A technique using a one-dimensional mapping for vector quantisation of images

The main problem for vector quantisation is the codebook generation. The LBG method solves it with an iterative approach. This algorithm needs a long training sequence and an initial approximation of the codebook. These problems may be overcome by using space filling curves, also called Peano´s curves, which are mappings from the unitary interval (image point) to the unitary hypercube. By using this kind of mapping the generation of the codebook, is reduced to the computation of the one-dimensional (optimum) quantiser associated to the probability density function (pdf) of the image points on the Hilbert curve. The paper describes the way of applying these mappings: a new algorithm is derived, generating codebooks for vector quantisation, and experimental results on image coding are provided.