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.

The surface growing framework presented by P. Besl and R. Jain (1988) has served as the basis for many range segmentation techniques. It has been augmented with alternative fitting techniques, model selection criteria, and solid modelling components. All of these approaches, however require global thresholds and large isolated seed regions. Range scenes typically do not satisfy the global threshold assumption since it requires data noise characteristics to be constant throughout the scene. Furthermore, as scene complexity increases, the number of surfaces, discontinuities, and outliers increase, hindering the identification of large seed regions. We present statistical criteria based on multivariate regression to replace the traditional decision criteria used in surface growing. We use local estimates and their uncertainties to construct criteria which capture the uncertainty in extrapolating estimated fits. We restrict surface expansion to very localized extrapolations, increasing the sensitivity to discontinuities and allowing regions to refine their estimates and uncertainties. Our approach uses a small number of parameters which are either statistical thresholds or cardinality measures, i.e. we do not use thresholds defined by specific range distances or orientation angles.

Despite many successful applications of robust statistics, they have yet to be completely adapted to many computer vision problems. Range reconstruction, particularly in unstructured environments, requires a robust estimator that not only tolerates a large outlier percentage but also tolerates several discontinuities, extracting multiple surfaces in an image region. Observing that random outliers and/or points from across discontinuities increase a hypothesized fit's scale estimate (standard deviation of the noise), our new operator; called MUSE (Minimum Unbiased Scale Estimator), evaluates a hypothesized fit over potential inlier sets via an objective function of unbiased scale estimates. MUSE extracts the single best fit from the data by minimizing its objective function over a set of hypothesized fits and can sequentially extract multiple surfaces from an image region. We show MUSE to be effective on synthetic data modelling small scale discontinuities and in preliminary experiments on complicated range data.

We propose a new approach to the problem of generating a simple topologically-closed geometric model from a point-sampled volume data set. We call such a model a Geometrically Deformed Model or GDM. A GDM is created by placing a 'seed' model in the volume data set. The model is then deformed by a relaxation process that minimizes a set of constraints that provides a measure of how well the model fits the features in the data. Constraints are associated with each vertex in the model that control local deformation, interaction between the model and the data set, and the shape and topology of the model. Once generated, a GDM can be used for visualization, shape recognition, geometric measurements, or subjected to a series of geometric operations. This technique is of special importance because of the advent of nondestructive sensing equipment (CT, MRI) that generates point samples of true three-dimensional objects.

The authors propose a methodology that will extract a topologically closed geometric model from a two-dimensional image. This is accomplished by starting with a simple model that is already topologically closed and deforming the model, based on a set of constraints, so that the model grows (shrinks) to fit the feature within the image while maintaining its closed and locally simple nature. The initial model is a non-self-intersecting polygon that is either embedded in the feature or surrounds the feature. There is a cost function associated with every vertex that quantifies its deformation, the properties of simple polygons, and the relationship between noise and feature. The constraints embody local properties of simple polygons and the nature of the relationship between noise and the features in the image.>