classes. Each unknown pixel is assigned to the class
with the highest probability at the pixel location. The
decision rule is as follows:
pOX oc )p(oé) 2 p(X|w;)p(w;) (1)
where X :the spectral multivariate vector
plo, ) : pdf of X, given that X is a member
of class c
p(æ, ): a priori probability of class c in the
image
i: class number among the m number of classes
in the image
The resultant likelihoods (D) can be used as surrogates
for probabilities.
1
D - [In( p(.X WPD pz ^^? = In(p(a,.) -— In(z)
£ (2)
b. FE
X x) > (A = 46)
2
Figure 1 shows the pdfs of two spectral classes, with
their overlap marked with diagonal lines. The
decision rule for this method is that all pixels are
assigned to the class with the higher pdf for that
spectral value. For example, even if a pixel with the
value of *a" belongs in reality to class B, it will be
classified as class A (Figure 1). This is an inevitable
result of overlapping class pdfs.
A B
a koX
Figure 1. The decision rule of a pixel-based maximum
likelihood classifier.
3. METHODS
Instead of pixels, groups of pixels that form image
segments were used for image classification in this
study. There are few studies that evaluate the use
statistic of segmented regions for classification (Kettig
and Landgrebe, 1976; Meyer et aL, 1996; Gougeon,
1995a; Janssen and Molenaar, 1995). However, most
studies employing aggregated information focus on
first order statistics and only use second order statistics
to a limited extent. In this section, new methods that
exploit multivariate statistics to improve the image
classification are suggested.
Figure 2 represents a conceptual comparison between
traditional classification and the methods developed in
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
this study. An example of the pixel-based approach
(Figure 2, left) is the traditional supervised maximum
likelihood classification. Within a patch, pixels from
the outliers of the class distribution are likely to be
misclassified. Window-based approaches use
arbitrary groupings and return the value of the window
to the central pixel (Figure 2, middle). In the case of
the object-based classification (Figure 2, right), patches
are not expected to consist of pixels with completely
homogeneous spectral radiances, but rather certain
levels of variability are expected. This approach,
therefore, incorporates a more realistic representation
of real phenomena. The variation in an object is used
as one characteristic of the object in this method,
whereas it is an obstacle with traditional pixel-based
classification methods. To treat this variation within
objects, multivariate normal distributions were assumed
for every group of pixels in each patch, and
multivariate variance-covariance matrices were
calculated. Two methods of exploiting this
information were investigated: maximum likelihood
based on the patch mean, and maximum likelihood with
Gaussian pdf.
Classification Methods
Pixet-based Whdow-based Obpect-Derteed
dod a d o AS / A TOM /
: A f / ^^ Fe 7 Z5 A,
/ rele /
Training Saerpées
Target area
Seeceo
Figure 2. Comparison of object-based classification
with traditional image classification approaches.
3-1. Maximum likelihood classification using the
patch mean
Maximum likelihood classification with the patch mean
uses a decision rule modified to use the mean vector of
a group of pixels, instead of individual pixels. When
the mean of the group is classified as belonging to a
certain class, all the pixels in the group are assigned to
that class. The decision rule is as follows:
p(X |æ.)ple,) = p(X |æ; )p(o; ) (3)
Where: — X : mean vector of a group
p Xlo,) :probability associated with the
mean of the group of pixels of class c, given
that the mean vector Y is a member of class
C
