In this paper, a novel similarity estimation method for two shapes in the automated thermal forming is proposed. One shape is given as a CAD surface, and the other is given as a set of points measured points. These two shapes are registered with respect to a reference coordinate system so that they are aligned as closely as possible using the ICP based method. Three geometric properties are considered in the method. The first property is the distance between them. At each measured point, the closest distance to the CAD surface is computed, and the defined tolerance for the distances is used as a similarity measure. The second measure is the average distance of the minimum distances to the CAD surface at the measured points. The third one is the average of the bending strain values at the measured points and at the points on the CAD surface that are orthogonal projection points of the measured ones. The proposed similarity is computed as the linear combination of the three properties with weight values, which are determined empirically. Extensive experiments show that the proposed similarity method successfully computes the similarity of a plate to its CAD shape in the forming process.

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