A new method of recognizing a two dimensional (2D) shape of a single perspective image taken from an unknown viewpoint is presented. This method is based on a set of new defined Fourier descriptors (FDs) to describe the contour of a planar shape lying in the three dimensional (3D) domain. In order to generate the 3D planar image from the 2D perspective image, we use inverse paraperspective transformation instead of general inverse perspective transformation. Based on the linear approximation of the transformation, new FDs for the 3D planar contour have been developed. They are proved to be merely dependent on the FDs of the 2D contour of the projected image and the slope of the world plane. Thereafter, opportunities for simple and efficient computation for 3D planar shape recognition can be realised.
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