analysis they are still signiﬁcant to the application of
two dimensional image data. The work of (Bovik
et al., 1986) illustrated the theoretical use of many
non-parametric tests within a two dimensional im-
age corrupted with noise sampled at four different
orientations. This work although largely theoretical
and lacking in a comprehensive analysis of the re-
sults, did however evaluate the high computational re-
quirements incurred by such ranking statistical tests.
In spite of the computational cost being greater than
the derivative based detectors, similar parametric tests
were used effectively by (Beauchemin et al., 1998) to
overcome the low signal to noise ratio that is evident
in detecting edges in synthetic aperture radar (SAR)
images, and also by (Huang and Tseng, 1988) to over-
come the blurring effect found with gaussian smooth-
ing ﬁlters.
To perform statistical tests effectively on two di-
mensional images and therefore allow comparisons to
be made to the more traditional techniques, a novel
edge detection algorithm was introduced by (Fes-
haraki and Hellestrand, 1994) that combined the use
of a 5×5 pixel image mask and the popular two dis-
tribution Student’s T test. This allowed them to ef-
fectively detect edges at eight different orientations in
both noiseless and noisy images. Comparisons to the
traditional gradient methods have illustrated a robust
performance in the presence of noise (Kundu, 1990)
and (Hou, 2003), who illustrated how statistics can
outperform Canny on images corrupted with impul-
sive noise. Also found by (Lim and Jan, 2002) (Lim
and Jan, 2006) was the possibility that a modiﬁed Stu-
dent’s T test could perform well on images with little
noise, however was outperformed by the Kolmogorov
Smirnov test in intense noise images.
All these methods, while removing the need for
the smoothing parameters evident in Canny and other
gradient based techniques, do not eliminate the need
for a subjective user threshold. Through the use of
a probability value of the test in question they per-
form a statistical conﬁdence test using lookup tables.
Work by (Bowring et al., 2004) has since indicated
the possibility of producing images superior to both
Canny and SUSAN (Smith and Brady, 1997) using
novel statistical methods without the need for a conﬁ-
dence check simply by varying the size of the image
mask and therefore the amount of data points used in
the tests. Furthermore work by (Williams et al., 2005)
illustrated how through the use of multiple masks of
varying scales applied to the same image and artiﬁ-
cial neural networks, it is possible to remove the need
for any subjective threshold when producing superior
statistical images, albeit at higher computational cost.
2 THE STATISTICAL EDGE
DETECTION FILTER
For all of the results presented here, the same ﬁlter
principle is used as that described by (Bowring et al.,
2004). The reader is directed to that work for a more
detailed full description of its operation. The statis-
tical edge-detection ﬁlter principle is shown in sim-
pliﬁed form in (Fig: 1). It details an edge section
of a mouse atlas image (MA) (Brune et al., 1999)
with a single square mask applied. Each mask used
is divided in two equal areas surrounding a central
pixel at various angles of 90
◦
, 60
◦
, 45
◦
etc. If the
mask lies entirely in a homogeneous region within
the image, then there will be little or no difference
in the computed statistical measures between both ar-
eas. The maximum difference will occur when the
mask lies directly over the boundary between the two
regions (as in Fig: 1), therefore generating greatly dif-
fering statistical measures for each of the regions. Us-
ing this technique, the likely edge direction is also de-
termined and is used for later non-maximal suppres-
sion of the image when necessary.
A
B
Figure 1: Illustrating a single statistical mask applied to an
image region at an angle of 0
◦
. Each mask is divided into
two equal sized regions A and B located around the central
pixel of interest.
2.1 Implementing the Statistical
Tests
For the analysis work, various statistical parametric
and non-parametric tests have been used to compare
two equal sized samples. Each of the tests used will
give a high response if the two data sets A and B come
from different regions of the image under evaluation,
and likewise low values if they are from the same re-
gion.
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