l∞ norm based second generation image coding

Abstract

Many second generation image coding techniques have been studied in recent years. Most of these methods consider the l 2 norm of the error introduced in the coded image, while for the l ∞ case only predictive or transform based methods were considered up to now, focusing on near-lossless coding. In this paper we present a first scheme for l ∞ norm in the framework of second generation image coding. The image is adaptively segmented into rectangular regions of varying size leading to a binary tree decomposition. The grey levels of the pixels within every leaf are approximated by means of l ∞ sub-optimal bilinear surfaces.

Approximations of One-Dimensional Digital Signals Under the$l^infty$Norm

“…But symmetrically we have (10) So the only possibility is that all these must be replaced by and, consequently, , which means that is parallel to , contrarily to the initial hypothesis that has no parallel sides. This argument also proves that if has parallel sides, 12 the optimal solution is still unique, even if this is not true for the pivot points.…”

“…Thus, if we set and , it is easy to see that (3) is equivalent to Thus, the approximation of with a variable tolerance can be obtained by approximating and jointly with the usual norm. This idea has been of practical utility, in the field of image coding, in [12], where a separable approach has been used for the problem of finding bidimensional suboptimal bilinear approximations. We refer the reader to [12] for more details.…”

“…This idea has been of practical utility, in the field of image coding, in [12], where a separable approach has been used for the problem of finding bidimensional suboptimal bilinear approximations. We refer the reader to [12] for more details.…”