A Comparative Study of Improved Artificial Bee Colony Algorithms Applied to Multilevel Image Thresholding

Table 2

The successful rate (SR) and maximum number of function calls (NFC_max) of the nine methods.

Image	𝑛	Between-class variance	Thresholds	PSO		DPSO		FODPSO		ABC		ABC/best/1		ABC/best/2		IABC/best/1		IABC/rand/1		CABC
		(a.k.a. VTR)		SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax	SR	NFCmax
Starfish	2	2546.885	85, 157	1.00	1350	1.00	3200	1.00	4200	1.00	1150	0.96	500	1.00	650	1.00	450	1.00	1000	0.94	800
	3	2779.925	68, 119, 177	1.00	2050	1.00	5600	0.92	8600	1.00	1900	1.00	850	1.00	950	1.00	800	1.00	1250	1.00	1000
	4	2865.707	60, 101, 138, 187	1.00	4550	0.98	11100	0.60	14700	1.00	6500	1.00	2000	1.00	3350	1.00	2200	1.00	3900	0.96	5350
	5	2912.859	52, 86, 117, 150, 194	0.72	7450	0.56	15000	0.26	12900	0.66	7250	0.88	5150	0.90	7500	1.00	4600	0.76	7300	0.76	6650
Snow	2	5261.705	80, 169	1.00	1150	1.00	3500	1.00	6700	1.00	1500	1.00	700	1.00	950	1.00	550	1.00	1100	0.98	1000
	3	5624.289	71, 139, 207	1.00	2150	1.00	8800	0.94	6600	1.00	2150	1.00	750	1.00	900	1.00	750	1.00	1150	0.94	1150
	4	5729.116	50, 92, 144, 208	0.98	4150	0.98	12000	0.68	15000	1.00	3500	1.00	1550	1.00	2150	1.00	2250	1.00	4050	1.00	4250
	5	5785.138	49, 91, 140, 192, 231	0.58	7100	0.60	14900	0.12	14900	0.98	7200	1.00	2700	1.00	3900	1.00	2550	1.00	6550	0.92	7000
Fox	2	12937.730	54, 173	1.00	550	1.00	2200	1.00	3100	1.00	650	1.00	300	1.00	400	1.00	350	1.00	500	1.00	450
	3	12973.370	28, 85, 190	1.00	1200	1.00	4500	0.98	7100	1.00	2050	1.00	700	1.00	1100	1.00	850	1.00	1750	0.76	1400
	4	12990.700	23, 58, 123, 208	0.96	2500	0.86	8200	0.60	8300	1.00	3150	0.88	1250	1.00	1950	1.00	1350	1.00	2400	0.82	2450
	5	12998.990	19, 40, 79, 139, 214	0.98	3550	0.02	12300	0.88	8100	0.98	5500	1.00	2450	1.00	3300	1.00	2200	0.98	6400	0.80	5650
Human	2	3064.796	108, 179	1.00	1350	1.00	3300	1.00	4200	1.00	1050	1.00	350	1.00	650	1.00	550	1.00	750	0.96	950
	3	3270.671	89, 145, 194	1.00	2650	1.00	4700	0.94	9500	1.00	2250	1.00	750	1.00	1000	1.00	800	1.00	1100	0.92	950
	4	3336.302	87, 140, 180, 213	0.98	4200	0.90	11200	0.40	15000	0.98	6200	0.98	7500	1.00	4000	1.00	3800	0.74	7000	0.56	7450
	5	3373.672	74, 110, 147, 183, 215	0.70	7050	0.48	14300	0.24	14600	0.66	7350	0.84	3600	1.00	5100	1.00	4600	0.92	4450	0.40	6800
Burro	2	3161.277	64, 131	1.00	1400	1.00	3100	0.98	5800	1.00	1750	0.96	450	1.00	1100	1.00	850	1.00	1400	0.98	1800
	3	3293.718	57, 107, 165	1.00	3150	1.00	6400	0.98	8800	1.00	2100	1.00	850	1.00	1200	1.00	1050	1.00	1400	1.00	1150
	4	3353.639	49, 79, 122, 171	0.96	3800	0.88	13000	0.34	15000	1.00	3850	0.72	1400	0.96	2200	1.00	1700	1.00	2650	0.98	2900
	5	3382.261	45, 70, 101, 140, 177	0.66	7200	0.78	14700	0.66	12500	0.44	7500	0.90	7050	0.82	6250	0.92	7000	0.48	7450	0.20	6950
Mountain	2	2372.923	61, 128	1.00	1750	1.00	2800	1.00	5400	1.00	1100	0.96	350	1.00	650	1.00	450	1.00	600	0.94	550
	3	2496.113	33, 77, 131	1.00	2150	1.00	6300	0.96	9300	1.00	2400	1.00	1000	1.00	1250	1.00	800	1.00	1950	1.00	1800
