A Fast Unsupervised Scheme for Polygonal Approximation

This paper proposes a fast and unsupervised scheme for a polygonal approximation of a closed digital curve. It is demonstrated that the approximation scheme is faster than state-of-the-art approximation and is competitive with the same in Rosin's measure and in its aesthetic aspect. The scheme comprises of three phases: initial segmentation, iterative vertex insertion, and iterative merging, followed by vertex adjustment. The initial segmentation is used to detect sharp turnings - the vertices that seemingly have high curvature. It is likely that some of important vertices with low curvature might have been missed out at the first phase and so iterative vertex insertion is used to add vertices in a region where the curvature changes slowly but steadily. The initial phase may pick up some undesirable vertices and so merging is used to eliminate the redundant vertices. Finally, vertex adjustment is used to facilitate enhancement in the aesthetic look of the approximation. The quality of the approximations is measured using Rosin's measure. The robustness of the proposed scheme with respect to geometric transformation is observed.