Cost-effective implementation of order-statistics-based vector filters using minimax approximations

M. Emre Celebi; Hassan A. Kingravi; Rastislav Lukac; Fatih Celiker

doi:10.1364/JOSAA.26.001518

Journal of the Optical Society of America A
Vol. 26,
Issue 6,
pp. 1518-1524
(2009)
•https://doi.org/10.1364/JOSAA.26.001518

Cost-effective implementation of order-statistics-based vector filters using minimax approximations

M. Emre Celebi, Hassan A. Kingravi, Rastislav Lukac, and Fatih Celiker

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M. Emre Celebi, Hassan A. Kingravi, Rastislav Lukac, and Fatih Celiker, "Cost-effective implementation of order-statistics-based vector filters using minimax approximations," J. Opt. Soc. Am. A 26, 1518-1524 (2009)

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Abstract

Vector operators based on robust order statistics have proved successful in digital multichannel imaging applications, particularly color image filtering and enhancement, in dealing with impulsive noise while preserving edges and fine image details. These operators often have very high computational requirements, which limits their use in time-critical applications. This paper introduces techniques to speed up vector filters using the minimax approximation theory. Extensive experiments on a large and diverse set of color images show that proposed approximations achieve an excellent balance among ease of implementation, accuracy, and computational speed.

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Equations (18)

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Function	ε	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$
ARCSIN	$2.097814 e - 05$	$2.097797 e - 05$	1.412840	$1.429881 e - 02$	$6.704361 e - 02$	$6.909677 e - 02$
ARCOS	$1.048949 e - 05$	1.570786	$- 9.990285 e - 01$	$- 1.429899 e - 02$	$- 9.481335 e - 02$	$- 1.381942 e - 01$

p	ε	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$
2	$1.785517 e - 01$	$8.214528 e - 01$	$- 3.186948 e - 01$	$2.544088 e - 02$
3	$8.259345 e - 02$	$9.174126 e - 01$	$- 5.631179 e - 01$	$1.015041 e - 01$	$- 5.519183 e - 03$
4	$3.337085 e - 02$	$9.666313 e - 01$	$- 7.620584 e - 01$	$2.145386 e - 01$	$- 2.509526 e - 02$	$1.032877 e - 03$

Term	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$
Numerator	$3.206619 e - 02$	$- 1.195191 e - 02$	$1.756974 e - 03$	$- 1.199261 e - 04$	$3.182685 e - 06$
Denominator	$3.206627 e - 02$	$2.011147 e - 02$	$5.853684 e - 03$	$9.780143 e - 04$	$1.251598 e - 04$

Term	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$
Numerator	$- 1.519742 e - 04$	$- 6.835769 e - 02$	$- 8.856923 e - 01$	$- 5.369609 e - 01$	1.491165
Denominator	$1.532270 e - 02$	$3.987796 e - 01$	1.461793	$6.827004 e - 01$	$- 4.469776 e - 02$

Filter	Measure	Uncorrelated Impulsive		Correlated Impulsive		Mixed
Filter	Measure	Mean(%)	Stdev(%)	Mean(%)	Stdev(%)	Mean(%)	Stdev(%)
BVDF	MAE	$- 1.000$	1.648	$- 0.926$	1.558	$- 0.022$	0.310
	MSE	$- 0.571$	1.924	0.171	2.426	$- 0.131$	1.103
	NCD	$- 0.783$	1.283	$- 0.759$	1.154	0.007	0.193
	Time	1381.783	16.576	1371.314	16.479	1408.964	11.964
AMNFE	MAE	$- 0.025$	0.137	$- 0.016$	0.136	$- 0.001$	0.137
	MSE	$- 0.070$	0.526	$- 0.064$	0.754	$- 0.006$	0.317
	NCD	$- 0.020$	0.177	$- 0.031$	0.195	$- 0.004$	0.176
	Time	142.700	0.225	143.496	0.214	140.814	0.187
EVMF	MAE	$- 0.141$	0.524	$- 0.108$	0.489	0.000	0.133
	MSE	$- 0.376$	1.732	$- 0.203$	1.496	0.013	0.241
	NCD	$- 0.147$	0.837	$- 0.149$	0.625	$- 0.004$	0.138
	Time	236.582	0.672	236.105	0.646	215.000	0.449

Filter	Measure	20%		30%		40%
Filter	Measure	Mean (%)	Stdev (%)	Mean (%)	Stdev (%)	Mean (%)	Stdev (%)
BVDF	MAE	$- 0.753$	1.311	$- 0.626$	1.070	$- 0.419$	0.861
	MSE	0.193	2.994	0.027	2.630	$- 0.073$	1.855
	NCD	$- 0.607$	1.016	$- 0.530$	0.881	$- 0.424$	0.802
	Time	1342.074	15.480	1328.939	14.784	1301.070	14.026
AMNFE	MAE	$- 0.032$	0.231	0.030	0.342	$- 0.001$	0.315
	MSE	$- 0.125$	0.945	0.021	1.172	0.006	0.812
	NCD	$- 0.045$	0.349	0.034	0.478	0.027	0.395
	Time	143.460	0.241	145.513	0.226	145.362	0.249
EVMF	MAE	$- 0.030$	0.676	0.013	0.534	0.067	0.476
	MSE	$- 0.056$	1.539	0.046	1.105	0.065	0.867
	NCD	$- 0.004$	0.829	0.026	0.633	0.088	0.547
	Time	228.346	0.551	222.356	0.431	216.354	0.423

Abstract

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Tables (6)

Equations (18)

Journal of the Optical Society of America A