To extract the features from a coupler curve is one of key issues in the synthesis of path generating mechanism. Fourier transformation is widely used at present. A new method of feature extraction, named mathematical morphology based method, emerges in resent years. Based on the essential operations of mathematical morphology, the shape spectrum (SS) of the coupler curve is computed. SS is rotation-scale-translation invariant. Therefore, as a means of describing coupler curve, it has possesses advantage over that based on Fourier transformation. In this paper, what kind information involved in SS of a curve is revealed. It is shown that the largest radius of internally tangent circle and the area inside of the curve can be inferred from its SS. This paper also shows that SS is without the information of the structure feature which is necessary to describe a nonsimple closed coupler curve. Eight-figure-shaped coupler curve is the simplest nonsimple closed curve. To describe such curve, three structure parameters of the curve should be involved besides that provided by SS of curve. A method using five numbers to describe and differentiate an eight-figure-shaped coupler curve is proposed in this paper. The five numbers can be obtained from its SS and the structure of the curve. A new formula to compute the similarity between two eight-figure-shaped couplers using the five numbers is presented.

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