Lemniscate transform: A new efficient technique for shape coding and representation

In this paper, a new algorithm for visual shape coding and representation using a powerful theorem on algebraic curve has been presented. The algorithm codes the closed shape, which does never intersect itself, by means of the foci of the closed curve and a distance parameter ´p´ such that the product of distances of any point on the shape from the foci is approximately constant and is equal to ´p´. The computation of the foci co-ordinates and ´p´ parameter has been presented as a solution to a linearized least-square problem. The reconstruction algorithm is based on straightforward implementation of the theorem. Some experimental results have also been provided indicating the success of the algorithm.