In this communication some algorithms for polygonal approximation of closed digital curve under a non-parametric framework are compared with an unsupervised approach to polygonal approximation. The two approaches are compared with respect to number of vertices, maximum error, measures W E and W E 2, Rosin's measure and relative execution time. The algorithms are tested using images from MPEG7 dataset and it is observed that the algorithms under non-parametric framework produce too many vertices many of which are redundant resulting in rough approximations whereas the unsupervised approach produces less number of vertices with low value of W E and W E 2 leading to smooth approximations and high value of Rosin's measure, but its relative execution time is high. © 2020 Elsevier Inc.