Image compression by linear splines over adaptive triangulations

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 th...

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Bibliographic Details
Published in:Signal processing 2006-07, Vol.86 (7), p.1604-1616
Main Authors: Demaret, Laurent, Dyn, Nira, Iske, Armin
Format: Article
Language:English
Subjects:
Adaptive thinning
Applied sciences
Coding, codes
Delaunay triangulations
Exact sciences and technology
Image compression
Image processing
Information, signal and communications theory
Linear splines
Miscellaneous
Scattered data coding
Signal and communications theory
Signal processing
Telecommunications and information theory
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Summary: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.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2005.09.003