human visual system by Krose, the discriminability 
orders are almost the same. Therefore we can 
conclude that 2D Gabor filters can be regarded as 
texture discriminator. 2D Gabor function is desirable 
representation of textural detector, it not only 
satisfies the requirement of visual texture percep- 
tion, gives good statistical description of textons, 
but also provides a reasonable explanation of 
texture descrimination in theory and experiment 
from the viewpoint of psychophysics and physiology. 
Now we give following theorem: 
Theorem: Visual detection or catch of textural 
primitive distribution in retinal image can be 
described or represented by oriented 2D Gabor 
function G(x,y) (1), we known the oriented 2D 
Gabor function as textural detector 
G(x,») » eG. y)exp[2 gi Qux * v,y)] (1) 
where 
(x',y') 2 (xcos o4 ysin g,—xsin q 4- y cos o), (2) 
1 (x7) ty 
py) = XD ——— —— (3) 
glx.) zig P 20 
  
The selection of parameters in textural detector (1) 
is in accordance with following formula (Jixian 
Zhang ,1994; Fogel and Sagi, 1989): 
B =log,[(1+0.1874/ of,) / (1-0.1874/ of,)] (4) 
where B is the spatial frequency bandwidth (octaves), 
o is the standard deviation corresponding to the 
gaussian envelope, and f, is the optimal spatial 
frequency. 
As textural detector, the Gabor implementation 
effectively unifies the solution of the conflicting 
problems of determining local textural structures 
(features, texture boundaries) and identifying the 
spatial extents of textures contributing significant 
spectral information, e.g., the densities of oriented 
and/or elongated textons. 
3. TEXTURAL DETECTOR BASED 
MULTISCALE TEXTURE ANALYSIS 
Figure 1 shows the flow chart of the multiscale tex- 
ture analysis method proposed in this paper. Because 
of the outstanding ability to represent signal, ap- 
proach to wavelet multiscale decomposition is inte- 
grated in our method, and window size is corre- 
y 
Textural Detector Based Wavelet 
Multicale Decomposition Function 
Selection 
Y 
ultiscale Decomposition of Textural Image 
in Direction q 
  
  
  
  
[ Muttiscale Textural Primitive Planes | 
  
    
     
  
Nonlinear Processing 
Textural Feature Planes 
  
( Multiscale Texture Feature Fusion | 
y 
[rue Discrimination and seperation 
  
  
Figure 1. Flow Chart of the Multiscale Texture 
Analysis Method 
3.1 Selection for Multiscale Decomposable 
Function 
In order to capture textural feature effectively, se- 
lected wavelet function for multiscale decomposition 
should be compatible with the textural detector. A 
2D Gabor function satisfies the condition of wavelet 
and is therefore an admissible wavelet (Mallat,1989). 
In the view of our point, the wavelet decomposable 
function may be considered as the textural detector 
of the form 
G(x,y) 7 g(x,y)sin(2 zf (xcos 0— ysin 0) + o) (5) 
Or 
G(x,y) 7 g,(x. y)sinQ # (xcos 0- ysin 0) + 9) (6) 
where 
Cd Lo zn Jul Ve) 
d | i 4 = hl (7) 
is the Gaussian envelope, g,(x,y) is the first 
deviation of g(x,y), 9-0,z/2. 
To simplify our description, we now consider such a 
multiscale decomposition where the basic wavelet 
v(x, y, 0) is the same as (5) 
spondly changed according to the size of analysis x y! 
scale and texture attribute. Wo.y, 6) — exp(- 4 — + j2af (xcos 0— ysin 0)) (8) 
1000 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
    
     
    
   
  
  
     
     
  
   
   
    
   
    
    
   
   
    
  
   
    
    
    
     
    
    
     
   
  
   
   
  
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