Application of scale space to image coding

The continuous formulation of scale space is briefly reviewed. It is shown that deriving a discrete formulation of scale space requires the solution to a more general problem; the optimum approximation of a signal by local patterns. The consequences of the theory for the Laplacian image pyramid are discussed. A pyramid coding scheme based on the discrete scale-space formulation is derived. Preliminary coding results on real images are presented. Down to 1 b/pixel, the quality of the coded images is usually very close to that of the originals. Bit rates below 0.5 b/pixel imply a too coarse quantization, or even deletion, of the prediction error image at the smallest scale and, consequently, always result in images that are noticeably unsharp. In the intermediate region, different degrees of quantization noise and unsharpness are present. At comparable data rates, the linear variation coder generates less quantization noise in uniform regions, while the scale-space coder gives a slightly better edge reproduction