Carsten Garnica 
  
  
      
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™ 
a) gradients in the 
b) gradients in the image 
C) gradients in the image 
d) gradients in the image 
  
  
original image filtered by filtered by MHN filtered by the 
Gaussian Kernel, new extended MHN 
sigma=2.0 approach 
  
  
  
  
  
  
  
Figure 4. Gradient magnitudes in the filtered images 
A more quantitative assessment of the capability to reduce noise effects is expressed by numerical values as shown in 
table 5. Here, a comparison of the standard deviation of the gray values in homogeneous areas is given, after the 
different filters have been applied. 36 homogeneous areas of the size 7*7 pixels were selected by visual inspection, 
differentiated by the amount of noise in the original images. It can be seen, that all algorithms perform well as long as 
the amount of noise is low. In the cases of high noise, the new approach performs just as good as the Gaussian Kernel 
smoothing with sigma=2.0, but much better than the conventional MHN algorithm. 
  
  
  
  
  
  
  
  
  
  
Image / Filter applied original image | Gauss Kernel, | Gauss Kernel, MHN new approach 
sigma = 0.5 sigma = 2.0 
standard low noise 0.80 0.64 0.37 0.53 0.45 
deviation medium noise 3.42 2.50 1.10 1.67 1.12 
of gray value high noise 6.11 4.31 1.33 2.67 1.26 
  
  
  
  
Table 5. Standard deviation in homogeneous areas 
4.3 Effects on the following feature extraction 
Of further interest is the impact of the mentioned pre-processing steps onto following edge extraction processes. As an 
example Figure 6 shows the image overlaid with the results of such an edge extraction. The new smoothing algorithm 
(d) produces an output image that is almost noise-free, but that still contains all existing significant image structures. It 
is now possible to apply feature extraction algorithms like interest point operators, line extractors or to perform an 
image segmentation producing results not being affected by effects of noise. Since the edges are geometrically and 
radiometrically preserved, the results of an edge extraction algorithm are of superior quality. In contrast to the Gaussian 
Kernel Filter (b) the corners are not rounded off, and edges that lie closely together remain separately detectable. In 
  
  
         
  
  
  
  
  
: “Pe 2 
* x 
j * v * ext 
a) original image b) filtered by Gaussian c) filtered by MHN d) filtered by 
Kernel new extended MHN 
approach 
  
  
  
  
  
  
  
  
  
Figure 6. Image overlaid with the results of Canny edge extraction 
  
324 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.