Segmentation involves separating an object from the background. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, within the level-set framework. Following the work of Leventon et al., we revisit the use of principal component analysis (PCA) to introduce prior knowledge about shapes in a more robust manner. To this end, we utilize Kernel PCA and show that this method of learning shapes outperforms linear PCA, by allowing only shapes that are close enough to the training data. In the proposed segmentation algorithm, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description allows to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, clutter, partial occlusions, or smearing.

The ability to analyze and merge data across sites, vendors, and field strengths depends on one’s ability to acquire images with the same image quality including image smoothness, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). SNR can be used to compare different magnetic resonance scanners as a measure of comparability between the systems. This study looks at the SNR and CNR ratios in structural fast spin-echo T2-weighted scans acquired in five individuals across ten sites that are part of Functional Imaging Research of Schizophrenia Testbed Biomedical Informatics Research Network (fBIRN). Different manufacturers, field strengths, gradient coils, and RF coils were used at these sites. The SNR of gray matter was fairly uniform (41.3-43.3) across scanners at 1.5 T. The higher field scanners produced images with significantly higher SNR values (44.5-108.7 at 3 T and 50.8 at 4 T). Similar results were obtained for CNR measurements between gray/white matter at 1.5 T (9.5-10.2), again increasing at higher fields (10.1-28.9 at 3 T and 10.9 at 4 T).

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation.

Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image resolution and contrast, thereby reducing the diagnostic value of this imaging modality. As a result, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Among the many methods that have been proposed to perform this task, there exists a class of approaches that use a multiplicative model of speckled image formation and take advantage of the logarithmical transformation in order to convert multiplicative speckle noise into additive noise. The common assumption made in a dominant number of such studies is that the samples of the additive noise are mutually uncorrelated and obey a Gaussian distribution. The present study shows conceptually and experimentally that this assumption is oversimplified and unnatural. Moreover, it may lead to inadequate performance of the speckle reduction methods. The study introduces a simple preprocessing procedure, which modifies the acquired radio-frequency images (without affecting the anatomical information they contain), so that the noise in the log-transformation domain becomes very close in its behavior to a white Gaussian noise. As a result, the preprocessing allows filtering methods based on assuming the noise to be white and Gaussian, to perform in nearly optimal conditions. The study evaluates performances of three different, nonlinear filters—wavelet denoising, total variation filtering, and anisotropic diffusion—and demonstrates that, in all these cases, the proposed preprocessing significantly improves the quality of resultant images. Our numerical tests include a series of computer-simulated and in vivo experiments.

The introduction and development, over the last three decades, of magnetic resonance (MR) imaging and MR spectroscopy technology for in vivo studies of the human brain represents a truly remarkable achievement, with enormous scientific and clinical ramifications. These effectively non-invasive techniques allow for studies of the anatomy, the function and the metabolism of the living human brain. They have allowed for new understandings of how the healthy brain works and have provided insights into the mechanisms underlying multiple disease processes which affect the brain. Different MR techniques have been developed for studying anatomy, function and metabolism. The primary focus of this review is to describe these different methodologies and to briefly review how they are being employed to more fully appreciate the intricacies associated with the organ, which most distinctly differentiates the human species from the other animal forms on earth.

The multicontrast capability of magnetic resonance imaging (MRI) is discussed in its role in the search for phenotypes of multiple sclerosis (MS). Aspects of MRI specificity, putative markers for pathogenetic components of disease and issues of spatial and temporal distribution are discussed. While particular reference is made to MS, the concepts apply to common pathological features of many neurologic diseases and to neurodegenerative disease in general. The assessment and dissociation of disease activity and disease severity, as well as the combination of varied metrics for the purposes of inferential and predictive disease modeling, are explored with respect to biomarkers and clinical outcomes. By virtue of its noninvasive nature and multicontrast capabilities depicting multiple facets of MS pathology, MRI lends itself to the systematic search of pathogenetically distinct subtypes of MS in large populations of patients. In conjunction with clinical, immunological, serological and genetic information, clusters of MS patients with distinct clinical prognosis and diverse response profiles to available and future treatments may be identified.

This paper presents a family of techniques that we call congealing for modeling image classes from data. The idea is to start with a set of images and make them appear as similar as possible by removing variability along the known axes of variation. This technique can be used to eliminate "nuisance" variables such as affine deformations from handwritten digits or unwanted bias fields from magnetic resonance images. In addition to separating and modeling the latent images-i.e., the images without the nuisance variables-we can model the nuisance variables themselves, leading to factorized generative image models. When nuisance variable distributions are shared between classes, one can share the knowledge learned in one task with another task, leading to efficient learning. We demonstrate this process by building a handwritten digit classifier from just a single example of each class. In addition to applications in handwritten character recognition, we describe in detail the application of bias removal from magnetic resonance images. Unlike previous methods, we use a separate, nonparametric model for the intensity values at each pixel. This allows us to leverage the data from the MR images of different patients to remove bias from each other. Only very weak assumptions are made about the distributions of intensity values in the images. In addition to the digit and MR applications, we discuss a number of other uses of congealing and describe experiments about the robustness and consistency of the method.

A statistical model is presented that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image artifacts, anatomical labelmaps, and a structure-dependent hierarchical mapping from the atlas to the image space. The algorithm produces segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. On this set of images, the new approach performs significantly better than similar methods which sequentially apply registration and segmentation.

White matter hyperintense lesions on T2-weighted images are associated with late-life depression. Little work has been carried out examining differences in lesion location between elderly individuals with and without depression. In contrast to previous studies examining total brain white matter lesion volume, this study examined lobar differences in white matter lesion volumes derived from brain magnetic resonance imaging. This study examined 49 subjects with a DSM-IV diagnosis of major depression and 50 comparison subjects without depression. All participants were age 60 years or older. White matter lesion volumes were measured in each hemisphere using a semiautomated segmentation process and localized to lobar regions using a lobar atlas created for this sample using the imaging tools provided by the Biomedical Informatics Research Network (BIRN). The lobar lesion volumes were compared against depression status. After controlling for age and hypertension, subjects with depression exhibited significantly greater total white matter lesion volume in both hemispheres and in both frontal lobes than did control subjects. Although a similar trend was observed in the parietal lobes, the difference did not reach a level of statistical significance. Models of the temporal and occipital lobes were not statistically significant. Older individuals with depression have greater white matter disease than healthy controls, predominantly in the frontal lobes. These changes are thought to disrupt neural circuits involved in mood regulation, thus increasing the risk of developing depression.