Advanced distortion-invariant minimum average correlation energy (MACE) filters

David Casasent; Gopalan Ravichandran

doi:10.1364/AO.31.001109

Applied Optics
Vol. 31,
Issue 8,
pp. 1109-1116
(1992)
•https://doi.org/10.1364/AO.31.001109

Advanced distortion-invariant minimum average correlation energy (MACE) filters

David Casasent and Gopalan Ravichandran

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David Casasent and Gopalan Ravichandran, "Advanced distortion-invariant minimum average correlation energy (MACE) filters," Appl. Opt. 31, 1109-1116 (1992)

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Abstract

The original minimum average correlation energy (MACE) filter is addressed by using a new database (strategic relocatable objects, missile launchers) and including noise performance, depression angle, and resolution effects on the number of training set images that are required. Major attention is given to our new MACE filter algorithms for distortion-invariant pattern recognition: shifted-MACE filters (to suppress large false correlation peaks), minimum variance-MACE filters (for improved noise performance), multiple symbolic encoded filters (to reduce the effect of false correlation peaks), and Gaussian-MACE filters (to improve noise performance and intraclass recognition and reduce the training set size).

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Test Number	Images (Type, Size)	Number of training Images	Number of Errors
Test 1: Number of training images	SCUD-B, 30°	22	3
	(32 × 32)	24	1
		25	1
		26	1
		27	0
Test 2: Resolution	SCUD-B, 30°	32	3
	(64 × 64)	33	2
		34	0
Test 3: Object detail dependence	APC, 30°	14	3
	(32 × 32)	15	2
		16	0
Test 4: Depression angle dependence	SCUD-B, 70°	32	3
	(32 × 32)	33	2
		34	1
		35	0
Test 5: Depression angle/object detail	ZSU-23,70°	25	3
	(32 × 32)	26	2
		27	0

Test Number	Test Conditions	Training Set for P_c = 100%
Test 1	Central peak only	27 True class
		No false class
Test 2	Full correlation plane	27 True class
		4 False class

Test Conditions	PSR Data
All 36 true-class images	PSR(AV) = 116–284
	PSR(SD) = 33–70
Only 27 true-class training images	PSR(AV) > 200
	PSR(SD) > 50
All 36 false-class images	PSR(AV) < 78
	PSR(SD) < 22
	Maximum peak = 0.46

Filter	ZSU-23	SA-13	FROG-D	SCUD-B
1	1	0	1	0
2	1	0	0	1
3	0	1	1	0
4	0	1	0	1

Test No.	Test Conditions	Data
1	Only central correlation peak considered	P_c = 100%
2	Full correlation plane tests (no shifted false images used)	20 false-class images with sidelobes >0.5 for each filter
3	Symbolic processing of Test 2 data (no shifted false images used)	Three false-class images with sidelobes >0.5 at the same pixel
4	Symbolic processing using three shifted training images (full correlation plane)	P_c = 100%

Filter	ZSU-23	SA-13	FROG-D	SCUD-B
1	24(T)	2(F),1(S)	19(T)	2(F)
2	25(T)	3(F)	2(F),1(S)	21(T)
3	3(F),1(S)	28(T)	20(T)	3(F)
4	3(F)	29(T)	2(F)	21(T)

Test Conditions	MACE Performance	G-MACE Performance
Training set for P_c = 100% (central peak only)	27 True class	24 True class
Correlation plane sidelobes	Six sidelobes	Two sidelobes
PSR(AV) for true class	116–284	≈10% worse than MACE

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