Polygonal Approximation of 2-D Binary Images

In many morphological shape decomposition algorithms, either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine decomposition. In our paper, we present a morphological shape approximation algorithm that decomposes a two dimensional (2D) binary shape into a collection of convex polygonal components. A single convex polygonal approximation for a given image is first identified. This first component is determined incrementally by selecting a sequence of basic shape primitives. These shape primitives are chosen based on shape information extracted from the given shape at different scale levels. Additional shape components are identified recursively from the difference image between the given image and the first component. Simple operations are used to repair certain concavities caused by the set difference operations. After decomposition the original shape can be reconstructed exactly by the union of all convex components and finer details can also be included. Our paper has been implemented using MATLAB software