The DSC value is a simple and useful summary measure of spatial overlap, which can be applied to studies of reproducibility and accuracy in image segmentation. We observed generally satisfactory but variable validation results in two clinical applications. This metric may be adapted for similar validation tasks.

Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge-Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image to image ¡ being the inverse of the optimal mapping from ¡ to £ ¢ The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge-Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the ¤ ¦ ¥ Kantorovich-Wasserstein or "Earth Mover's Distance" under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extended this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing.

In this paper, we give an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles. This technique relies on certain conformal mappings from differential geometry. Our method provides a new way to automatically assign texture coordinates to complex undulating surfaces. We demonstrate a finite element method that can be used to apply our mapping technique to a triangulated geometric description of a surface.

A multichannel statistical classifier for detecting prostate cancer was developed and validated by combining information from three different magnetic resonance (MR) methodologies: T2-weighted, T2-mapping, and line scan diffusion imaging (LSDI). From these MR sequences, four different sets of image intensities were obtained: T2-weighted (T2W) from T2-weighted imaging, Apparent Diffusion Coefficient (ADC) from LSDI, and proton density (PD) and T2 (T2 Map) from T2-mapping imaging. Manually segmented tumor labels from a radiologist, which were validated by biopsy results, served as tumor "ground truth." Textural features were extracted from the images using co-occurrence matrix (CM) and discrete cosine transform (DCT). Anatomical location of voxels was described by a cylindrical coordinate system. A statistical jack-knife approach was used to evaluate our classifiers. Single-channel maximum likelihood (ML) classifiers were based on 1 of the 4 basic image intensities. Our multichannel classifiers: support vector machine (SVM) and Fisher linear discriminant (FLD), utilized five different sets of derived features. Each classifier generated a summary statistical map that indicated tumor likelihood in the peripheral zone (PZ) of the prostate gland. To assess classifier accuracy, the average areas under the receiver operator characteristic (ROC) curves over all subjects were compared. Our best FLD classifier achieved an average ROC area of 0.839(+/-0.064), and our best SVM classifier achieved an average ROC area of 0.761(+/-0.043). The T2W ML classifier, our best single-channel classifier, only achieved an average ROC area of 0.599(+/-0.146). Compared to the best single-channel ML classifier, our best multichannel FLD and SVM classifiers have statistically superior ROC performance (P=0.0003 and 0.0017, respectively) from pairwise two-sided t-test. By integrating the information from multiple images and capturing the textural and anatomical features in tumor areas, summary statistical maps can potentially aid in image-guided prostate biopsy and assist in guiding and controlling delivery of localized therapy under image guidance.

In this work, we formulate a new minimizing flow for the optimal mass transport (Monge-Kantorovich) problem. We study certain properties of the flow, including weak solutions as well as short-and long-term existence. Optimal transport has found a number of applications, including econometrics, fluid dynamics, cosmology, image processing, automatic control, transportation, statistical physics, shape optimization, expert systems, and meteorology.

In this paper, using certain conformal mappings from uniformization theory, we give an explicit method for flattening the brain surface in a way which preserves angles. From a triangulated surface representation of the cortex, we indicate how the procedure may be implemented using finite elements. Further, we show how the geometry of the brain surface may be studied using this approach.

Detailed measurements of water diffusion within the prostate over an extended b-factor range were performed to assess whether the standard assumption of monoexponential signal decay is appropriate in this organ. From nine men undergoing prostate MR staging exams at 1.5 T, a single 10 mm thick axial slice was scanned with a line scan diffusion imaging (LSDI) sequence in which 14 equally spaced b-factors from 5 to 3500 s/mm 2 were sampled along three orthogonal diffusion sensitization directions in 6 minutes. Due to the combination of long scan time and limited volume coverage associated with the multi-b-factor, multi-directional sampling, the slice was chosen online from the available T2-weighted axial images with the specific goal of enabling the sampling of presumed noncancerous regions of interest (ROI's) within the central gland (CG) and peripheral zone (PZ). Histology from pre-scan biopsy (N = 9) and post-surgical resection (N = 4) was subsequently employed to help confirm that the ROIs sampled were non-cancerous. The CG ROIs were characterized from the T2-weighted images as primarily mixtures of glandular and stromal benign prostatic hyperplasia (BPH) which is prevalent in this population. The water signal decays with bfactor from all ROI's were clearly non-monoexponential and better served with bi-vs monoexponential fits, as tested using λ 2 based F-test analyses. Fits to biexponential decay functions yielded inter-subject fast diffusion component fractions on the order of 0.73 ± 0.08 for both CG and PZ ROIs, fast diffusion coefficients of 2.68 ± 0.39 and 2.52 ± 0.38 μm 2 /ms and slow diffusion coefficients of 0.44 ± 0.16 and 0.23 ± 0.16 um 2 /ms for CG and PZ ROI's, respectively. The difference between the slow diffusion coefficients within CG and PZ was statistically significant as assessed with a Mann-Whitney non-parametric test (P < 0.05). We conclude that a monoexponential model for water diffusion decay in prostate tissue is inadequate when a large range of b-factors is sampled and that biexponential analyses are better suited for characterizing prostate diffusion decay curves.

Abstract. We investigate new approaches to quantifying the white matter connectivity in the brain using Diffusion Tensor Magnetic Resonance Imaging data. Our first approach finds a steady-state concentration/heat distribution using the three-dimensional tensor field as diffusion/conductivity tensors. Our second approach casts the problem in a Riemannian framework, deriving from each tensor a local warping of space, and finding geodesic paths in the space. Both approaches use the information from the whole tensor, and can provide numerical measures of connectivity. BackgroundDiffusion Tensor Magnetic Resonance Imaging (DT-MRI) measures the selfdiffusion of water in biological tissue. The utility of this method stems from the fact that tissue structure locally affects the Brownian motion of water molecules. Consequently, a coherent organization of tissue (over scales comparable to that of a voxel) will be reflected in the DT-MRI diffusion measurements.Neural fiber tracts contain parallel axons whose membranes restrict diffusion, so the self-diffusion of water is most probable along the tracts. Thus in DT-MRI imagery of the brain, the local structure of the diffusion tensor can be treated as an approximation to the local neural fiber structure. The diffusion tensor is a low-pass, Gaussian approximation to the actual microscopic structure of the neuroanatomy, but it provides a fast and non-invasive anatomical measurement.In DT-MRI, the diffusion tensor field is calculated from a set of diffusionweighted images by solving the Stejskal-Tanner equation (eq. 1). This equation describes how the signal intensity at each voxel decreases in the presence of diffusion:Here S 0 is the non-diffusion-weighted image intensity at the voxel and S k is the intensity measured after the application of the kth diffusion-sensitizing T.