International Archives of the Photogrammetry, Remote Sensing and Spatial [Information Sciences, Vol XXXV, Part B4. Istanbul 2004
If (nj > nj && ni? n foralli- j ) then x £c; (1)
where x = centre pixel,
ni & nj = the number of adjacent pixels belong
to class i and j
nt = threshold
Usually a moving 3*3 window is used and threshold 5 applied
for this purpose, the effect of this algorithm is to smooth the
classified image by weeding out isolated pixels that were
initially given labels that were dissimilar labels assigned to the
surrounding pixels. (Mather, 1999)
2.2 Thomas Filter
Thomas (Thomas, 1980)introduce a method based on proximity
function which is described as follows:
q:q
f.- S ANS, if x; € w; then q;=2 else qi-0 (2)
if xs € w; then qs=2 else qs=1 (1=2,4,6,8) (=1,2,3,...k)
where qi = weight of ith pixel
q5= center pixel
oj = jth class
di52-distance between ith and center pixel.
As shown in figurel this algorithm uses direct adjacent for its
calculation. Like the majority filter, Tomas filter remove
isolated pixels and relable considering direct neighbours. It
might also reallocate a previously unclassified pixel that had
been placed in the reject class by the classification algorithm.
(mather, 1999)
co
6
Cn
N
4
Figurel: direct neighbor pixels
2.3 Transition Matrices
Transition Probability Matrices is an algorithm which uses
temporal information and expresses the expectation that cover
types will change during a particular period of time (Franciscus
Johannes, 2000) Knowledge about the dependency of crops to
seasons and their mutual sequences is valuable for defining the
conditional probability as P(class c at time t»/ class ; at time
tj) . The statistical concept of marcov chains is closely related
to this subject, as it describes the dependencies between a state
at t; and the previous states (tj,to,L1,...) this algorithm concern
to agriculture area.
2.4 Probability Label Relaxation
Probabilistic label relaxation is a postclassification context
algorithm which begins by assuming that a classification based
on spectral data alone has been carried out. This algorithm was
introduced by hurries in 1985.This method is based on the key
992
concepts of probability, compatibility coefficient, neighborhood
function, and updating rule (Richards 1993).
2.4.1 Probabilities: Probabilities for each pixel describe the
chance that the pixel belongs to each of the possible classes. In
the initial stage, a set of probabilities could be computed from
pixel based and subpixel classifiers. These algorithms
performed by spectral data alone, maximum likelihood and
linear spectral Unmixing are among these algorithms. In this
research for LSU classification the fraction of each
endemember is consider as initial stage.
k
S p; (07) 196 «505 «1 (3)
£i Jj nj
where pj(w;) = probabilities of pixel / belongs to class j
2.4. Compatibility Coefficient: A compatibility coefficient
describes the context of the neighbour and how compatible it is
to have pixel m classified as «y and neighbouring pixel n
classified as «.it is defind as
N i (w ERE )
r (VE > WI ) = log (4)
1 C uds K
>, N; (Wy SW] ) AN; (wi. Ww] )
where N i (w k^ WI ) = the frequency of occurrence of class
oy was neighbours at pixel i and j;
2.4.5 Neighbourhood Function: A neighborhood function
is a function of the label probabilities of the neighboring pixels,
compatibility coefficients, and neighborhood weights. It
defined as:
ro ue ques vy (5)
q; GE i ij 2 Vie WP (Wy s
where | Ny» the number of neighbors considered for pixel i
di7the weight factor of neighbors
N,= number of classes
T=number of iteration
2.4.4 Updating Rule: A neighborhood function allows the
neighborhoods to influence the possible classification of the
center pixel and update the probabilities, by multiplying the
label probabilities by the neighborhood function. These new
values are divided by their sum in order to the new set of label
probabilities sums to be one.
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