Image Processing Reference
In-Depth Information
occurrence matrices have been reduced to only three different measures. In principle, these
measurements are again invariant to linear shift in illumination (by virtue of brightness
comparison) and to rotation (since order is of no consequence in their description and
rotation only affects co-occurrence by discretisation effects). As with Fourier, scale can
affect the structure of the co-occurrence matrix, but the description can be made scale
invariant.
entropy(CCD20)=7.052·10
5
entropy(CCD21)=5.339·10
5
entropy(CCD29)=6.445·10
5
inertia(CCD20)=5.166·10
8
inertia(CCD21)=1.528·10
9
inertia(CCD29)=1.139·10
8
energy(CCD20)=5.16·10
8
energy(CCD21)=3.333·10
7
energy(CCD29)=5.315·10
7
(a) French canvas (detail)
(b) French canvas
(c) Beach sand
Code 8.3
Measures of co-occurrence matrices of the three Brodatz textures
Grey level difference statistics (a first-order measure) were later added to improve
descriptional capability (Weszka, 1976). Other statistical approaches include the statistical
feature matrix (Wu, 1992) with the advantage of faster generation.
8.3.4
Combination approaches
The previous approaches have assumed that we can represent textures by purely structural,
or purely statistical description, combined in some appropriate manner. Since texture is not
an exact quantity, and is more a nebulous one, there are naturally many alternative descriptions.
One approach (Chen, 1995) suggested that texture combines geometrical structures (as,
say, in patterned cloth) with statistical ones (as, say, in carpet) and has been shown to give
good performance in comparison with other techniques, and using the
whole
Brodatz data
set. The technique is called Statistical Geometric Features (SGF), reflecting the basis of its
texture description. This is not a dominant texture characterisation: the interest here is that
we shall now see the earlier
shape measures
in action, describing texture. Essentially,
geometric features are derived from images, and then described by using statistics. The
geometric quantities are actually derived from
NB
- 1 binary images
B
which are derived
from the original image
P
(which has
NB
brightness levels). These binary images are given
by
1
if
P
=
xy
,
(8.9)
B
() =
otherwise
1,
NB
xy
,
0
Then, the points in each binary region are connected into regions of 1s and 0s. Four
geometrical measures are made on these data. First, in each binary plane, the number of
regions of 1s and 0s (the number of connected sets of 1s and 0s) is counted to give
NOC
1
and
NOC
0. Then, in each plane, each of the connected regions is described by its
irregularity
which is a local shape measure of a region
R
of connected 1s giving irregularity
I
1 defined
by
