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.