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The present paper proposes a new algorithm for automatic generation of polygonal approximations of 2D closed contours based on a new thresholding method. The new proposal computes the significance level of the contour points using a new symmetric version of the well-known Ramer, DouglasPeucker method, and then a new Adaptive method is applied to threshold the normalized significance level of the contour points to generate the polygonal approximation. The experiments have shown that the new algorithm has good performance for generating polygonal approximations of 2D closed contours. Futhermore, the new algorithm does not require any parameter to be tuned.