The power of the structural element approach is that it emphasizes 
the shape aspects of the tonal primitives. Its weakness is that 
it can only do so for binary images. 
   
   
    
     
   
  
  
  
  
   
     
  
  
  
  
  
  
  
  
   
   
    
   
  
   
     
   
   
  
The power of the co-occurence approach is that it characterizes 
the spatial inter-relationships of the gray tones in a textural 
pattern and can do so in a way that is invariant under monotonic 
gray tone transformations. Its weakness is that it does not 
capture the shape aspects of the tonal primitives. Hence, it is 
not likely to work well for textures composed of large-area pri- 
mitives. 
The power of the auto-regressive linear estimator approach is that 
it is easy to use the estimator in a mode which sythesizes tex- 
tures from any initially given linear estimator. In this sense, 
the auto-regressive approach is sufficient to capture everything 
about a texture. Its weakness is that the texture it can charac- 
terize are likely to consist mostly of micr-textures. 
2.1. The Autocorrelation Function and Texture 
From one point of view, texture relates to the Spatial size of the 
tonal primitives on an image. Tonal primitives of larger size are 
indicative of coarser textures; tonal primitives of smaller size 
are indicative of finer textures. The autocorrelation function 
is a feature which tells about the size of the tonal primitives. 
We describe autocorrelation function with the help of a thought 
experiment. Consider two image transparencies which are exact 
copies of one another. Overlay one transparency on top of the 
other and with a uniform source of light, measure the average 
light transmitted through the double transparency. Now, translate 
one transparency relative to the other and measure only the 
average light transmitted through the portion of the image where 
one transparency overlaps the other. A graph of these measurements 
as a function of the (x,y) translated and normalized with respect 
to the (0,0) translation depicts the two-dimensional autocorre- 
lation function of the image transparency. 
Let I (u,v) denote the transmission of an image transparency at 
position (u,v). We assume that outside some bounded rectangular 
region 0 «cu xL, and OxvzxL, the image transmission is zero. 
Let (x,y) denote the x-translátion and y-translation, respectively. 
The autocorrelation function for the image transparency d is 
formally defined by: 
  
] co 
«TRE I A le ve v 
p(x,y) = , 
7 12 (uv) du dv 
XY wo 
  
  
|x| < L, and P « Ly 
If the tonal primitives on the image are relatively large, then 
the autocorrelation will drop off slowly with distance. If the 
tonal primitives are small, then the autocorrelation will drop '