Image Processing Reference
In-Depth Information
aerialimages.Beforebeingputtogethertheyarealsomeanandvariancenormalized
photometricallyinthatallpatcheshavethesamemeanandthesamevariance.Thisis
done to attempt that segmentation be done on elaborate texture measurements rather
than based on simple (nontexture) features such as gray level and variance, which
can be influenced by illumination. Since the boundaries are known and the patches
are photometrically normalized, an advantage of using such images is that one can
evaluate and compare the results with other segmentation techniques by sharing the
test image and its results only. The ground truth of the boundaries is shown in Fig.
16.8
Thesegmentationistobedonebysomegrouping,inunsupervisedmanner.How
to do this grouping and estimating of region boundaries (without training a neu-
ral network or a classifier) is suggested in Chapter 16. To stay within the scope of
this chapter, however, we only study the texture features. First, five fully circular
(isotropic) subbands are obtained by convolution. The (absolute) frequency centers
of the subbands are in (octavelike) geometric progression with the factor 1.2 be-
tween successive subbands, see Fig. 9.14. The following real measurement for each
subband has been computed:
I
11
I
20
I
40
I
60
Total
#Real scalars
1
2
2
2
7
so that effectively 35 measurements per image point are available. The elements
I
22
,I
33
are excluded because the respective measurements are well approximated
through
I
11
when the input image is a subband that contains only a narrow ring of
frequencyrange.Inthelattercase,
I
n
2
forall
n
,estimatethevariancewithinanar-
rowringoffrequencies.Thementionedgroupingfollowedbyaboundaryestimation
using the above features have been applied. The result is shown as a color image
in the Fig. 14.8 where color represents the identity label of the found textures. Ac-
cordingly, the same color represents the same texture. All seven texture patches are
correctly identified, and the boundaries are reasonably well drawn without training.
,
n
2
Example 14.2. InFig.14.9weshowamoredifficulttexturepatchcompositioncon-
sistingofsevendifferenttexturesina4
4 arrangementasbefore.Again,theindivid-
ual patches are photometrically normalized, and the same texture measures detailed
abovehavebeenutilizedintheautomaticgroupingandboundaryestimationprocess.
The seven texture patches are correctly identified, and the boundaries are reasonably
well drawn, although the boundary quality is somewhat worse.
×
Exercise 14.1.
We have studied only
I
n,
0
,I
n
2
above. What do other complex mo-
,
n
2
ments of the power spectrum with
p
q
, e.g.,
I
4
,
2
,I
5
,
1
, can you estimate? Does
I
qp
contain new information compared to
I
pq
?
HINT:
(
ω
x
+
iω
y
)
p
(
ω
x
−
≥
iω
y
)
q
=(
ω
x
+
iω
y
)
p−q
|
ω
|
2
q
.
