Improved Bat Algorithm Applied to Multilevel Image Thresholding

Table 5

Mean of the CPU times (in milliseconds) and mean of the iteration numbers obtained for the PSO, DE, CS, FA, BA, and IBA based on Kapur’s entropy criterion for six test images over 50 runs.

Alg.	𝐾	Barbara		Living room		Boats		Goldhill		Lake		Aerial
		Mean time (ms)	Mean iteration	Mean time (ms)	Mean iteration	Mean time (ms)	Mean iteration	Mean time (ms)	Mean iteration	Mean time (ms)	Mean iteration	Mean time (ms)	Mean iteration
PSO	2	2.18	9.22	102.82	1165.14	3.08	11.84	2.54	8.84	2.41	8.86	2.62	10.7
	3	3.30	14.28	21.96	218.56	16.23	136.58	3.18	13.54	3.65	14.58	3.24	13.9
	4	49.00	495.36	77.23	853.62	123.62	1367.86	10.22	97.86	26.99	295.76	4.03	19.76
	5	88.16	1050.8	153.53	1725.22	74.46	814.22	23.56	258.5	77.64	893.98	58.54	695.92
DE	2	3.56	14.59	4.34	18.92	3.38	16.92	2.15	16.44	5.0	15.74	3.81	17.01
	3	6.3	30.0	8.02	70.60	8.84	43.32	7.94	69.30	6.24	30.04	6.51	30.96
	4	24.46	240.68	33.62	322.91	46.92	477.16	48.36	125.48	22.12	165.08	14.12	124.56
	5	47.8	527.96	77.14	801.21	65.48	683.29	22.2	116.28	55.9	603.01	56.38	624.16
CS	2	71.04	194.54	53.30	129.84	53.84	135.58	82.29	209.48	70.48	183.36	56.32	150.88
	3	150.71	420.42	125.48	322.42	128.92	330.22	149.68	441.64	138.23	375.66	104.75	292.22
	4	189.31	518.58	222.48	570.6	170.28	436.02	180.31	500.11	220.44	604.58	174.84	482.26
	5	301.65	786.64	499.42	1303.8	247.15	631.36	280.55	720.34	336.29	915.92	193.21	532.76
FA	2	15.01	11.96	17.02	11.9	16.39	12.32	13.66	10.08	15.92	12.32	13.86	11.0
	3	34.07	29.82	37.24	29.7	36.24	29.24	32.08	28.66	34.56	29.42	32.83	29.18
	4	43.30	38.6	50.25	77.9	54.68	117.8	41.11	36.6	43.84	37.66	43.18	38.96
	5	50.15	44.04	104.74	515.06	76.22	241.94	48.95	42.01	50.31	43.6	50.46	45.46
BA	2	1.78	2.04	96.82	722.92	24.17	142.96	2	1.8	1.6	1.74	1.22	5.06
	3	2.52	6.74	89.78	734.8	64.96	421.48	2.84	6.94	2.32	8.82	3.6	14.4
	4	40.2	146.46	124.16	1098.72	115.34	969.66	6.76	37.18	56.88	397.8	32.6	134.52
	5	60.9	412.92	175.32	1718.82	98.42	785.04	30.92	157.92	39.24	238.12	64.48	463.78
IBA	2	2.12	9.14	6.34	25.14	5.36	10.02	2.88	8.92	2.28	9.18	2.7	11.18
	3	3.84	16.8	5.3	22.8	5.5	22.4	3.84	16.62	5	17.5	5.96	19.88
	4	7.16	26.26	9.92	35.48	10.3	43.3	6.28	28.82	7.14	26.98	7.48	30.98
	5	8.66	40.06	24.7	134.38	14.4	50.9	7.88	38.62	9.5	42.7	9.5	44.98