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