Pattern discrimination by multiple circular harmonic components

Yuan-Neng Hsu; Henri H. Arsenault

doi:10.1364/AO.23.000841

Applied Optics
Vol. 23,
Issue 6,
pp. 841-844
(1984)
•https://doi.org/10.1364/AO.23.000841

Pattern discrimination by multiple circular harmonic components

Yuan-Neng Hsu and Henri H. Arsenault

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Yuan-Neng Hsu and Henri H. Arsenault, "Pattern discrimination by multiple circular harmonic components," Appl. Opt. 23, 841-844 (1984)

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Abstract

Multiple circular harmonic components of the same target can be used jointly to discriminate between the target and other objects. Two methods are considered: Coherent superposition and decision making in multidimensional space. Experimental results for the discrimination between a tank and a truck are given.

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r	$f_{r}^{'} (4)$	$f_{r}^{'} (6)$	$f_{r}^{'} (8)$
1	0.0169 + j0.0001	0.0002 + j0.0001	− 0.008j + j0.0000
2	0.0145 + j0.0223	0.0762 + j0.0004	0.0292 − j0.0103
3	0.0125 + j0.0580	− 0.0212 + j0.0014	0.0211 − j0.0029
4	− 0.6736 − j0.2512	− 0.0435 − j0.1324	0.1889 + j0.1365
5	− 0.8451 − j0.9387	0.5732 + j0.1636	0.0163 + j0.5355
6	1.9406 − j0.7905	2.0996 − j0.1860	− 0.3770 − j1.0357
7	1.9060 − j0.7660	0.8838 − j0.6331	− 0.9440 − j0.5907
8	1.59j8 − j0.7060	0.3511 − j0.8204	− 0.4945 − j0.5969
9	1.1263 − j0.3290	0.4909 − j0.4499	0.0400 − j0.5860
10	0.1805 + j0.4422	0.7696 + j0.2416	0.9891 + j0.3267
11	0.0505 − j0.0577	0.6915 − j0.1952	1.1506 + j0.4636
12	− 1.3661 + j0.0089	− 0.5856 − j0.6280	0.0656 + j0.8291
13	− 2.7109 + j0.3338	− 0.8151 − j0.5167	0.2520 + j0.9459
14	− 2.6494 + j0.8289	0.2334 − j0.1739	1.5173 + j0.8167
15	− 0.9449 + j0.4729	2.0799 + j0.1214	1.8292 + j0.0919
16	1.1367 + j0.1543	3.0513 + j0.0501	0.9693 − j0.6333
17	2.1446 + j0.1436	1.8871 − j0.1418	− 1.6535 − j0.4952

r	f_r(4)	f_r(6)	f_r(8)
1	1.6967 + j0.0001	0.0004 − j0.0320	− 0.0087 + j0.0000
2	2.6735 + j1.1573	− 0.0437 + j0.0011	0.0292 − j0.0103
3	1.7300 + j1.1261	− 0.0607 − j0.0628	0.0211 − j0.0029
4	0.8408 + j2.0820	0.1265 − j0.0113	0.1889 + j0.1365
5	− 0.1243 + j2.2173	0.1432 − j0.2680	0.0163 + j0.5355
6	− 1.2280 + j1.3009	1.1739 − j0.1359	− 0.3770 − j1.0357
7	− 0.7293 + j1.2090	1.2491 − j0.5763	− 0.9440 − j0.5907
8	− 2.0041 + j0.2213	0.0425 − j0.1600	− 0.4945 − j0.5969
9	− 2.4100 + j1.1468	− 1.8454 + j0.4687	0.0400 − j0.5860
10	− 1.6033 + j1.5458	− 2.2004 − j0.0607	0.9891 + j0.3267
11	− 0.0046 + j1.7126	− 1.2843 − j0.3093	1.1506 + j0.4636
12	2.4855 + j1.4352	− 1.2035 − j0.2088	0.0656 + j0.8291
13	2.6121 + j0.5054	− 1.0325 − j0.8487	0.2520 + j0.9459
14	2.4086 − j0.1871	0.3891 + j0.0962	1.5148 + j0.8167
15	− 0.2605 − j0.0854	2.3231 + j0.6994	1.8292 + j0.0919
16	− 2.3660 + j0.0755	4.3185 + j0.1645	0.9693 − j0.6333
17	− 3.2859 + j0.1389	3.6081 − j0.3069	− 1.6535 − j0.4952
Proper center (x,y)	(60,61)	(64,69)	(64,64)

Order (M_k)	4	6	8
Target output A (M_k)	6190.0	5002.5	2388.0
Object output B(M_k)	4567.5	3537.5	1708.0

Input SNR	1	1.3	1.6	2.0	2.5	3.0	3.5	4.0	4.5	5.0	6.0
P_n.d.	0.244	0.214	0.190	0.163	0.134	0.114	0.094	0.080	0.068	0.058	0.041
P_f.a.	0.243	0.213	0.190	0.161	0.135	0.111	0.095	0.080	0.067	0.057	0.039

r	$f_{r}^{'} (4)$	$f_{r}^{'} (6)$	$f_{r}^{'} (8)$
1	0.0169 + j0.0001	0.0002 + j0.0001	− 0.008j + j0.0000
2	0.0145 + j0.0223	0.0762 + j0.0004	0.0292 − j0.0103
3	0.0125 + j0.0580	− 0.0212 + j0.0014	0.0211 − j0.0029
4	− 0.6736 − j0.2512	− 0.0435 − j0.1324	0.1889 + j0.1365
5	− 0.8451 − j0.9387	0.5732 + j0.1636	0.0163 + j0.5355
6	1.9406 − j0.7905	2.0996 − j0.1860	− 0.3770 − j1.0357
7	1.9060 − j0.7660	0.8838 − j0.6331	− 0.9440 − j0.5907
8	1.59j8 − j0.7060	0.3511 − j0.8204	− 0.4945 − j0.5969
9	1.1263 − j0.3290	0.4909 − j0.4499	0.0400 − j0.5860
10	0.1805 + j0.4422	0.7696 + j0.2416	0.9891 + j0.3267
11	0.0505 − j0.0577	0.6915 − j0.1952	1.1506 + j0.4636
12	− 1.3661 + j0.0089	− 0.5856 − j0.6280	0.0656 + j0.8291
13	− 2.7109 + j0.3338	− 0.8151 − j0.5167	0.2520 + j0.9459
14	− 2.6494 + j0.8289	0.2334 − j0.1739	1.5173 + j0.8167
15	− 0.9449 + j0.4729	2.0799 + j0.1214	1.8292 + j0.0919
16	1.1367 + j0.1543	3.0513 + j0.0501	0.9693 − j0.6333
17	2.1446 + j0.1436	1.8871 − j0.1418	− 1.6535 − j0.4952

Abstract

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Tables (4)

Equations (18)

Applied Optics