Introduction to texture description, segmentation and classification - Feature Extraction and Image Processing - page 301

and of the weighted irregularity) are shown in Code 8.4 . Again, the set of measures is
different for each texture. Of note, the last measure, mW ( , does not appear to offer
much discriminatory capability here whereas the measure M ( WI 1) appears to be a much
more potent descriptor. Classification, or discrimination , is to select which class the measures
refer to.

M(NOC1)=52.0 M(NOC1)=178 M(NOC1)=81

m(NOC1)=8.75 m(NOC1)=11.52 m(NOC1)=22.14

M(WI1)=1.50 M(WI1)=1.42 M(WI1)=1.00

m(WI1)=0.40 m(WI1)=0.35 m(WI1)=0.37

(a) French canvas (detail) (b) French canvas (c) Beach sand

Code 8.4 Four of the SGF measures of the three Brodatz textures

8.4 Classification

8.4.1 The k-nearest neighbour rule

In application, usually we have a description of a texture sample and we want to find which
element of a database best matches that sample. Thus is classification : to associate the
appropriate class label (type of texture) with the test sample by using the measurements
that describe it. One way to make the association is by finding the member of the class (the
sample of a known texture) with measurements which differ by the least amount from the
test sample's measurements. In terms of Euclidean distance, the difference d between the
M descriptions of a sample, s , and the description of a known texture, k , is

M

2

d = ( sk - ) (8.16)

i i

i =1

which is also called the L 2 norm . Alternative distance metrics include: the L 1 norm which
is the sum of the modulus of the differences between the measurements

M

L = | s - k | (8.17)

1 i i

i =1

and the Bhattacharyya distance B

M

B = - ln s k (8.18)

i i

i =1

but this appears to be used less, like other metrics such as the Matusita difference.
If we have M measurements of N known samples of textures and we have O samples of
each, then we have an M -dimensional feature space that contains the N O points. If we

select the point, in the feature space, which is closest to the current sample, then we have
selected the sample's nearest neighbour . This is illustrated in Figure 8.5 where we have a