Ine 
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be uses as textural parameters. An object should be defined in 
the. following way to be smooth: 
1) Be Imax a relative maximum of density inside the image of a 
single object, then there is no point inside the image which 
has a higher density. 
2) If Imin is a relative minimum inside the image of a single 
object, then there is no point inside the image which has a 
lower density. 
3) The density of the points surrounding of highest respectively 
lowest density is equal or lower Imax respectively equal or 
greater Imin. 
4) There is no turning point on a straight profile through the 
image of a single object. 
Objects which have images which a smooth structure should be 
called image-significant elementary objects, their images should 
be called significant elementary object images 
4. The Texture Conditions 
  
Each image structure is given by the operator D with 
D: (x',y') ——» density 
A texture should be a special case of image structure. The "tex- 
ture"can be defined in the following way: 
T1 The image structure in the image section G, is caused by at 
least two image-significant elementary objBets. 
T2 There is a mask M sa that for each position of the mask in 
the image section G, T4 is satisfied. If the image is a digi— 
tal one the mask will be a square, else the mask will be a 
circle. The amount of the area of the mask is given by 
F = ( [VF 7%] + 4)? C [x] greatest integer less x) 
where &. 
Il 
AM + pe w d + 6-c 
where @ the expectance value and 6 standard deviation of 
the distribution of of the amount of the areas of the sig- 
nificant elementary object images. 
c is called significance factor which is destinated by the 
equation 
F(c,0,7) = 8 
where the function F is the distribution function of the 
standardized Gaussian distribution and S is a significance 
level. c should be always greater or equal 1. 
The constant value q is calculated from the equation 
F 
Il 
m+e meq + CoS. = 4eP 
Bln 
n 
deviation of the size of the structure elements of a chess 
board pattern, which has n-1 elements of the same size and 
one element, which has a size 4P-times larger than the size 
of one of the other elements. 
where m = n+4P-1 and s = e . m and s are mean and standard-