Introduction to texture description, segmentation and classification - Feature Extraction and Image Processing - page 294

statistical and combination approaches. Clearly the frequency content of an image will
reflect its texture; we shall start with Fourier. First though we shall consider some of the
required properties of the descriptions.

8.3 Texture description

8.3.1 Performance requirements

The purpose of texture description is to derive some measurements that can be used to
classify a particular texture. As such, there are invariance requirements on the measurements,
as there were for shape description. Actually, the invariance requirements for feature extraction,
namely invariance to position, scale and rotation, can apply equally to texture extraction.
After all texture is a feature, albeit a rather nebulous one as opposed to the definition of a
shape. Clearly we require position invariance: the measurements describing a texture
should not vary with the position of the analysed section (of a larger image). Also, we
require rotation invariance but this is not as strong a requirement as position invariance;
the definition of texture does not imply knowledge of orientation, but could be presumed
to. The least strong requirement is that of scale , for this depends primarily on application.
Consider using texture to analyse forests in remotely sensed images. Scale invariance
would imply that closely spaced young trees should give the same measure as widely
spaced mature trees. This should be satisfactory if the purpose is only to analyse foliage
cover. It would be unsatisfactory if the purpose was to measure age for purposes of
replenishment, since a scale-invariant measure would be of little use as it could not, in
principle, distinguish between young trees and old ones.
Unlike feature extraction, texture description rarely depends on edge extraction since
one main purpose of edge extraction is to remove reliance on overall illumination level.
The higher order invariants, such as perspective invariance, are rarely applied to texture
description. This is perhaps because many applications are like remotely sensed imagery,
or are in constrained industrial application where the camera geometry can be controlled.

8.3.2 Structural approaches

The most basic approach to texture description is to generate the Fourier transform of the
image and then to group the transform data in some way so as to obtain a set of measurements.
Naturally, the size of the set of measurements is smaller than the size of the image's
transform. In Chapter 2 we saw how the transform of a set of horizontal lines was a set of
vertical spatial frequencies (since the point spacing varies along the vertical axis). Here,
we must remember that for display we rearrange the Fourier transform so that the d.c.
component is at the centre of the presented image.
The transforms of the three Brodatz textures of Figure 8.2 are shown in Figure 8.3 .
Figure 8.3 (a) shows a collection of frequency components which are then replicated with
the same structure (consistent with the Fourier transform) in Figure 8.3 (b). (Figures 8.3 (a)
and (b) also show the frequency scaling property of the Fourier transform: greater
magnification reduces the high frequency content.) Figure 8.3 (c) is clearly different in that
the structure of the transform data is spread in a different manner to that of Figures 8.3 (a)
and (b). Naturally, these images have been derived by application of the FFT which we
shall denote as