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An overview of the algorithms for various filters may be found
in some review papers as (Lee et al., 1994) and (Shi and Fung,
1994) and will not be recapitulated in this paper. The original
papers dealing with the algorithms used, along with the ab-
breviation used in this paper are as follows for the geometric
algorithms:
EPOS Edge Preserving Optimized Speckle Filter
(Hagg and Sties, 1994)
GEOM Geometric Filter (Crimmins, 1985)
R-LEE Refined Lee Filter (Lee, 1981)
and for the statistical algorithms:
FRO Frost Filter (Frost et al., 1982)
E-FRO Enhanced Frost Filter (Lopes et al., 1990b)
LEE Lee Filter (Lee, 1980)
E-LEE Enhanced Lee Filter (Lopes et al., 1990b)
KUAN Kuan Filter (Kuan et al., 1985)
G-MAP Gamma Map Filter (Lopes et al., 19903)
4 COMPARISON CRITERIA
This section aims at the definition of criteria which are more
objective than those used in other review papers. A unique
criterion for the rating of speckle filters is not available, thus
subjective criteria are used in most papers dealing with filter
comparison. Since speckle filters are almost adaptive to the
signal in order to preserve the image contents, measurements
on standard signals may not be generalized to describe the
performance of the filter. Non adaptive filters, which approx-
imate a spectrum in the frequency domain as the mean filter,
may be characterized by the impulse response which describes
the behavior of the filter completely. Using filters adaptive
to the signal statistic within a moving window requires the
observation of different signal to noise ratios in order to de-
termine the behavior of the filter. In addition, filters using a
geometric approach, and therefore depending on the actual
geometry of the image contents, require the observation of
different geometric arrangements to characterize the perfor-
mance of the algorithm. In order to compare the preservation
of edges and points, a similar factor of speckle reduction for
the filters observed must be supposed.
4.1 COMPARISON BASIS
There is a contradiction between the efficiency of image
smoothing and the preservation of edges, lines and point ob-
jects within an image. Using a mean filter, the size of the
filter matrix is bound to the smoothing capability; a large
matrix results in a large number of samples for averaging.
On the other hand, the blurring of edges within the image
is extended to an area around the edge, which is limited by
the filter matrix size, thus large matrices will result in more
distortions of the image contents. Thus the radiometric and
the geometric image quality show a contradictory behavior
with regard to the matrix size. Adaptive filtering algorithms
try to optimize both, the radiometric and geometric quality,
but the contradiction is just understated not eliminated. In
order to compare the filter performance it is obvious, that
one of the quality criteria must be retained while the other
one is explored. A method where the criteria are reckoned up
137
proofs to be not practicable, since the relationship between
the radiometric and the geometric quality depends on the
adaptive algorithm used for filtering. Thus we try to adjust
the radiometric quality of all methods compared, i.e. we fix
the amount of reducing speckle variation. This radiometric
quality may be calculated easily from a homogeneous region
from the image. The geometric quality is then estimated in
a more complicated procedure described below.
In Section 2 of this paper we regarded the radiometric qual-
ity of an image as the essential criterion for the purpose of
image classification. For that reason we tried to reduce the
image speckle by a large amount. Some implementations
of the filters used are limited to a 11 x 11 matrix size. A
mean filter with the corresponding matrix of size N = 11
and sample size S — NN — 121 reduces speckle variation by
R = 0/00 = 1/V5S = 1/11 = 0.0909, where c denotes the
standard deviation of a homogeneous area within the filtered
image, oo that within the speckled image. The speckle re-
duction R of adaptive algorithms is quite less using the same
matrix size, so we aim at a decrease of the standard deviation
of 10 percent. Notice that the measurement of R is indepen-
dent of the mean grey level since the multiplicative noise
model also fits for the smoothed image. Therefore the factor
within the standard deviation representing the mean cancels
out in the nominator and the denominator. The measure-
ment is done from some large homogeneous areas at several
greylevels within a test image. Since the speckle reduction ca-
pability of most filters is adjustable only by the matrix size, it
is hard to meet the above requirement. Another way to adjust
the smoothing performance is to apply filters several times,
as it is necessary for the GEOM filter. Other filter parameters
are generally used to optimize the filter performance at edges
and therefore they are not available to adjust the smoothing
capability in homogeneous areas. A good compromise for the
adjustment of the filter algorithms was found by the values
shown in Table 1 which are used for all examinations. The
total values of speckle reduction are shown in Section 5. The
FILTER | WINDOW | ITER | DAMP
EPOS 11 1 0.75
GEOM 11 4 -
R-LEE 9 2 =
FRO 11 1 10
E-FRO 11 1 10
LEE 11 1 =
E-LEE 11 1 5
KUAN 11 1 -
G-MAP 11 1 =
Table 1: Filter parameters
R-LEE filter algorithm reduces the variation less than other
filters, since approximately one halve of the matrix elements
is used to calculate a mean value. Applying two iterations at
a 9 x 9 matrix size results in a speckle reduction similar to the
other algorithms. Also with the GEOM filter 4 iterations was
necessary to achieve approximately the same smoothing ca-
pability. The damping factor was adjusted by evaluating the
rating criteria mentioned below for several values. Neverthe-
less unacceptably low speckle reduction values R are rejected
from the list of parameters in order to obtain a close field of
radiometric image quality.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
