A perceptually motivated three-component image model-part II: applications to image compression

Edge-oriented uniform intra prediction

We propose an intra prediction solution to block-based image compression. In order to adapt to local image features during intra prediction, we consider the distinct image singularities within the model of piece-wise smooth functions. With such singularities, i.e., edges in this paper, intra prediction can be performed by solving Laplace equations. Moreover, since edges exhibit spatial correlations, we design a rate-distortion optimized method for edge extraction and edge coding. Our edge-oriented intra prediction thus consists of the prediction of smooth regions as well as the prediction of edges. We compare our intra prediction with that in H.264 and achieve superior performance. Our intra prediction can also be integrated into a block-based image coding scheme, which is comparable to JPEG2000 in terms of objective quality. An important advantage of our intra prediction is the improvement in visual quality at low bit-rate due to the preservation of edges.

An axiomatic approach to image interpolation

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.