Image logic algebra and its optical implementations

Masaki Fukui; Ken-ichi Kitayama

doi:10.1364/AO.31.000581

Image logic algebra and its optical implementations

Masaki Fukui and Ken-ichi Kitayama

Applied Optics
Vol. 31,
Issue 5,
pp. 581-591
(1992)
•https://doi.org/10.1364/AO.31.000581

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Masaki Fukui and Ken-ichi Kitayama, "Image logic algebra and its optical implementations," Appl. Opt. 31, 581-591 (1992)

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History
- Original Manuscript: November 9, 1990
- Published: February 10, 1992

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Abstract

A generic language for optical parallel processing image logic algebra (ILA), is proposed. In ILA a neighborhood configuration pattern (NCP) is introduced, and image transformations are defined by the use of NCP operations. The comprehensive relationship of ILA to symbolic substitution, optical array logic, mathematical morphology, and binary image algebra are clarified. Furthermore, an architecture that is suited for ILA and its optical implementations is proposed.

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Corrections

Masaki Fukui and Ken-ichi Kitayama, "Image logic algebra and its optical implementations: errata," Appl. Opt. 31, 4630-4630 (1992)
http://proxy.osapublishing.org/ao/abstract.cfm?uri=ao-31-23-4630

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Operation	Image by image	and, or
	Image	not
	NCP by NCP	and, or
	NCP	not
Transformation	Image	SHIFT, TEST, IC, MI
	Image by NCP	Extended erosion, dilation

r₁/r₂	ϕ	1	0	*
ϕ	ϕ	1	0	*
1	1	1	*	*
0	0	*	0	*
*	*	*	*	*

r₁/r₂	ϕ	1	0	*
ϕ	ϕ	ϕ	ϕ	ϕ
1	ϕ	1	ϕ	1
0	ϕ	ϕ	0	0
*	ϕ	1	0	*

Operation Kernel of OAL	NCP of ILA				Operation Kernel of OAL	NCP of ILA
Operation Kernel of OAL	P_AB	P_ÂB	$P_{A \bar{B}}$	$P_{\bar{A} \bar{B}}$	Operation Kernel of OAL	P_AB	P_ÂB	$P_{A \bar{B}}$	$P_{\bar{A} \bar{B}}$
[..]	[.]	[.]	[.]	[.]	[PP]	[.]	[.]	[.]	[1]
[NN]	[1]	[.]	[.]	[.]	[UU]	[.]	[0]	[0]	[.]
[NP]	[.]	[.]	[1]	[.]	[.1]	[0]	[0]	[.]	[.]
[0.0]	[.]	[0]	[.]	[0]	[01]	[.]	[0]	[.]	[.]
[PN]	[.]	[1]	[.]	[.]	[1.]	[0]	[.]	[0]	[.]
[0.0]	[.]	[.]	[0]	[0]	[10]	[.]	[.]	[0]	[.]
[EE]	[0]	[.]	[.]	[0]	[11]	[0]	[.]	[.]	[.]
[00]	[.]	[.]	[.]	[0]	[DD]	[0]	[0]	[0]	[1]

Operation Kernel	Function	Operation Kernel	Function
[..]	1	[PP]	A(r) + B(r)
[NN]	$\bar{A (r)} + \bar{B (r)}$	[UU]	$\bar{A (r)} \cdot B (r) + A (r) \cdot \bar{B (r)}$
[NP]	$\bar{A (r)} + B (r)$	[0.1]	B(r)
[0.0]	$\bar{A (r)}$	[01]	$\bar{A (r)} \cdot B (r)$
[PN]	$A (r) + \bar{B (r)}$	[1.0]	A(r)
[0.0]	$\bar{B (r)}$	[10]	$A (r) \cdot \bar{B (r)}$
[EE]	$A (r) \cdot B (r) + \bar{A (r)} \cdot Z \bar{B (r)}$	[11]	A(r) · B(r)
[00]	$\bar{A (r)} \cdot \bar{B (r)}$	[DD]	0

r	x⁽⁰⁾	x⁽¹⁾
ϕ	0	0
1	0	1
0	1	0
*	1	1

r	ϕ	1	0	*
$\bar{r}$	*	0	1	ϕ

r	x⁽⁰⁾	x⁽¹⁾
ϕ	0	0
1	0	1
0	1	0
*	1	1

r	ϕ	1	0	*
$\bar{r}$	*	0	1	ϕ

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