Fast intersection checking for parametric deformable models

Parametric active deformable models for image-based segmentation offer a distinct advantage over level sets: speed. This paper presents an extension to active deformable models that makes real-time volume segmentation possible on mid-range off-the-shelf hardware and without the use of specialized graphics hardware. The proposed method uses region-based parametric deformable models. A region-based parametric model, represented by a polygon, must remain non-self intersecting (simple) while undergoing deformation. The simplicity constraint can be enforced by allowing topological changes or by restricting motions of the curve. In either case, intersections of curve segments must be detected otherwise catastrophic divergence results. Good performance relies on the efficiency of the intersection check operation. This paper presents a parameter-free and efficient technique for on-line simplicity checking of polygons undergoing motion. We present timing results validating our approach; in particular, we segment 3-D ultrasound data at 20 volumes per second.