518
e The spatial textures are different.
2. SEGMENTATION USING GMRF
MODEL
2.1 GMRF Model
SAR data are generally processed using mul-
tilook averaging techniques in order to reduce
the speckle level. It has been shown that the
probability density function (pdf) of multilook
SAR intensities is the Gamma distribution (Rig-
not and Chellappa 1993, Lee et al 1994). How-
ever, according to the Central Limit Theorem in
statistics, such data distributions can be consid-
ered to be approximately normal (Gaussian) dis-
tributions with the error in an acceptable limit
(Dong et al, 1998a). One of the advantages of
assuming Gaussian distributions is that mathe-
matical descriptions for such a distribution are
more complete. It has been shown that the seg-
mentation results using Gaussian distribution is
slightly better than that of a Gamma distribu-
tion (Dong et al, 1998a).
The GMRF model assumes that the distribution
of the intensity of a uniform area in SAR image
is to be Gaussian. Secondly it assumes that the
texture is only of local features, i.e., the value of
a pixel is correlated only with its nearby pixels.
Therefore, if we have n-channel measurements,
the conditional probability density function of
the measurement vector X given a region S can
be written as,
1
@n-PjcH7
eep {-3E"C7B} (1)
p(X|S) =
where T' denotes transpose, E is a zero mean
Gaussian noise vector in which each of its ele-
ment is a linear combination of noise errors tak-
ing account of measurements of its spatial neigh-
bouring pixels, as,
N
e; = (zig-£f)- 3 tir (2ix — ii)
k=l
12d un (2)
where x; denotes the ith measurement at the
current pixel position 0, z; is the mean value
of the ith measurement for cluster S, and zi,
k = 1,2, -- -, N, is the measurement of the neigh-
bourhood position k for ith measurement. C
denotes a n x n symmetrical noise covariance
matrix with its element cj; — E(ei;e;). tix are
model parameters reflecting textures in the im-
age (Panjwani and Healey 1995). If all t;x — 0,
the definition of of the covariance matrix can
be regarded as the traditional definition without
considering textures.
Consider an image having been partitioned into
a finite number of segments and each segment
to be only a part of (or a whole of) a uniform
object. The conditional probability of all pixels
in Segment S belonging to that segment is the
product of conditional probability densities of all
pixels in S. We have (Dong et al 1998b),
p(X,S;seS) = [[».(X.IS)
SES
- [entero] eoo m
where M, is the number of pixels in the cluster,
S. Finding the maximum conditional probabil-
ity in (3) is equivalent to finding the minimum
determinant of C. Therefore, the optimal model
parameters tj, can be found by minimising C.
2.2 Segmentation
The segmentation using the GMRF model is im-
plemented in two steps: initial segmentation fol-
lowed by segment merging.
Initial segmentation is essential when using the
GMRF model in segmentation process, as the
model parameter estimation requires segment
statistics. Because the model possesses the fea-
ture of merging only, it is very important to en-
sure that each initial segment is only part of (or
the whole of) one cluster. Although each pixel
definitely belongs to only one cluster, it cannot
be considered as the initial segmentation, as its
statistics cannot be computed. "Techniques of
wavelet filtering, edge detection and watershed
process are used to obtain the initial segmenta-
tion (Dong et al, 1998b). The initial segmenta-
tion is generally conservative in order to ensure
that each segment belongs to no more than one
cluster.
Starting from the initial segmentation, the pro-
cess of segment merging is iterated. A merging
ratio, which is the ratio of a priori merging max-
imum likelihood probability to a posterior merg-
ing maximum likelihood probability, is used as
a criterion to determine the process of segment
merging (Dong et al, 1998b) At each iteration,
all spatially adjacent segments are considered,
and only the pair which has the minimum merg-
ing ratio is merged. In the end either a number
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998
~~ bead A IM 3) em A
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