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•A new measurement “NCA” is proposed for fair assessing of polygonal approximations.•A new evaluation methodology for quality measurements is also proposed.•This evaluation methodology is based on the “optimal quality curve” concept.•The “optimal quality curve” can characterize the performance of the measurements.•The new proposal “NCA” obtained the best results in the comparative study.
Two proposals related to the evaluation of polygonal approximations are presented in this document. First, a new measurement, called normalized compression ratio and adjustment error (NCA), to provide a fair evaluation of the performance of the polygonal approximations of 2D closed curves is proposed. Second, a new methodology for evaluation of measurements for assessing polygonal approximations is also proposed. This methodology is based on the optimal quality curve concept, which can characterize the performance of the measurements. A simple visual analysis of the optimal quality curve allows possible drawbacks or weaknesses of the measurement to be detected. The new evaluation methodology is used to compare the performance of the proposed NCA and the most popular measurements, such as Rosin’s Merit, FOM or versions of FOM. Experiments show that NCA obtains the best results and, therefore, may be used to fairly evaluate the performance of polygonal approximations.