Multiple degree of freedom object recognition using optical relational graph decision nets

David P. Casasent; Andrew J. Lee

doi:10.1364/AO.27.001886

Applied Optics
Vol. 27,
Issue 9,
pp. 1886-1892
(1988)
•https://doi.org/10.1364/AO.27.001886

Multiple degree of freedom object recognition using optical relational graph decision nets

David P. Casasent and Andrew J. Lee

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David P. Casasent and Andrew J. Lee, "Multiple degree of freedom object recognition using optical relational graph decision nets," Appl. Opt. 27, 1886-1892 (1988)

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Abstract

Multiple degree of freedom object recognition concerns objects with no stable rest position with all scale, rotation, and aspect distortions possible. We assume that the objects are in a fairly benign background, so that feature extractors are usable. In-plane distortion invariance is provided by use of a polar–log coordinate transform feature space, and out-of-plane distortion invariance is provided by linear discriminant function design. Relational graph decision nets are considered for multiple degree of freedom pattern recognition. The design of Fisher linear discriminant functions and synthetic discriminant functions for use at the nodes of binary and multidecision nets is discussed. Case studies are detailed for two-class and multiclass problems. Simulation results demonstrate the robustness of the processors to quantization of the filter coefficients and to noise.

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Test	Training image results	Test image results	Percent correct	Remarks
1	45/45	66/72	94.9	No LDF quantization and no noise added
				Number of LDF quantization levels
2	45/45	67/72	95.7	1024
3	45/45	66/72	94.9	512
4	44/45	62/72	90.6	256
5	42/45	62/72	88.9	128
6	41/45	63/72	88.9	64
7	41/45	63/72	88.9	32
8	41/45	63/72	88.9	16
				Standard deviation of added noise
9	45/45	66/72	94.9	0.1
10	45/45	67/72	95.7	0.2
11	9/45	17/72	22.2	0.3
12	6/45	10/72	13.7	0.4

Test	Training image results	Test image results	Percent correct	Remarks
1	45/45	72/72	100.0	No LDF quantization and no noise added
				Number of LDF quantization levels
2	45/45	72/72	100.0	1024
3	45/45	72/72	100.0	512
4	45/45	72/72	100.0	256
5	45/45	72/72	100.0	128
6	45/45	71/72	99.1	64
7	45/45	63/72	92.3	32
8	0/45	4/72	3.4	16
				Standard deviation of added noise
9	45/45	72/72	100.0	0.1
10	45/45	71/72	91.1	0.2
11	15/45	22/72	31.6	0.3
12	5/45	8/72	11.1	0.4

Test	Training image results	Test image results	Percent correct	Remarks
1	45/45	66/72	94.9	No LDF quantization and no noise added
				Number of LDF quantization levels
2	45/45	67/72	95.7	1024
3	45/45	66/72	94.9	512
4	44/45	62/72	90.6	256
5	42/45	62/72	88.9	128
6	41/45	63/72	88.9	64
7	41/45	63/72	88.9	32
8	41/45	63/72	88.9	16
				Standard deviation of added noise
9	45/45	66/72	94.9	0.1
10	45/45	67/72	95.7	0.2
11	9/45	17/72	22.2	0.3
12	6/45	10/72	13.7	0.4

Test	Training image results	Test image results	Percent correct	Remarks
1	45/45	72/72	100.0	No LDF quantization and no noise added
				Number of LDF quantization levels
2	45/45	72/72	100.0	1024
3	45/45	72/72	100.0	512
4	45/45	72/72	100.0	256
5	45/45	72/72	100.0	128
6	45/45	71/72	99.1	64
7	45/45	63/72	92.3	32
8	0/45	4/72	3.4	16
				Standard deviation of added noise
9	45/45	72/72	100.0	0.1
10	45/45	71/72	91.1	0.2
11	15/45	22/72	31.6	0.3
12	5/45	8/72	11.1	0.4

Abstract

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Equations (11)

Applied Optics