Gray-tone image processing by threshold superposition in an optical cellular-logic binary-image processor

Liren Liu; Xuejun Zhang; Zibei Zhang

doi:10.1364/AO.33.004383

Applied Optics
Vol. 33,
Issue 20,
pp. 4383-4391
(1994)
•https://doi.org/10.1364/AO.33.004383

Gray-tone image processing by threshold superposition in an optical cellular-logic binary-image processor

Liren Liu, Xuejun Zhang, and Zibei Zhang

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Liren Liu, Xuejun Zhang, and Zibei Zhang, "Gray-tone image processing by threshold superposition in an optical cellular-logic binary-image processor," Appl. Opt. 33, 4383-4391 (1994)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A parallel architecture for gray-tone image processing is proposed that utilizes the concept of threshold sum–superposition into a cellular two-layer logic binary-image processor. Various processing functions constituted by gray-tone dilation, erosion, fuzzy-logic operations, and arithmetic operations are obtained. The optoelectronic implementation is illustrated.

Full Article | PDF Article

More Like This

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Lan Shao, Liren Liu, and Guoqiang Li
Appl. Opt. 35(17) 3109-3116 (1996)

One-operation image algebra and optoelectronic cellular two-layer logic array

Liren Liu, Zibei Zhang, and Xuejun Zhang
J. Opt. Soc. Am. A 11(6) 1789-1797 (1994)

Fuzzy solid sets for mathematical morphology and optical implementation

Liren Liu
J. Opt. Soc. Am. A 12(12) 2636-2644 (1995)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (3)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (6)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (27)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Logic Symbol	Logic Operation	Normalized Output Operation
Logic Symbol	Logic Operation	$\sum_{n = 1}^{N} F (f_{n}, g_{n})$	$\sum_{n = 1}^{N} F (f_{N - n + 1}, g_{n})$
F₀	F	0	0
F₁	X ∩ Y	f.∧.g	f + g − 1
			(0: f + g < 1)
F₂	X ∩ Y^c	f − g
		(0: f < g)	$f \land \bar{g}$
F₃	X	f	f
F₄	X^c ∩ Y	g − f
		(0: f > g)	$\bar{f} \land g$
F₅	Y	g	g
F₆	xor	\|f − g\|	1 − \|f + g − 1\|
F₇	or	f ∨ g	f + g
			(1: f + g > 1)
F₈	nor		1 − f − g
		$\bar{f} \land \bar{g}$	(0: f + g > 1)
F₉	xnor	1 − \|f − g\|	\|f + g − 1\|
F₁₀	Y^c
		$\bar{g}$	$\bar{g}$
F₁₁	X ∪ Y^c	1 + f − g
		(1: f > g)	$f \lor \bar{g}$
F₁₂	X^c
		$\bar{f}$	$\bar{f}$
F₁₃	X^c ∪ Y	1 − f + g
		(1: f < g)	$\bar{f} \lor g$
F₁₄	nand		2 − f − g
		$\bar{f} \lor \bar{g}$	(1: f + g < 1)
F₁₅	T	1	1

F^out		Fⁱⁿⁿ = X
Logic Symbol	Logic Operation	Fⁱⁿⁿ = X
Logic Symbol	Logic Operation	(0, 0) ∉ S	(0, 0) ∈ S
F₀	F	∅	∅
F₁	and	X ∩ (X ⊕ S)	X
F₂	X ∩ Y^c	X ∩ (X ⊕ S)^c	∅
F₃	X	X	X
F₄	X^c ∩ Y	X^c ∩ (X ⊕ S)	X^c ∩ (X ⊕ S)
F₅	Y	X ⊕ S	X ⊕ S
F₆	xor	(X^c ∩ (X ⊕ S)) ∪	X^c ∩ (X ⊕ S)
		(X ∩ (X ⊕ S^c)
F₇	or	X ∪ (X ⊕ S)	X ⊕ S
F₈	nor	X^c ∩ (X ⊕ S)^c	(X ⊕ S)^c
F₉	xnor	(X ∩ (X ⊕ S)) ∪	X ∪ (X ⊕ S)^c
		(X^c ∩ (X ⊕ S)^c)
F₁₀	Y^c	(X ⊕ S)^c	(X ⊕ S)^c
F₁₁	X ∪ Y^c	X ∪ (X ⊕ S)^c	X ∪ (X ⊕ S)^c
F₁₂	X^c	X^c	X^c
F₁₃	X^c ∪ Y	X^c ∪ (X ⊕ S)	W
F₁₄	nand	X^c ∪ (X ⊕ S)^c	X^c
F₁₅	T	W	W

