141.

[Cover] [Contents] [Index]

Page 224

values of 1, 5, 10, 100 and ∞ (the noise-free case). One of these images with SNR=5 is shown in Figure 5.21b. Each image was divided into adjacent blocks of size 16×16. Texture features were then extracted for these blocks, and subjected to clustering analysis. The results are discussed in Section 5.6.3.

5.6.2 Choice of texture features

Successful classification requires that texture features derived from each approach have to be carefully chosen. The selection of suitable texture features is generally image dependent. However, for some texture extraction approaches, the associated parameters can be determined through theoretical analysis whilst in other cases the texture features can only be extracted through trial and error methods.

5.6.2.1 Multifractal dimension

From Section 5.1.3, it is clear that the range of parameter q is infinite (i.e. from −∞ to +∞), and thus will result in a considerable range of D(q) values. The question of the selection of a set of suitable values of q thus arises. The term ‘suitable’ is not just of concern in order to reduce the computational requirements, but also for the achievement of higher texture segmentation accuracy. In short, we are interested in the use of lower input data dimension to obtain higher segmentation accuracy. To solve this problem, it is necessary to consider the behaviour of D(q) in terms of q.

Using binomial expansion theory, one can rewrite the numerator of Equation (5.28) as:

(5.57)

and if the measuring scale L=1/2ⁿ, then D(q) can be derived as:

(5.58)

Based on Equation (5.58), it is known that D(q) will be constant if p₀= 0.5 or 1 (whatever the value of q), otherwise, D(q) can be portrayed with different values of q and p₀. The resulting behaviour of D(q) is shown in Figure 5.22, which indicates that D(q) changes considerably if q is approximately within the range [−5, 5]. In other words, there is no need to choose a value of q outside this range, as the resulting value of D(q) will be

[Cover] [Contents] [Index]