Performance evaluation of minimum average correlation energy filters

A. Mahalanobis; David P. Casasent

doi:10.1364/AO.30.000561

Performance evaluation of minimum average correlation energy filters

A. Mahalanobis and David P. Casasent

Applied Optics
Vol. 30,
Issue 5,
pp. 561-572
(1991)
•https://doi.org/10.1364/AO.30.000561

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A. Mahalanobis and David P. Casasent, "Performance evaluation of minimum average correlation energy filters," Appl. Opt. 30, 561-572 (1991)

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History
- Original Manuscript: October 2, 1989
- Published: February 10, 1991

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Abstract

A new SDF type correlation filter referred to as the minimum average correlation energy (MACE) filter has been recently described in the literature. In this paper, we experimentally address the distortion tolerance and noise properties of this filter. The MACE filter has attractive properties that include: easily detectable peaks, distortion invariance, simplified training set selection, solutions to input bias effects, performance in noise and real background clutter, and less clutter with its reduced number of training set images. Each of these properties is investigated in detail in this paper.

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Test Number	Object Class	Specified Peak at Center	Number of Errors	Percent Correct	Avg PSR	Avg N	Remarks
1	T1	1.0	8	78%	13.4	26.5	9 Training Images per Object
2	T2	1.0	7	81%	12.6	24.2
3	APC	0.0	6	83%	11.1	22.6
4	T1	0.0	13	64%	19.4	28.4
5	T2	1.0	11	69%	15.1	26.9
6	T1	1.0	4	89%	12.8	24.3	18 True Class Training Images per Object
7	T2	1.0	3	92%	12.6	23.9
8	APC	0.0	9	75%	10.4	19.6
9	T1	0.0	6	83%	17.6	24.7
10	T2	1.0	14	61%	12.3	22.9
11	T1	1.0	3	91%	11.3	24.1	18 Training Images per Object
12	T2	1.0	2	94%	10.4	19.2
13	APC	0.0	3	91%	9.3	20.1
14	T1	0.0	2	94%	14.4	22.2
15	T2	1.0	3	91%	10.4	21.4
16	T1	1.0	1	97%	11.4	17.6	19 Images per Object (CS on Edge)
17	T2	1.0	2	94%	12.2	19.4
18	APC	0.0	2	94%	13.5	18.2

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

	Filter h₁ (no constant bias vector)		Filter h₂ (constant bias vector used)
Bias	PSR	Peak	PSR	Peak
0.1	100.2	1.0	98.0	1.0
0.5	100.0	1.0	98.0	1.0
1.0	100.0	1.0	98.0	1.0
10.0	94.1	0.99	98.0	1.0
20.0	90.1	0.92	98.0	1.0
30.0	88.7	0.86	98.0	1.0
40.0	80.5	0.84	98.0	1.0
50.0	71.5	0.81	98.0	1.0
60.0	69.0	0.78	98.0	1.0
70.0	65.0	0.75	98.0	1.0

Phase Levels	Amplitude Levels	T1	T2	APC	Probability of Correct Recognition
2	16	16	11	12	0.26
	8	11	9	10	0.27
	4	5	4	4	0.12
	2	9	5	5	0.11
8	16	27	24	23	0.69
	8	18	11	18	0.43
	4	12	7	9	0.26
	2	9	5	5	0.18
16	128	31	32	32	0.88
	64	31	32	31	0.87
	32	31	30	30	0.84
	16	30	27	28	0.79
	8	19	15	20	0.50
	4	14	9	10	0.31
	2	10	6	7	021
32	128	34	33	34	0.94
	64	34	33	34	0.94
	32	34	33	33	0.93
	16	32	31	32	0.88
	8	25	24	26	0.70
	4	17	14	13	0.41
	2	16	11	9	0.33

Test Number	Object Class	Specified Peak at Center	Number of Errors	Percent Correct	Avg PSR	Avg N	Remarks
1	T1	1.0	8	78%	13.4	26.5	9 Training Images per Object
2	T2	1.0	7	81%	12.6	24.2
3	APC	0.0	6	83%	11.1	22.6
4	T1	0.0	13	64%	19.4	28.4
5	T2	1.0	11	69%	15.1	26.9
6	T1	1.0	4	89%	12.8	24.3	18 True Class Training Images per Object
7	T2	1.0	3	92%	12.6	23.9
8	APC	0.0	9	75%	10.4	19.6
9	T1	0.0	6	83%	17.6	24.7
10	T2	1.0	14	61%	12.3	22.9
11	T1	1.0	3	91%	11.3	24.1	18 Training Images per Object
12	T2	1.0	2	94%	10.4	19.2
13	APC	0.0	3	91%	9.3	20.1
14	T1	0.0	2	94%	14.4	22.2
15	T2	1.0	3	91%	10.4	21.4
16	T1	1.0	1	97%	11.4	17.6	19 Images per Object (CS on Edge)
17	T2	1.0	2	94%	12.2	19.4
18	APC	0.0	2	94%	13.5	18.2

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

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Metrics

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σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%

σ	Tank T1	Tank T2	APC
0	97%	94%	94%
1	97%	94%	94%
2	97%	91%	91%
4	94%	91%	91%
8	94%	91%	89%
12	91%	89%	89%
16	89%	89%	86%