A cooperative framework for segmentation using 2D active contours and 3D hybrid models as applied to branching cylindrical structures

Hybrid models are powerful tools for recovery in that they simultaneously provide a gross parametric as well as a detailed description of an object. However, it is difficult to directly employ hybrid models in the segmentation process since they are not guaranteed to locate the optimal boundaries in cross-sectional slices. Propagating 2D active contours from slice to slice, on the other hand, to delineate an object's boundaries is often effective, but may run into problems when the object's topology changes, such as at bifurcations or even in areas of high curvature. Here, we present a cooperative framework to exploit the positive aspects of both 3D hybrid model and 2D active contour approaches for segmentation and recovery. In this framework the user-defined parametric component of a 3D hybrid model provides constraints for a set of 2D segmentations performed by active contours. The same hybrid model is then fit both parametrically and locally to this segmentation. For the hybrid model fit we employ several new variations on the physically-motivated paradigm which seek to speed recovery while guaranteeing stability. A by-product of these variations is an increased generality of the method via the elimination, of some of its ad hoc parameters. We apply our cooperative framework to the recovery of branching cylindrical structures from 3D image volumes. The hybrid model we employ has a novel parametric component which is a fusion of individual cylinders. These cylinders have spines that are arbitrary space curves and cross-sections which may be any star shaped planar curve.