Therefore, the fBm index H (and hence D) can be 
easily obtained from the slope of this variance 
plotted as a function of scale in a log-log plot. 
4.2 Local Fractal Dimension 
Local fractal dimension is considered as a function 
of scales, from (16), we obtain local fractal dimen- 
sion as 
DQ^) = log, (Var (1,.(n))) ~ og, (var (#, (n) (18) 
S. MULTISCALE TEXTURE FEATURE FUSION 
Fusion of multiscale texture features is following 
feature extraction and is- according to the lateral 
inhibition and end-inhibition in neurodynamics. Both 
competitive fusion and cooperative fusion are 
developed. 
5.1 Local Competitive Interactions 
Competitive interactions help in noise suppression 
and reducing the effects of illumination (Grossberg, 
1987; Manjunath, 1993). These steps can be modeled 
by non-linear lateral inhibition between features. 
Two types of such interactions are identified: 
competition between spatial neighbors 
with each orientation, and competition between dif- 
ferent orientations at each spatial position. 
5.1.1 Competition Between Spatial Neighbors with 
Each Orientation: A cell of prescribed orientation 
excites like-oriented cells corresponding to its 
location and inhibits like-oriented cells correspond- 
ing to nearby locations at the next processing stage 
(Grossberg, 1987). : 
Let Y(s,0) be the output of a cell at position s 7 (x, y) 
in a given scale with a preferred orientation 0, 
1(s,0) be the excitatory input to that cell from the 
previous processing stage (texture measures in mult- 
iscale analysis), N, be the local spatial neighborhood 
of s. These interactions are modeled by non-linear 
lateral inhibition between features as 
AX (s, 0) « -a,,X(s,0) - I(s,0) LIT (19) 
Y(s,0) = g[ X(s, 0)] (20) 
where (a, b) are positive weights, g(x) is a non- 
linear function such as g(x)= | 
(1+exp(-6x)) 
   
5.1.2 Competition between different orientations 
at Each spatial position: This competition defines a 
push-pull opponent process. If a given orientation 0 
at position s = (x, y) is excited, then other orienta- 
tion Q(0z 9) is inhibited (especially in perpendicu- 
lar orientation) and vice versa. 
Still, let Y(s,0 be the output of a cell in this step, 
the output from previous competition Y(s,0) be the 
input /(s,0) to that cell. The competitive dynamics is 
represented by 
AX (s, 0) 2 —a,, X (5,0) - I(s,0) 2b, XY (s, 9) 
Y(s,0)= g[X(s,0)] 
(21) 
(22) 
5.2 Competition Between Scale Interactions 
Scale interactions are used for the representation of 
end-inhibition property exists among hypercomplex 
cells in the visual cortex of mammals. These cells 
respond to small lines and edges in their receptive 
field, and their response decreases as the length of 
lines or edges increases (hence these are often re- 
ferred to as end detectors) (Manjunath, 1993). These 
cells appear to play an important role in localizing 
line-ends and texture boundaries. 
If Q,(s,0) denotes the response of such a cell at 
position s = (X, y) receiving inputs from two chan- 
nels 1 and j (& >a’) with preferred orientation 6, 
then 
0,(s,0)=g(a1(s,0)- al (s,0) (23) 
5.3 Cooperative Fusion 
This final stage involves grouping similar orienta- 
tions. The cooperative fusion process receives 
inputs from the competitive stage and from end-de- 
tectors described in local competitive interactions 
If. .Z(s,0) 
output of this process, then 
and scale interactions. represents the 
Z(s,0 = g([d(s-s")Y(s',  +O,(s', 9))ds" 
d(s=(x,y),0) = 
(24) 
exp[-Qo) Jes cos 0+ ysin 6) + (7x sin 6+ ycos 6) (25) 
d(s,0) represents the receptive field of Z(s,0),0 is 
the preferred orientation , @ is the corresponding 
orthogonal direction, and A is the aspect ratio of 
the Gaussian. 
1002 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996