F^out		Fⁱⁿⁿ = X^c
Logic Symbol	Logic Operation	Fⁱⁿⁿ = X^c
Logic Symbol	Logic Operation	(0, 0) ∉ S	(0, 0) ∈ S
F₀	F	∅	∅
F₁	and	X ∩ (X ⊖ Š)^c	X ∩ (X ⊖ Š)^c
F₂	X ∩ Y^c	X ∩ (X ⊖ Š)	X ⊖ Š
F₃	X	X	X
F₄	X^c ∩ Y	X^c ∩ (X ⊖ Š)^c	X^c
F₅	Y	(X ⊖ Š)^c	(X ⊖ Š)^c
F₆	xor	X^c ∩ (X ⊖ Š))∪ X^c ∩ (X ⊖ Š)^c)	X^c ∪ (X ⊖ Š)
F₇	or	X ∪ (X ⊖ Š)^c	W
F₈	nor	X^c ∩ (X ⊖ Š)	∅
F₉	xnor	X^c ∩ (X ⊖ Š))∪ X^c ∩ (X ⊖ Š)^c)	X ∩ (X ⊖ Š)^c
F₁₀	Y^c	X ⊖ Š	X ⊖ Š
F₁₁	X ∪ Y^c	X ∪ (X ⊖ Š)	X
F₁₂	X^c	X^c	X^c
F₁₃	X^c ∪ Y	X^c ∪ (X ⊖ Š)^c	(X ⊖ Š)^c
F₁₄	nand	X^c ∪ (X ⊖ Š)	X^c ∪ (X ⊖ Š)
F₁₅	T	W	W

F^out		Fⁱⁿⁿ = X
F^out		$\sum_{n = 1}^{N} F (f_{n}, f_{n} \oplus S)$		$\sum_{n = 1}^{N} F (f_{N - n + 1}, f_{n} \oplus S)$
Logic Symbol	Logic Operation	(0, 0) ∉ S	(0, 0) ∈ S	(0, 0) ∉ S	(0, 0) ∈ S
F₀	F	0	0	0	0
F₁	X ∩ Y	f ∧ (f ⊕ S)	f	f + (f ⊕ S) − 1	f + (f ⊕ S) − 1
				(0: f + f ⊕ S < 1)	(0: f + f ⊕ S < 1)
F₂	X ∩ Y^c	f − f ⊕ S	0
		(0: f < f ⊕ S)		$f \land (\bar{f \oplus S})$	$f \land (\bar{f \oplus S})$
F₃	X	f	f	f	f
F₄	X^c ∩ Y	f ⊕ S − f	f ⊕ S − f
		(0: f > f ⊕ S)		$\bar{f} \land (f \oplus S)$	$\bar{f} \land (f \oplus S)$
F₅	Y	f ⊕ S	f ⊕ S	f ⊕ S	f ⊕ S
F₆	xor	\|f ⊕ S − f\|	f ⊕ S − f	1 − \|f + f ⊕ S − 1\|	1 − \|f + f ⊕ S − 1\|
F₇	or	f ∨ (f ⊕ S)	f ⊕ S	f + f ⊕ S	f + f ⊕ S
				(1: f + f ⊕ S > 1)	(1: f + f ⊕ S > 1)
F₈	nor			1 − f − f ⊕ S	1 − f − f ⊕ S
		$\bar{f} \land (\bar{f \oplus S})$	$\bar{f \oplus S}$	(0: f + f ⊕ S > 1)	(0: f + f ⊕ S > 1)
F₉	xnor	1 − \|f ⊕ S − f\|	1 − (f ⊕ S − f)	\|f + f ⊕ S − 1\|	\|f + f ⊕ S − 1\|
F₁₀	Y^c
		$\bar{f \oplus S}$	$\bar{f \oplus S}$	$\bar{f \oplus S}$	$\bar{f \oplus S}$
F₁₁	X ∪ Y^c	1 − (f ⊕ S − f)	1 − (f ⊕ S − f)
		(1: f > f ⊕ S)		$f \lor (\bar{f \oplus S})$	$f \lor (\bar{f \oplus S})$
F₁₂	X^c
		$\bar{f}$	$\bar{f}$	$\bar{f}$	$\bar{f}$
F₁₃	X^c ∪ Y	1 + (f ⊕ S − f)	1
		(1: f < f ⊕ S)		$\bar{f} \lor (f \oplus S)$	$\bar{f} \lor (f \oplus S)$
F₁₄	nand			2 − f − f ⊕ S	2 − f − f ⊕ S
		$\bar{f} \lor (\bar{f \oplus S})$	$\bar{f}$	(1: f + f ⊕ S < 1)	(1: f + f ⊕ S < 1)
F₁₅	T	1	1	1	1

