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 which is chosen depends only upon position and is in this sense isotropic. While 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 well-defined 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 novel directional level set segmentation framework employing the theory of Finsler active contours. The framework provides a natural way to perform segmentation of image data in oriented domains. We share examples of this technique on diffusion-weighted magnetic resonance imagery (DW-MRI) for the segmentation of neural fiber bundles and we show examples of texture based segmentation using structure tensors. We also demonstrate that for some applications higher accuracy is achieved by the proposed framework than by level set methods that employ Riemannian metrics. This gain is attributed to the relaxation of the tensor model constraint which is imposed upon the metric in the Riemannian case. 1

In this paper, we describe a method for segmenting fiber bundles from diffusion-weighted magnetic resonance images using a locally-constrained region based approach. From a pre-computed optimal path, the algorithm propagates outward capturing only those voxels which are locally connected to the fiber bundle. Rather than attempting to find large numbers of open curves or single fibers, which individually have questionable meaning, this method segments the full fiber bundle region. The strengths of this approach include its ease-of-use, computational speed, and applicability to a wide range of fiber bundles. In this work, we show results for segmenting the cingulum bundle. Finally, we explain how this approach and extensions thereto overcome a major problem that typical region-based flows experience when attempting to segment neural fiber bundles.