„zu 
application to real image data, the matrices are restricted to 
the nearest-neighbourhood (d=1, angles: oc, 45°, 90°, 1359). Four 
of these features, which can be extracted from these matrices and 
are regarded as particular useful will be defined here. In what 
follows: p(i,j) is the (i,j)th element of the given matrix divided 
by the sum of all matrix elements. These features are: 
Contrast: CON = z (i-3)?p(i,j) (21) 
Angular Second Moment: ASM ip(i,j)* (22) 
Entropy: ENT fpíi,i)log p(íi,j) (23) 
or rg eg S 
Correlation: COR si-3{pti, 9) mam, J| x5 (24) 
where m m.5..8, are the mean and the standard deviation of 
the row sums and the column sums, respectively, of the matrix. 
Another set of textural features can be based on grey level run 
lengths statistics. In this case the pixels of the image that lie 
along some given line will be examined. It is the assumption that 
there are occasionally runs of consecutive pixels, which all have 
a grey value of the same range (e.g. grey steps (0-7), (8-15) etc.). 
According to Galloway /28/ the number p(i,j) of run length j - in 
some direction (e.g. o>, 45°, 90°, 1359) ~ consists of pixels whose 
grey levels lie in the range i. Then we can define the following 
features: 
Long Runs Emphasis: LRE - k z j?p(i,j) (25) 
Grey Level Distribution:GLD k Dp, 31)? (26) 
Run Length Distribution:RLD k :G pli, i)? (27) 
j i 
with k^1 e zp(i,j) 
Run Percentage: RPC: = NT“ Yp(i,j) (28) 
where N° is the number of pixels in the evaluated region. 
Further possibilities to define textural features are given by the 
evaluation of the Fourier power spectrum |F|? of the specific 
image region f. It is well known that the radial and angular 
- 22 - 
1 
4 
s 
distribution of values in |F|? is sensitive to coarseness and 
directionality, respectively, of the texture. The different in- 
put data and results are shown in figure 24 and figure 25. These 
examples represent the different classes of man made objects 
(housing area) and natural objects (forest). A texture with many 
edges or lines in a given direction will have high values of |F|? 
concentrated around the perpendicular direction, while in a non- 
directional texture |F|? should also be nondirectional. Thus a 
set of features can be obtained by the averages A of |F|? taken 
over intersections of ring- and wedge-shaped regions for various 
values of inner and outer radii r4 and rj, as well for lower and 
upper angles o, and PE 
1 
YdF(v)1? u^t v^ « rj 
r,a -1 
tan (vfu) < 
93 
For digital pictures as shown in figure 24 one uses the discrete 
Fourier transform. This transform, however, treats the input image 
f as periodic. 
Normally this assumption does not apply, therefore the transform 
is affected by the discontinuities that exist between opposite 
edges. According to picture 25 these have the effect of intro- 
ducing misleading high values in |F|? along the u and v axes. 
In general all these computations (equ. 17 - 29) described above 
can also be carried out for differentiated images. Figure 26 re- 
presents the result of such a differentiation process applied to 
figure 24, displayed again as a two-dimensional grey level image 
but containing only contour and structural elements. These are 
obviously well suited data for the definition and extraction 
Of textural features. 
The emphasis of textural elements can be stressed by the genera- 
tion of line drawings out of the differentiated images. Figure 27 
demonstrates that simple contour following algorithms yield ade- 
quate results, as there is no need to get the exact shape of the