Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours

In this chapter we focus on formulating and implementing on abstract domains such as arbitrary graphs popular methods and techniques developed for image analysis, in particular multiscale morphology and active contours. To this goal we extend existing work on graph morphology to multiscale dilation and erosion and implement them recursively using level sets of functions defined on the graph’s nodes. We propose approximations to the calculation of the gradient and the divergence of vector functions defined on graphs and use these approximations to apply the technique of geodesic active contours for object detection on graphs via segmentation. Finally, using these novel ideas, we propose a method for multiscale shape skeletonization on arbitrary graphs.