Hierarchical representation of objects using shock graph methods

Binary images can be represented by their morphological skeleton transform also called as Medial axis transform (MAT). Shock graphs are derived from the skeleton and have emerged as powerful 2-D shape representation method. A skeleton has number of braches. A branch is a connected set of points between an end point and a joint or another end point. Every point also called as shock point on a skeleton can be labeled according to the variation of the radius function. The labeled points in a given branch are to be grouped according to their labels and connectivity, so that each group of same-label connected points will be stored in a graph node. One skeleton branch can give rise to one or more nodes. Finally we add edges between the nodes so as to produce a directed acyclic graph with edges directed according to the time of formation of shock points in each node. We have generated shock graphs using two different approaches. In the first approach the skeleton branches and the nodes have labels 1, 2, 3 or 4 where as the second approach excludes type 2 label making the graph simpler. All the joints are called as the branch points. We have compared the merits and demerits of the two methods.