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  4. Fast and memory-efficient quantile filter for data in three and higher dimensions
 
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2014
  • Konferenzbeitrag

Titel

Fast and memory-efficient quantile filter for data in three and higher dimensions

Abstract
Quantile and median filters are usually implemented by accumulating a histogram in a mask with side length 2r + 1, and then selecting the desired quantile from the histogram. Fully updating the histogram for every pixel in a d-dimensional image leads to an O(rd) algorithm per pixel. Huang et al. proposed to shift the histogram pixel-by-pixel to reduce the complexity to O(rd-1) per pixel. We also show how to transfer their algorithm to higher dimensions, in this contribution. Perreault and He&bert extended this idea to reach O(1) runtime per pixel in arbitrary dimension. Thus, from an algorithmic point of view, quantile filtering of d-dimensional data is a solved problem. But the memory requirements of that algorithm grow with a power of D - 1. In this contribution, we therefore propose a novel hybrid quantile filter algorithm which is situated between the two aforementioned methods in terms of memory requirements, and which is faster for a wide range of mask sizes due to reduced overhead.
Author(s)
Mosbach, D.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
Hagen, H.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
Godehardt, M.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
Wirjadi, O.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
Hauptwerk
IEEE International Conference on Image Processing, ICIP 2014. Proceedings. Vol.4
Konferenz
International Conference on Image Processing (ICIP) 2014
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DOI
10.1109/ICIP.2014.7025592
Language
Englisch
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