_F^out		Fⁱⁿⁿ = X^c
_F^out		$\sum_{n = 1}^{N} F (f_{n}, \bar{f_{n} ⊖ Š})$		$\sum_{n = 1}^{N} F (f_{N - n + 1}, \bar{f_{n} ⊖ Š})$
Logic Symbol	Logic Operation	(0, 0) ∉ S	(0, 0) ∈ S	(0, 0) ∉ S	(0, 0) ∈ S
F₀	F	0	0	0	0
F₁	X ∩ Y	f − ⊖ Š	f − ⊖ Š
		(0: f < ⊖ Š)		$f \land \bar{(f ⊖ Š)}$	$f \land \bar{(f ⊖ Š)}$
F₂	X ∩ Y^c	f ∧ (f ⊖ Š)	f ⊖ Š	f + f ⊖ Š − 1	f + f ⊖ Š − 1
				(0: f + f ⊖ Š < 1)	(0: f + f ⊖ Š < 1)
F₃	X	f	f	f	f
F₄	X^c ∩ Y			1 − f − f ⊖ Š	1 − f − f ⊖ Š
		$\bar{f} \land \bar{(f ⊖ Š)}$	$\bar{f}$	(0: f + f ⊖ Š > 1)	(0: f + f ⊖ Š > 1)
F₅	Y
		$(f ⊖ Š)$	$(f ⊖ Š)$	$(f ⊖ Š)$	$(f ⊖ Š)$
F₆	xor	1 − \|f − f ⊖ Š\|	1 − (f − f ⊖ Š)	\|f+ f ⊖ Š − 1\|	\|f+ f ⊖ Š − 1\|
F₇	or	1 + f − f ⊖ Š	1
		(1: f > f ⊖ Š)		$f \lor \bar{(f ⊖ Š)}$	$f \lor \bar{(f ⊖ Š)}$
F₈	nor	f ⊖ Š − f	0
		(0: f > f ⊖ Š)		$\bar{f} \land (f ⊖ Š)$	$\bar{f} \land (f ⊖ Š)$
F₉	xnor	\|f − f ⊖ Š\|	\|f − f ⊖ Š\|	1 − \|f + f ⊖ Š − 1\|	1 − \|f + f ⊖ Š − 1\|
F₁₀	Y^c	f ⊖ Š	f ⊖ Š	f ⊖ Š	f ⊖ Š
F₁₁	X ∪ Y^c	f ∨ (f ⊖ Š)	f	f + f ⊖ Š	f + f ⊖ Š
				(1: f + f ⊖ Š > 1)	(1: f + f ⊖ Š > 1)
F₁₂	X^c
		$\bar{f}$	$\bar{f}$	$\bar{f}$	$\bar{f}$
F₁₃	X^c ∪ Y			2 − f − f ⊖ Š	2 − f − f ⊖ Š
		$\bar{f} \lor \bar{(f ⊖ Š)}$	$\bar{f} ⊖ Š$	(1: f + f ⊖ Š < 1)	(1: f + f ⊖ Š < 1)
F₁₄	nand	1 − (f − f ⊖ Š)	1 − (f − f ⊖ Š)
		(1: f < f ⊖ Š)		$\bar{f} \lor (f ⊖ Š)$	$\bar{f} \lor (f ⊖ Š)$
F₁₅	T	1	1	1	1

m	Logic Sequence
m	Fⁱⁿⁿ : n	F^out : n or N − n + 1
1	F(1)	∅
2	F(2)	∅
⋮	⋮	⋮
M − 1	F(M − 1)	∅
M	(any)	F(M)

Abstract

Cited By

Figures (3)

Tables (6)

Equations (27)

Applied Optics