Histogram-based weighted median filtering used for noise reduction of digital elevation model data

Abstract

A new histogram-based robust filter developed for noise reduction of digital elevation model data is presented. When large percentage of data points in data matrices are contaminated with outlier noise, the noise reduction process can give better results than traditional median filtering, if elements with a potentially higher chance of being noise are eliminated by weighting from the input dataset before the median value is calculated. However, on the same matrices, there are likely to be subsets of data where unfiltered input is more reasonable for the calculation. The new method implementing weighting between these two cases is presented below, with its initial tuning and a comparison with both standard median filtering and the Most Frequent Value (MFV) method, as the latter being much more efficient than the usual methods. Following the description of the procedures, their effectiveness is compared for noise reduction in digital elevation model data systems, at various noise levels. The comparison is done mainly by three measures, with most of the focus on the \({L}_{1}\) norm data distance results. Finally, a modified version of the method—which includes Steiner’s MFV filter as a core part—is also introduced, with similar examination. The method to be presented has been shown to be superior to conventional median filtering for most noise rates, and in many cases also to Steiner' MFV, for handling non-zero mean noises. The modified version of the method—with the help of Steiner's MFV—has also achieved this in handling zero mean noise, in the field of application described in the paper.