Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter

Javier García; Tomasz Szoplik; Carlos Ferreira

doi:10.1364/AO.31.004823

Applied Optics
Vol. 31,
Issue 23,
pp. 4823-4828
(1992)
•https://doi.org/10.1364/AO.31.004823

Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter

Javier García, Tomasz Szoplik, and Carlos Ferreira

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Javier García, Tomasz Szoplik, and Carlos Ferreira, "Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter," Appl. Opt. 31, 4823-4828 (1992)

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Abstract

A shift-and-scale-invariant elliptic coordinate-transformed phase-only filter in proposed. The filter is built in three steps: the complex conjugate of a basic-size target spectrum is calculated, its phase-only part is taken, and then the elliptic coordinate transformation is made. In the extreme case the scale ratio of recognizable objects equals 1:1.5, permitting good recognition of object sizes S within the range 0.83 ≤ S ≤ 1.25. Discrimination abilities and relative Horner efficiencies of a few versions of the filter are calculated.

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	Stop Radius = 0			Stop Radius = 2			Stop Radius = 4

	a₁ = 1	a₂ = 1.1	a₃ = 1.2	a₁ = 1	a₂ = 1.1	a₃ = 1.2	a₁ = 1	a₂ = 1.1	a₃ = 1.2
Patternsa	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8
R	1.09	1.02	1.00	1.06	1.08	1.00	1.20	1.00	1.00
R_b	1.00	1.08	1.04	1.00	1.23	1.12	1.00	1.11	1.09
R_s		1.00	1.07		1.00	1.03		1.00	1.14
H	0.35	0.35	0.46	0.29	0.33	0.41	0.34	0.31	0.43
H_b	0.47	0.32	0.50	0.43	0.32	0.49	0.46	0.29	0.47
H_s		0.33	0.33		0.28	0.26		0.29	0.30
M	0.20	0.18	0.32	0.13	0.13	0.22	0.13	0.11	0.20
M_b	0.37	0.21	0.37	0.28	0.17	0.30	0.26	0.15	0.29
M_s		0.16	0.19		0.09	0.12		0.12	0.14
A	0.21	0.11	0.23	0.14	0.11	0.15	0.18	0.10	0.18
A_b	0.13	0.09	0.14	0.07	0.07	0.11	0.07	0.06	0.09
A_s		0.12	0.16		0.08	0.12		0.09	0.14
K	0.20	0.17	0.32	0.16	0.15	0.29	0.18	0.14	0.32
K_b	0.16	0.14	0.19	0.10	0.10	0.15	0.12	0.10	0.16
K_s		0.16	0.21		0.15	0.19		0.13	0.22
O	0.21	0.28	0.30	0.21	0.29	0.32	0.23	0.31	0.34
O_b	0.19	0.21	0.30	0.18	0.22	0.31	0.21	0.22	0.35
O_s		0.12	0.20		0.13	0.22		0.13	0.25

	Recognizable Scale Factors

Stop Radii	1.22	1.43	1.50
0	0.64	0.52	0.49
2	0.66	0.56	0.50
4	0.68	0.53	0.52

	Recognizable Scale Factors

Stop Radii	1.22	1.43	1.50
0	100.0	59.2	53.0
2	80.3	45.4	39.2
4	72.3	44.0	34.7

	Stop Radius = 0			Stop Radius = 2			Stop Radius = 4

	a₁ = 1	a₂ = 1.1	a₃ = 1.2	a₁ = 1	a₂ = 1.1	a₃ = 1.2	a₁ = 1	a₂ = 1.1	a₃ = 1.2
Patternsa	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8	b₁ = 0.7	b₂ = 0.9	b₃ = 0.8
R	1.09	1.02	1.00	1.06	1.08	1.00	1.20	1.00	1.00
R_b	1.00	1.08	1.04	1.00	1.23	1.12	1.00	1.11	1.09
R_s		1.00	1.07		1.00	1.03		1.00	1.14
H	0.35	0.35	0.46	0.29	0.33	0.41	0.34	0.31	0.43
H_b	0.47	0.32	0.50	0.43	0.32	0.49	0.46	0.29	0.47
H_s		0.33	0.33		0.28	0.26		0.29	0.30
M	0.20	0.18	0.32	0.13	0.13	0.22	0.13	0.11	0.20
M_b	0.37	0.21	0.37	0.28	0.17	0.30	0.26	0.15	0.29
M_s		0.16	0.19		0.09	0.12		0.12	0.14
A	0.21	0.11	0.23	0.14	0.11	0.15	0.18	0.10	0.18
A_b	0.13	0.09	0.14	0.07	0.07	0.11	0.07	0.06	0.09
A_s		0.12	0.16		0.08	0.12		0.09	0.14
K	0.20	0.17	0.32	0.16	0.15	0.29	0.18	0.14	0.32
K_b	0.16	0.14	0.19	0.10	0.10	0.15	0.12	0.10	0.16
K_s		0.16	0.21		0.15	0.19		0.13	0.22
O	0.21	0.28	0.30	0.21	0.29	0.32	0.23	0.31	0.34
O_b	0.19	0.21	0.30	0.18	0.22	0.31	0.21	0.22	0.35
O_s		0.12	0.20		0.13	0.22		0.13	0.25

	Recognizable Scale Factors

Stop Radii	1.22	1.43	1.50
0	0.64	0.52	0.49
2	0.66	0.56	0.50
4	0.68	0.53	0.52

Abstract

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Equations (6)

Applied Optics