Optimal Differential Filter on Hexagonal Lattice - Computational Intelligence Paradigms in Advanced Pattern Classification - page 85

(a) Sqr 3 × 3 (b) Sqr 5 × 5 (c) Hex 1 (d) Hex 2

(e) Sqr 3 × 3 (f) Sqr 5 × 5 (g) Hex 1 (h) Hex 2

5 (k) Hex 1 (l) Hex 2
Fig. 12 Results for f ex 3 . Errors of gradient intensity for four images are mapped to luminance
values in (a), (b), (c) and (d). Errors of orientation detection (arctangent) for four images are
mapped to luminance values as (e), (f), (g) and (h). Errors of orientation detection (Overing-
ton) for four images are mapped to luminance values as (i), (j), (k) and (l).

(i) Sqr 3 × 3 (j) Sqr 5 ×

80 0.025 0.025

70

0.02 0.02

60

50

0.015 0.015

40

0.01 0.01

30

20

0.005 0.005

10

0 0 0

f ex1 f ex2 f ex3 f ex1 f ex2 f ex3 f ex1 f ex2 f ex3

Sqr 3x3
Sqr 5x5

Hex 1
Hex 2

Sqr 3x3
Sqr 5x5

Hex 1
Hex 2

Sqr 3x3
Sqr 5x5

Hex 1
Hex 2

(a) (b) (c)

Fig. 13 Means of errors of Table 3, Table 4 and Table 5: (a) gradient intensity, (b) orientation
detection by arctangent, and (c) orientation detection by Overington's method.

on square lattices with arctangent, while being computationally lighter. The derived
filters thus reduce calculation time and to simplifies circuit implementation.
The standard image processing framework is still, however, to use square lattices.
We hope that, in the near future, hexagonal lattices will become widely adopted and
give better results when used with the derived gradient filters.