Active Geodesics: Region-based Active Contour Segmentation with a Global Edge-based Constraint.

We present an active geodesic contour model in which we constrain the evolving active contour to be a geodesic with respect to a weighted edge-based energy through its entire evolution rather than just at its final state (as in the traditional geodesic active contour models). Since the contour is always a geodesic throughout the evolution, we automatically get local optimality with respect to an edge fitting criterion. This enables us to construct a purely region-based energy minimization model without having to devise arbitrary weights in the combination of our energy function to balance edge-based terms with the region-based terms. We show that this novel approach of combining edge information as the geodesic constraint in optimizing a purely region-based energy yields a new class of active contours which exhibit both local and global behaviors that are naturally responsive to intuitive types of user interaction. We also show the relationship of this new class of globally constrained active contours with traditional minimal path methods, which seek global minimizers of purely edge-based energies without incorporating region-based criteria. Finally, we present some numerical examples to illustrate the benefits of this approach over traditional active contour models.