Local or global minima: Flexible dual-front active contours

Most variational active contour models are designed to find local minima of data-dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a "desirable" local minimum as opposed to an undesirable configuration due to noise or complex image structure. As such, there has been much research into the design of complex region-based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge-based energy functionals whose sensitivity to noise and texture is significantly worse. Unfortunately, most of these more "robust" region-based energy functionals are applicable to a much narrower class of imagery compared to typical edge-based energies due to stronger global assumptions about the underlying image data. Devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image-based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima. Such implementations have been proposed for capturing global minima. However, sometimes the completely-global minimum is just as undesirable as a minimum that is too local. In this paper, we propose a novel, fast, and flexible dual front implementation of active contours, motivated by minimal path techniques and utilizing fast sweeping algorithms, which is easily manipulated to yield minima with variable "degrees" of localness and globalness. By simply adjusting the size of active regions, the ability to gracefully move from capturing minima that are more local (according to the initial placement of the active contour/surface) to minima that are more global allows this model to more easily obtain "desirable" minimizers (which often are neither the most local nor the most global). Experiments on various 2D and 3D images and comparisons with some active contour models and region-growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications.