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

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