Non-Euclidean pyramids

Maria Arrate Munoz Barrutia; Thierry Blu; Michael A. Unser

doi:10.1117/12.408661

4 December 2000 Non-Euclidean pyramids

Maria Arrate Munoz Barrutia, Thierry Blu, Michael A. Unser

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408661
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the l_p 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.

Citation Download Citation

Maria Arrate Munoz Barrutia, Thierry Blu, and Michael A. Unser "Non-Euclidean pyramids", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408661

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