The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
1019 
histogram change reflects the variation of spatial information, 
i.e., texture, and can be measured by the generalized Fisher 
information content K : 
Kj = X “ v < ln v - 
, hj(Lj ) - 4hfL J+i ) 
(1) 
where Lj and L J+ . are two consecutive coefficients at 
Clustering at level nw+m is repeated using the cluster centres 
computed from the clustering result at level nw+m-1. These 
steps are iterated until the clustering result at level nw + m-1 is 
stable. After that, the same steps are repeated with v m+m ~ 1 and 
ynw+m-i vectors This procedure is concatenated until the 
clustering result is achieved at the highest level nw. As shown 
in Figure 2, this inter-scale decision fusion yields better 
clustering result than the classical classification at single scale 
due to the use of information extracted from multi-scale 
features. 
decomposition level J and J +1 generated from the original 
image ¿o > hf) denotes the bin count, v , does intensity (gray 
value), and m does the number of bins. 
As aforementioned, the Haar wavelet coefficients consist of 
four components L = {L u , L lh , L hl , L HH } such that K : in 
equation (1) is extended as equation (2) 
K J =K(L J ,L J+l ) = 
K(L, 
On the one hand, the texture-based image segmentation yields 
compact rock detection results, however, they are still not fine 
enough to directly determine rock boundaries as shown in 
figure 3 (D). It leads the need for boundary refinement as to be 
discussed in the next stage. 
'LLJ’L LLj+ ,) 
J LH J ’ ^LH J+l ) 
(2) 
-‘HLJ ’ L hlj+ j) 
HHJ’L H l{j+1) 
This measurement is concatenated with measurements in the 
next two levels until the measurement K J+n between L J+n and 
to form a texture feature vector. As a result, the texture 
feature vector v is formed as equation (3), where the images 
with the decomposition levels of j to J + n +1 used for 
computing Kj to K J+n . 
v = [K J ,K Jt ,,-K Jt ,] T (3) 
Texture feature classification. For inter-scale decision fusion, 
the multi-scale texture features are extracted with windows of 
various sizes. If the feature vector V is composed of n Fisher 
information K from level J to J + n computed by the 
window with size M x 2nw by N x 2nw where scale level nw is 
integer, the feature vector y nw is rewritten as 
v-=[/cr,KZ,-KZ] T № 
With the same manner, the m-th feature vector for inter-scale 
decision fusion is determined by a window with size 
M*2(nw+m) by Nx2(nw+m)as 
F nw+m r iv nw+m rs nw+m is nw+m T ( 
— [Ay 5^7+1 + W J ' ' 
Once the multi-scale texture feature vectors are ready, the k- 
means clustering for inter-scale decision fusion is performed as 
below. The k-means clustering starts with the lowest level (the 
coarsest resolution) feature vector v m+m . As a result, image 
pixels belong to one of the clusters such that each image pixel 
has a label. Let the normalized label value be denoted by 
LB" w+m , the input feature vector c nw+m ~' for clustering at next 
(D) (C) 
Figure 2. Rock detection using texture-based segmentation 
[Input rock image (A), with K-means clustering (B), with inter 
scale decision fusion clustering (C), and detected rock (D)] 
3.2 Rock boundary delineation using active contours 
Active contours by level set method. This study exploits an 
active contour for boundary refinement. Level set method is 
suggested to describe the evolution of a (contour) curve by 
Osher and Sethian (1988). In contrast to the traditional snake 
method, the numerical schemes for the active contours based on 
level set method benefit automatic handling of the topological 
change during the curve propagation. In this method, a curve is 
represented as a level set of a given function, i.e., the 
intersection between this function and a horizontal plane. To be 
specific, the zero level set ¥(0 = {(x,y) | tf>(x,y,t) = 0} of a time- 
varying surface function <!>{x,y,t) , gives the position of a 
contour at timeL The evolution equation for a contour curve 
propagation is defined as equation (7) (Sethian, 1990). 
(f)' + F | Vtf) |= 0 given 0( x ,t = 0) (7) 
For level set method, the evolution equation evolves the contour 
curve with three simultaneous motions determined by each 
speed function with 
level nw+m-1 can be written as equation (6) 
C 
nw+m-1 
nw+m y nw+m-1 jT 
T 1 nnw+m-X is nw+m-1 jsnw+m-\ 
— [Ld ,Ay >A y+1 
is nw+m-11T 
'^J+n J 
. (6) 
F = F p +F'+F a - (8) 
In the above equation, F p denotes the expanding speed of the 
contour defined by a constant speed F 0 in its normal direction 
such as F p =F 0 . F c is the moving speed proportional to the