well in this aspect. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
level of original FBM BLANKET SAVR 
resolution FD 
2.2 2.24 2.51 2.41 
Level 1 2.5 2.40 2.85 2.64 
2.8 2.92 2.71 2.84 
2.2 2.00 2.53 2.43 
Level 2 2.5 2.54 2.87 2.64 
2.8 2.70 2.80 2,79 
2.2 1.64 2.40 2.38 
Level 3 2.5 1.86 2.54 2.54 
2.8 2.01 2.71 2.75 
2.2 1.98 2.52 2.28 
Level 4 2.5 2.68 2.65 2.57 
2.8 2.97 2.70 2.74 
window size 21X21 8X8 21X21 
  
  
  
  
  
  
  
Table: 2 the FD values estimated from 
multiresolution images 
3.4 Window size and direction 
As the generated test fractal images are 
simulated, the size of window can affect the 
FD estimates. It is shown in Tab. 1 and Tab. 2 
that besides the BLANKET method of which 
window size is small ( 8 x 8) , the other 
methods have used large window with size 21 X 
21. By comparision the BLANKET method can 
obtain good FD values in very small window 
of size 4X4 and thus its time consumption 
of FD estimation is lower than others. 
Direction is one of the important properties 
of the FD. By changing window size and window 
Shape, we can estimate the FD values in a 
certain direction, It should be mentioned 
that some of the above methods can provide 
the FD values of a single profile of images, 
namely, FBM, FBV, DCF and SAVR methods, 
4. FRACTAL FEATURE BASED IMAGE SEGMENTATION 
The  fractal-based approaches have been 
applied in several different types of image 
analysis application (Peleg, 1984, Petland, 
1984, Keller, 1989, Stein, 1987). Stein has 
made use of the fact that man- made objects 
are not fractal structures and, accordingly, 
will not provide reasonable fits to fractal 
models. In reality, this kind of techniques 
54 
which use the differences between the FD of 
natnral phenomena and that of man-made 
objects to dectect objects is not always 
reliable and effective, because of the 
problems discussed in section 1. However, the 
FD of subsets of an image can be taken as a 
useful texture measure which can be used to 
discriminate features in an image. 
4,1 Feature extraction 
The SAVR method and BLANKET method can 
provide the FD estimates from both fractal 
and nonfractal image data, and their straight 
linearities are quite well accross the long 
ranges of scales, Therefore both methods can 
be applied in feature extraction and image 
segmentation on real image data. Fig 4 and 
Fig.6 illustrate the feature extraction by 
BLANKET method in which the maximun of r is 
13 pixel and the window size is 3X3. The FD 
values of points located in the center of the 
window are calculated by using the sliding 
window in the original images, thus, we 
obtained the processed images in which the 
grey value of each point denotes the 
transformed FD value which has converted from 
the value ranging in 2.0-3.0 into the value 
  
(a) (b) (e) 
Fig.4 Fractal-based feature extraction 
(a) original image 
(b) image convoluted by Sobel operator 
(c) D-feature image 
  
Fig. 6 Fractal-based image segmentation 
(à original image 
(b D-feature image 
(c) binary image 
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Fig. 6