robust algorithms are presented to compute the solution to Poisson's equation, the displacement map, and the shape characteristic. We first illustrate our technique on two-dimensional synthetic examples and natural silhouettes. We then perform two shape analysis studies on three-dimensional neuroanatomical data extracted from magnetic resonance (MR) images of the brain. In the first study, we investigate changes in the caudate nucleus in Schizotypal Personality Disorder (SPD) and confirm previously published results on this structure. In the second study, we present a data set of caudate nuclei of premature infants with asymmetric white matter injury. Our method shows structural shape differences that volumetric measurements were unable to detect.

We developed a three-dimensional (3D) digitized atlas of the human brain to visualize spatially complex structures. It was designed for use with magnetic resonance (MR) imaging data sets. Thus far, we have used this atlas for surgical planning, model-driven segmentation, and teaching. We used a combination of automated and supervised segmentation methods to define regions of interest based on neuroanatomical knowledge. We also used 3D surface rendering techniques to create a brain atlas that would allow us to visualize complex 3D brain structures. We further linked this Information to script files in order to preserve both spatial information and neuroanatomical knowledge. We present here the application of the atlas for visualization in surgical planning far model-driven segmentation and for the teaching of neuroanatomy. This digitized human brain has the potential to provide important reference information for the planning of surgical procedures. It can also serve as a powerful teaching tool, since spatial relationships among neuroanatomical structures can be more readily envisioned when the user is able to view and rotate the structures in 3D space. Moreover, each element of the brain atlas is associated with a name tag, displayed by a user controlled pointer. The atlas holds a major promise as a template for model-driven segmentation. Using this technique, many regions of interest can be characterized simultaneously on new brain images.