Image Processing Reference
In-Depth Information
Fig. 14.8. The P1 texture patch composition consisting of real aerial images (
left
) and its
automatic segmentation using group direction tensors for 2, 4, and 6-folded symmetries
14.6 Group Direction Tensors as Texture Features
In the previous sections, we discussed group direction features that were shown to
be invariant to translation. This is a property one wishes to have in texture features
because textures are precisely defined as images in which the same geometric struc-
ture repeats itself. The texture properties measured around any point should not vary
as long as the point is within the same texture. How powerful the group direction
features are and how they can be used as texture features will be studied in further
detail next.
The group direction of a texture for
n
-folded symmetry is determined by the two
complex moments,
I
n,
0
,
and
I
n
2
,
(14.21)
,
n
2
of the power spectrum. This s pair represents three real scalars, the first being a com-
plex scalar (two real scalars), the second being a (nonnegative) real scalar. They can
be applied to the original image directly or to a bandpass-filtered version of the orig-
inal, forcing the quantities to be measured for only a certain frequency range (scale)
of the image. Assuming bandpass filtering, the result of which is a number of im-
ages that differ in their absolute frequency contents, then one can extract the group
direction tensor elements for every image, increasing the description power. Band-
pass decompositions can be efficiently implemented by a variety of ways, e.g., the
Laplace pyramid discussed in Sect. 9.5. Therefore the two complex moments pro-
vide evidence for the joint presence of
n
2
directions contained in a narrow frequency
ring and within a local support around a point in an image. We discuss the practical
issues by way of two examples below.
Example 14.1. In Fig. 14.8 we show the P1 texture patch that has to be segmented
based on local image features. The texture patches in the composition are cut from
