Image recognition with the discrete rectangular-wave transform

O. K. Ersoy; D. Y. Kim

doi:10.1364/JOSAA.5.000005

Journal of the Optical Society of America A
Vol. 5,
Issue 1,
pp. 5-18
(1988)
•https://doi.org/10.1364/JOSAA.5.000005

Image recognition with the discrete rectangular-wave transform

O. K. Ersoy and D. Y. Kim

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O. K. Ersoy and D. Y. Kim, "Image recognition with the discrete rectangular-wave transform," J. Opt. Soc. Am. A 5, 5-18 (1988)

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Abstract

The discrete rectangular-wave transform (DRWT) is obtained by replacing the sines and cosines in the discrete Fourier transform (DFT) with the bipolar rectangular-wave function. The DRWT matrix contains no numbers other than ±1, ±j, and their combinations. There are also both parallel and sequential fast algorithms and architectures for its electro-optical or electronic implementation, which are much faster and easier than fast-Fourier-transform algorithms and architectures. In recognition tasks, the DRWT is used mainly as a feature extractor and is followed by a classification classification algorithm. In experiments involving shape and image recognition, the DRWT is observed to have better performance than the DFT, especially when the classes of objects to be recognized are similar. The DRWT can also be used in a number of ways for distortion-free recognition.

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Equations (28)

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N	Values of c(m, N)
8	0.75	0.25
16	0.625	0.125	0.125	0.125
32	0.8125	−0.1875	0.0625	−0.1875	−0.1875	0.3125	0.0625	0.3125
64	0.759191	−0.181985		0.0900735	−0.181985	−0.093750		0.273897
	−0.0275735	0.0386029		0.0533088	−0.055147	−0.0275735		−0 055147
	−0.093750	0.0386029		0.0900735	0.273897
128	0.763859	−0.134031		0.0153034	−0.047955	−0.0905756		0.0186303
	−0.0594284	−0.0456101		0.0266544	−0.0174346	−0.0594284		−0.0174347
	−0.0317441	−0.0456101		0.0153034	0.0186303	−0.0466643		−0.047955
	0.0747702	−0.134031		−0.0031744	0.255267			0.0318550
	0.0266544	0.011920		0.0318550	0.011920	−0.0905756		0.0842131
	0.747702	0.255267

Test Object	Type of Normalization	Euclidean Distance from the Following Library Object

		a	b	c	d	e	f
a	I	0	0.2500	0.3684	0.3216	0.2679	0.4985
	II	0	0.293	0.4219	0.3814	0.355	0.422
	III	0	0.293	0.4219	0.3814	0.355	0.422
b	I	0	0.2500	0	0.4899	0.3067	0.5429
	II	0.293	0	0.4105	0.3862	0.3428	0.3873
	III	0.293	0	0.4105	0.3862	0.3428	0.3873
c	I	0.3684	0.4864	0	0.1887	0.2824	0.4607
	II	0.4219	0.4105	0	0.1231	0.4405	0.092
	III	0.4219	0.4105	0	0.1231	0.4405	0.092
d	I	0.3216	0.4899	0.1887	0	0.2906	0.4761
	II	0.3814	0.3862	0.1231	0	0.4216	0.184
	III	0.3814	0.3862	0.1231	0	0.4216	0.184
e	I	0.2679	0.3067	0.2824	0.2906	0	0.4799
	II	0.355	0.3428	0.4405	0.4216	0	0.415
	III	0.355	0.3428	0.4405	0.4216	0	0.415
f	I	0.4985	0.5429	0.4607	0.4761	0.4799	0
	II	0.422	0.3873	0.092	0.184	0.415	0
	III	0.422	0.3873	0.092	0.184	0.415	0

Test Object	Type of Normalization	Euclidean Distance from the Following Library Object

		a	b	c	d	e	f
a	I	0	0.2553	0.3762	0.3258	0.2767	0.5671
	II	0	1.354	0.6161	0.6296	0.7224	0.5730
	III	0	0.6816	0.3695	0.3241	0.2848	0.3328
b	I	0.2553	0	0.5021	0.4979	0.3253	0.6251
	II	1.354	0	1.402	1.366	1.352	1.356
	III	0.6816	0	0.7352	0.7562	0.6119	0.6372
c	I	0.3762	0.5021	0	0.1988	0.2984	0.5276
	II	0;6161	1.402	0	0.1988	0.2986	0.1995
	III	0.3695	0.7352	0	0.2201	0.2909	0.2105
d	I	0.3258	0.4979	0.1988	0	0.2925	0.5399
	II	0.6296	1.366	0.1988	0	0.2924	0.3124
	III	0.3241	0.7562	0.2201	0	0.3213	0.3467
e	I	0.2767	0.3253	0.2984	0.2925	0	0.5614
	II	0.7224	1.352	0.2986	0.2924	0	0.2972
	III	0.2848	0.6119	0.2909	0.3213	0	0.2821
f	I	0.5671	0.6251	0.5276	0.5399	0.5614	0
	II	0.5730	1.356	0.1995	0.3124	0.2972	0
	III	0.3328	0.6372	0.2105	0.3467	0.2821	0

SNR (dB)	Type of Normalization	% Correct Shape Recognition

		DFT Method	DRWT Method
3	I	16.7	33.3
	II	50	50
	III	50	83.3
10	I	50	66.7
	II	66.7	66.7
	III	66.7	100
20	I	83.3	83.3
	II	66.7	83.3
	III	66.7	100
30	I	83.3	83.3
	II	83.3	100
	III	83.3	100
∞	I	100	100
	II	100	100
	III	100	100

SNR (dB)	Type of Normalization	% Correct Shape Recognition

		DFT Method	DRWT Method
3	I	16.7	33.3
	II	50	66.7
	III	33.3	66.7
10	I	50	66.7
	II	66.7	66.7
	III	66.7	83.3
20	I	83.3	83.3
	II	66.7	83.3
	III	66.7	100
30	I	83.3	83.3
	II	83.3	83.3
	III	83.3	100
∞	I	100	100
	II	100	100
	III	100	100

Abstract

Cited By

Figures (10)

Tables (12)

Equations (28)

Journal of the Optical Society of America A