Image Processing Reference
In-Depth Information
T4 T7 T5 T1
T2
T1 T4
T6
T4
T2
T7
T2
T6
T5
T3
Fig. 16.8. A texture patch (P3) and the ground truth class identities (T1, T2,...,T7) represented
by color at each point
h
B
. Each boundary pixel receives the label of the class that gives the minimum
distance.
5. Decrease the value of
l
by one and repeat from step 1, until the bottom of the
pyramid is reached.
16.7 Texture Grouping and Boundary Estimation Integration
Here we integrate the unsupervised clustering and the boundary estimation process
discussed in the previous sections, by illustrating its effect on a patch image of tex-
tures (Fig. 16.8). It consists of regions corresponding to real texture images, as for
those in [37], put in a 256
256 image. Each texture patch was photometrically
normalized with respect to the mean and the variance, i.e., if the texture patch is rep-
resented by
f
, the normalized texture is obtained as
f
=
af
+
b
for some constants
a
and
b
to force the mean and the standard deviation
f
to equal specific values (128
and 30 here, for all patches). This was done to illustrate the multidimensional group-
ing because, otherwise, the textures would be too easy to separate by gray values,
being 1D features. There are, in total, seven different textures tiled as a 4
×
4 matrix,
and the patches are repeated to obtain all texture combinations astride the boundaries
for a maximal diversity. Accordingly, every texture is a neighbor of any other at least
once.
×
Exercise 16.1.
Is there an alternative way to construct Fig. 16.8, i.e., to obtain
4
×
4
patches of
T
-textures with
T
=7
,
8
16
, so that all texture crossovers are present?
A rotation of the result or a change of texture identities is not counted.
···
The symmetry derivatives applied to a log-polar decomposition of the spatial
frequencies discussed in Chap. 14 have been used as features. To be precise, there
