Image compression by linear splines over adaptive triangulations

Authors:
Laurent Demaret;Nira Dyn;Armin Iske
Affiliations:
Forschungszentrum für Umwelt und Gesundheit (GSF), Institut für Biomathematik und Biometrie (IBB), Neuherberg, Germany;Tel-Aviv University, School of Mathematical Sciences, Tel Aviv, Israel;Department of Mathematics, University of Hamburg, Hamburg, Germany
Venue:
Signal Processing
Year:
2006

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Abstract

This paper proposes a new method for image compression. The method is based on the approximation of an image, regarded as a function, by a linear spline over an adapted triangulation, D(Y), which is the Delaunay triangulation of a small set Y of significant pixels. The linear spline minimizes the distance to the image, measured by the mean square error, among all linear splines over D(Y). The significant pixels in Y are selected by an adaptive thinning algorithm, which recursively removes less significant pixels in a greedy way, using a sophisticated criterion for measuring the significance of a pixel. The proposed compression method combines the approximation scheme with a customized scattered data coding scheme. We compare our compression method with JPEG2000 on two geometric images and on three popular test cases of real images.