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.