Proceedings PaperImage Representation By Means Of Two Dimensional Polynomials
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In this paper, two different methods of representing an image using 2-D polynomials will be presented. In the first approach, the image is segmented into adjacent regions using a region growing algorithm. At the completion of this step, the grey level evolution of every region is approximated by a 2-D polynomial using the least square error method. In the second approach, the segmentation and approximation procedures are merged together. This is achieved by representing the matrix's image by a graph where every node is a mapping of a square of n times n pixels and every edge is a measure of similarity between the two nodes it connects. The graph is then iteratively transformed by using an isotropic node merging algorithm. Lastly, the reduced graph is transformed back to a matrix representation giving the final image. The two algorithms will be compared in terms of growing homogeneity, error control and optimality, and their respective results will be presented.