Appendix B
The section demonstrates an adapted pattern regularity approach based on the algorithm from [1] mentioned in Sect. 3.2.1. The approach is simplified to reduce
the number of factors considered, such as objective shape, background periodicity
and objects intensity.
B.1 Regularity of Triangle Tessellation
For a given M × N pixel size binary image I(m, n), as shown in Fig. B.1, and a
spacing vector (d x , d y ), a normalised autocorrelation function ρ xy (d x , d y ) can be
obtained:
ρ xy
d x , d y
=
1
S
M−1
m=0
N −1
n=0
I (m, n)I
m + d x , n + d y
(B.1)
where S is the normalisation factor expressed as:
S =
M−1
m=0
N −1
n=0
I
2
(m, n)
(B.2)
A polar representation ρ pol (i, d) of autocorrelation function is then constructed
by interpolating ρ xy (d x , d y ), as shown in Fig. B.2.
An intensity function can be defined as:
M pol (i, d) = 1 − ρ pol (i, d)
(B.3)
where for each angle i, it obtains the variation of intensity F i (d) with a spacing
distance of d.
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