An Interactive Deformable Model Segmentation Algorithm Driven by Morphological Dilations and Erosions Constrained by an Exclusion Band

Abstract

This study introduces an interactive image segmentation algorithm for extraction of ill-defined edges (faint, blurred or partially broken) often observed at small-scale imaging. It is based on a simplified deformable elastic model evolution paradigm. Segmentation is achieved as a two-step region-growing, shrinking and merging simulation constrained by an exclusion band built around the edges of the regions of interest, defined from a variation image. The simulation starts from a set of unlabeled markers and the respective elastic models. During the first step, model evolution occurs entirely outside the exclusion band, driven by alternate action-reaction movements. Forward and backward movements are performed by constrained binary morphological dilations and erosions. Constraints allow controlling how far models can move through narrow gaps. At the end of the first step, models remaining from merging operations receive unique and exclusive labels. On the second and final step, models expansion occurs entirely inside the exclusion band, now driven only by binary unconstrained morphological dilations. A point where two labeled models get into contact defines an edge point. The simulation goes on until the concurrent expansion of all models comes to a complete stop. At this point, the edges of the regions-of-interest have been extracted. Interactivity introduces the possibility to correct small imperfections in the edge positioning by changing a parameter controlling action-reaction or by changing marker’s size, position and shape. Slightly inspired by traditional approaches as PDE Level-Set based curve evolution and Immersion Simulation, the algorithm presents a solution to the problem of “synchronizing the concurrent evolution of a large number of models” and an “automatic stopping criterion” for the front propagation. Integer arithmetic implementation assures linear execution time. The results obtained for real applications show that even ill-defined edges can be located with the desired accuracy, thanks to algorithm features and to the interactivity exerted by the user during the segmentation procedure.