Manfred H. Günzl 
  
Using the former equation it is possible to derive 7, (w) out of sums and squaresums of the coordinates of the enclosed 
grid cells. With this it is possible to define the orientation compensated shape parameter 
  
  
2E? E 16 — Cc? oh (AV)? + 4C2, 
5 € 
"mas CT 32P 1A cI QU 
  
  
  
In addition it is also possible to compensate the influence of the aspect ratio by using its relation to the ratio of the 
eigenvalues €, and €». 
3 APPLICATION 
Applied to land use segmentation this shape parameter can be used to evaluate the plausibility of the shape of a segment. 
Especially when applied to region growing by merging the parameter enables the computationally highly efficient distinc- 
tion between plausible and implausible merging opportunities (— figure 4). Using 7, Or ,,,,, segmentation algorithms 
(D (II) 
  
Ton (79,02,12) = 2.26 
  
    
    
Jl n. (26, 26,16) ~ 1.34 
  
FRE t EE 
  
  
  
An B = 7... (52,50,32) = 2.40 "nm 
PEC 
  
Figure 4: Two examples of implausible merging opportunities caused by imaging interference. 
can be enabled to prefer rectangular shapes, and therefore, this is a mathematical tool to implement one facet of the human 
ability to assess land use shapes in remote sensed data. To demonstrate the "tidy" effect of the shape parameter the well 
known image of Lena Soderberg was segmented by recursive fusion of images pixels (— image 5(a)). In all cases the 
256 x 256 pixel image was reduced to 1000 segments. In example (b) the fusion criterion was to minimize the variance. 
In a greedy approach, from all possible fusions the one creating a region with the smallest variance was taken. In (c) 
the variance was multiplied by r,,,.. The fusion creating the region with the smallest product of 7,,, and the resulting 
variance was taken. The influence of 7,,, divides narrow elongated objects into several segments. This effect can be 
reduced by an additional compensation of the aspect ratio as shown in example (d). Further details will be published in 
the authors PhD thesis. 
Initially, this method was developed to enhance an ERS-SAR land use segmentation approach. Even manually, field 
boundary detection in ERS-SAR images was found to be very difficult. Using ERS C-band-VV data the only chance 
to delimit areas of different crop types or other slightly different kinds of land use, is to analyze time series during the 
vegetation period. A series of seven ERS-SAR-SLC scenes with a 35 day period from March till October was registrated 
to each other. The histogram-equalized signal intensity of the May data for a test side near Munich is shown in image 
6(a). Ground truth data was determined by GPS measurements. To get an absolute measurement of segmentation quality, 
an idealized dataset was build by filling GIS polygons of land use segments with their mean signal intensity (— image 
6(b)). After application of SAR speckle (— image 6(c)), these scenes were segmented and compared to the GIS data. To 
derive a measurement of quality for the segmentation, the GIS regions were checked whether they were completely and 
exclusively covered by a segment. If a segment covers more than 50% of a GIS-region and the region covers more than 
50% of the segment these two were taken as complementary. Let P; be the set of grid cells within the sth GIS region and 
S; the set of cells within the complementary segment. If there is no complementary segment, let S; — (). The error of 
incompleteness e; is given by 
3s card(P; n $;) 
eed 3 card(Pi) 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 355