PARAMETERIZING ARBITRARY SHAPES VIA FOURIER DESCRIPTORS FOR EVIDENCE-GATHERING EXTRACTION

According to the formulation of the Hough Transform, it is possible to extract any shape that can be represented by an analytic equation wit h a number of free parameters, Nevertheless, the extraction of arbitra ry shapes has centered on nonanalytic representations based on a table which specifies the position of edge points relative to a fixed refer ence point. In this paper we develop a novel approach for arbitrary sh ape extraction which combines the analytic representation of shapes wi th the generality of the characterization by Fourier descriptors. The formulation is based on a definition of the Hough Transform obtained b y considering the parametric representation of shapes and extends the descriptional power of the Hough Transform beyond simple shapes, thus avoiding the use of tables, Since we use an analytic representation of shapes, the developed technique inherits the robustness of the origin al formulation of the Hough Transform. Based on the developed formulat ion, and by using different strategies of parameter space decompositio n, various methods of shape extraction are presented. In these methods the parameter space is reduced by using gradient direction informatio n as well as the positions of grouped edge points. Different methods r epresent a compromise between speed, noise sensitivity, simplicity, an d generality, Some examples of the extraction process on a selection o f synthetic and real images are presented, showing the successful extr action of target shapes from noisy data. (C) 1998 Academic Press.