Carsten Garnica 
  
3.2 The Maximum Homogeneity Neighbour Filters (MHN) 
Maximum Homogeneity Neighbour Filters are checking the homogeneity of small areas (the size is often 3*3 pixels) 
within the close neighbourhood of the pixel in consideration. Different implementations use a different number of areas 
(Kuwahara et al.: 4 areas, Tomita et al.: 5 areas, Nagao et al.: 9 areas, Wang: 9 different areas) which are composed 
differently (Wang, 1994). They all have in common, that all pixels within the area are connected and that the pixel to be 
edited belongs to all areas. The choices of Wang, for example, are shown in figure 1. 
As criterion for the detection of the area with maximal homogeneity may serve the variance of the gray values within 
the area, or the minimum rank order difference. 
The new value for the pixel in consideration is then calculated either from the mean or the median value of the region of 
maximal homogeneity. 
  
Figure 1. Definition of the masks of the 9 small areas (Wang, 1994) 
3.3 The segmentation idea 
Algorithms for image segmentation take the radiometric properties of the pixels into consideration. While split-and- 
merge algorithms compare two image regions, region growing algorithms execute a test, whether a single pixel 
radiometrically fits to an existing region. Fitting means, that the value must lie within the interval given by the average 
gray value of the region plus and minus n-times (e.g. n=3.0) the standard deviation of gray values of the region. This 
means to have a variable threshold automatically determined in dependence of the gray value statistics. As the 
magnitude of the white noise is mostly unknown and furthermore signal dependent, this does simplify the application of 
such an algorithm. 
3.4 The new algorithm 
The MHN filter is lacking a high statistical significance, because of the fact, that only a few (e.g. 9) pixel are considered 
for the test of homogeneity. Such few pixel are rarely able to represent the statistical behaviour of larger regions. In our 
approach, the result of the MHN filter is only used as an indicator for a further statistical analysis of a larger 
neighbourhood. Every pixel within a given radius or rectangular box is tested onto its radiometric similarity to the area 
of highest homogeneity having been extracted by the MHN filter. The size of the larger test area is of minor importance 
and may amount up to 10 pixel in square. Finally, the gray value of the pixel currently being processed is calculated as 
the average of all pixels meeting the criterion. This processing has the advantage to consider a larger number of pixels 
for the filtering step resulting in a considerable improvement of the homogeneity of the image areas. 
The parameterisation for the algorithm is robust. The only two thresholds having to be adjusted are the boxsize for the 
statistical analysis of the neighbourhood pixels and the standard deviation factor, which can be put to 3.0 without 
scruple. This simplifies the use of the algorithm compared to the Gaussian Kernel Smoothing, for example, where the 
adjustment of the sigma threshold often turns out to be very critical. 
3.5 Upgrading of the algorithm to multi-channel images 
Up to now, only gray values have been considered. However, in the ongoing project colour images will be used too, 
making it necessary to have the algorithmic conception transformed into the colour space. It is obvious, that an 
upgrading of the gray value formulas into multi-channel formulas is quite simple. 
First, the criterion for the detection of the area of maximal homogeneity has to be replaced. It is of convenience to check 
the variances within the different channels separately and then to select that area, where the maximum of the standard 
deviations of all channels is minimal. Second, the judgement of the radiometrical correspondence of pixels from the 
larger neighbourhood has to be extended to all channels. This will be done by combining the results for each channel. If 
for this aggregation a logical addition of the investigations in all individual channels is used, one furthermore gets the 
advantage to increase the stability of the results. 
  
322 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
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