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Proceedings Paper

Non-Euclidean pyramids
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Paper Abstract

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the lp sense where p can take non-integer values. The underlying image model is specified using arbitrary shift- invariant basis functions such as splines. The solution is determined by an iterative optimization algorithm, based on digital filtering. Its convergence is accelerated by the use of first and second derivatives. For p equals 1, our modified pyramid is robust to outliers; edges are preserved better than in the standard case where p equals 2. For 1 < p < 2, the pyramid decomposition combines the qualities of l1 and l2 approximations. The method is applied to edge detection and its improved performance over the standard formulation is determined.

Paper Details

Date Published: 4 December 2000
PDF: 11 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408661
Show Author Affiliations
Maria Arrate Munoz Barrutia, Swiss Federal Institute of Technology Lausanne (Switzerland)
Thierry Blu, Swiss Federal Institute of Technology Lausanne (Switzerland)
Michael A. Unser, Swiss Federal Institute of Technology Lausanne (Switzerland)


Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)

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