	4	2551.955	33, 73, 109, 147	0.98	5750	0.96	13800	0.36	13700	1.00	4600	0.96	3000	1.00	2650	1.00	2000	1.00	2800	0.94	4500
	5	2580.336	32, 69, 99, 125, 159	0.70	7200	0.66	14800	0.28	14700	1.00	6500	0.98	1950	1.00	3200	1.00	2050	1.00	4300	0.72	6450
Girl	2	2639.526	72, 145	1.00	1350	1.00	3200	1.00	4900	1.00	1400	1.00	500	1.00	700	1.00	500	1.00	900	0.98	750
	3	2867.882	46, 96, 161	1.00	1900	1.00	6300	0.88	10000	1.00	2250	1.00	800	1.00	1200	1.00	800	1.00	1650	0.76	1800
	4	2971.761	42, 84, 128, 182	0.96	6950	0.94	14400	0.52	14900	1.00	4050	1.00	2500	1.00	2350	1.00	1900	1.00	2600	0.94	4650
	5	3022.602	37, 70, 102, 140, 189	0.74	7450	0.78	14500	0.66	14800	0.82	7350	0.98	2850	1.00	6900	1.00	4700	0.84	7450	0.48	6500
Scenery	2	4686.124	105, 180	1.00	1150	1.00	4100	1.00	6900	1.00	2150	1.00	750	1.00	1050	1.00	800	1.00	1550	0.96	3800
	3	4837.868	76, 142, 211	1.00	3500	1.00	8200	0.84	9700	0.98	4000	0.98	1350	1.00	3150	1.00	1450	0.96	4950	0.92	4050
	4	4944.489	67, 111, 169, 218	0.98	5050	0.96	11200	0.48	12400	1.00	3050	0.98	1800	1.00	1800	1.00	1300	1.00	2100	0.98	2200
	5	4983.329	64, 98, 141, 184, 221	0.84	7000	0.58	14400	0.22	13800	0.80	7500	0.98	7100	0.96	7300	0.98	4750	0.56	7200	0.58	7300
Penguin	2	1823.215	71, 159	1.00	1200	1.00	3100	1.00	3400	1.00	800	1.00	350	1.00	450	1.00	350	1.00	550	1.00	500
	3	1892.583	68, 119, 194	1.00	2200	1.00	4700	0.92	5600	1.00	1850	0.98	700	1.00	900	1.00	800	1.00	1100	0.98	1050
	4	1915.004	54, 76, 121, 195	0.54	4300	0.62	15000	0.22	13800	0.56	6750	0.70	5000	0.84	5550	0.88	6350	0.80	7300	0.76	7400
	5	1932.441	53, 75, 114, 167, 220	0.82	7250	0.56	12500	0.20	13200	0.90	6300	0.96	2200	1.00	3200	1.00	2150	1.00	3250	0.94	3600
Pillar	2	3306.612	87, 164	1.00	1050	1.00	3700	1.00	4700	1.00	1400	0.98	600	1.00	850	1.00	550	1.00	1200	0.94	1450
	3	3534.700	58, 113, 184	1.00	2450	1.00	5900	0.74	9000	1.00	4350	1.00	1600	1.00	2000	1.00	1300	1.00	2050	0.98	2000
	4	3651.357	48, 90, 141, 200	0.94	4900	0.96	10500	0.66	14000	0.84	6250	0.98	4950	0.98	3500	1.00	4050	0.98	4300	0.82	4300
	5	3714.997	40, 73, 111, 156, 208	0.80	6900	0.80	14300	0.54	11600	0.62	7500	0.90	5850	0.96	6350	0.98	5650	0.90	7150	0.84	6200
Waterfall	2	1444.433	81, 143	1.00	1050	1.00	3100	1.00	4000	1.00	1000	1.00	400	1.00	600	1.00	500	1.00	700	1.00	700
	3	1597.070	68, 108, 167	1.00	4850	1.00	7600	0.84	9800	1.00	2650	1.00	1000	1.00	1300	1.00	1200	1.00	1950	0.92	1750
	4	1669.214	59, 91, 126, 181	0.92	6750	0.90	13900	0.56	14200	1.00	5350	0.90	4100	1.00	2700	1.00	2350	1.00	3750	0.94	6600
	5	1708.521	53, 80, 106, 138, 190	0.60	6800	0.64	14000	0.58	13100	0.46	7150	0.96	3300	0.94	5900	1.00	4450	0.76	6550	0.56	6600
Bridge	2	3383.821	54, 135	1.00	1400	1.00	2500	1.00	5000	1.00	900	0.98	450	1.00	450	1.00	450	1.00	700	0.98	700
	3	3567.597	49, 108, 169	1.00	3650	0.98	6300	0.70	9300	1.00	2150	0.98	900	1.00	1550	1.00	900	1.00	1800	1.00	1650
	4	3660.335	34, 73, 117, 174	0.96	5450	0.92	13100	0.64	14000	0.80	7000	0.92	4800	1.00	4200	1.00	3400	0.90	4750	0.70	3700
	5	3710.264	26, 59, 90, 128, 179	0.70	6000	0.66	14900	0.68	14100	0.94	6950	0.94	3550	0.96	5000	0.96	3750	0.78	7350	0.22	6950