Using importance sampling for Bayesian feature space filtering

Authors:
Anders Brun;Björn Svensson;Carl-Fredrik Westin;Magnus Herberthson;Andreas Wrangsjö;Hans Knutsson
Affiliations:
Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization, Linköping University, Sweden;Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization, Linköping University, Sweden;Department of Mathematics, Linköping University, Sweden;Laboratory of Mathematics in Imaging, Harvard Medical School, Boston;Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization, Linköping University, Sweden;Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization, Linköping University, Sweden
Venue:
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Year:
2007

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Abstract

We present a one-pass framework for filtering vector-valued images and unordered sets of data points in an N-dimensional feature space. It is based on a local Bayesian framework, previously developed for scalar images, where estimates are computed using expectation values and histograms. In this paper we extended this framework to handle N-dimensional data. To avoid the curse of dimensionality, it uses importance sampling instead of histograms to represent probability density functions. In this novel computational framework we are able to efficiently filter both vector-valued images and data, similar to e.g. the wellknown bilateral, median and mean shift filters.