In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally multiplied by a scalar conformal factor based on image information such that the weighted length of curves lying on points of interest (typically edges) is small. The conformal factor that is chosen depends only upon position and is in this sense isotropic. Although directional information has been studied previously for other segmentation frameworks, here, we show that if one desires to add directionality in the conformal active contour framework, then one gets a welldefined minimization problem in the case that the factor defines a Finsler metric. Optimal curves may be obtained using the calculus of variations or dynamic programming-based schemes. Finally, we demonstrate the technique by extracting roads from aerial imagery, blood vessels from medical angiograms, and neural tracts from diffusion-weighted magnetic resonance imagery.

In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.

Abstract. In this paper, we present a novel approach for the segmentation of white matter tracts based on Finsler active contours. This technique provides an optimal measure of connectivity, explicitly segments the connecting fiber bundle, and is equipped with a metric which is able to utilize the directional information of high angular resolution data. We demonstrate the effectiveness of the algorithm for segmenting the cingulum bundle.

This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation approach by Bresson et al. allows for a convex optimization formulation of the segmentation problem, combining orientation statistics and spatial regularization. The approach compares favorably with segmentation by full-brain streamline tractography.

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