The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
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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