Improved Bat Algorithm Applied to Multilevel Image Thresholding

Table 4

Comparison of the mean values and standard deviations obtained for the PSO, DE, CS, FA, BA, and IBA based on Otsu’s criterion for six test images over 50 runs.

Alg.	𝐾	Barbara		Living room		Boats		Goldhill		Lake		Aerial
		Mean values	St. dev.	Mean values	St. dev.	Mean values	St. dev.	Mean values	St. dev.	Mean values	St. dev.	Mean values	St. dev.
PSO	2	2608.610778507	1.82𝐸−12	1627.909172752	0.00𝐸−00	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	3.64𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.163280467	2.27𝐸−12	1760.103018395	2.27𝐸−13	1994.536306242	1.59𝐸−12	2220.372641501	1.36𝐸−12	4112.631097687	4.55𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.260804034	6.66𝐸−03	1828.864376614	1.59𝐸−12	2059.866220175	4.22𝐸−04	2295.380095430	1.48𝐸−03	4180.883976390	7.41𝐸−03	1955.085619462	7.65𝐸+00
	5	2890.975549258	5.05𝐸−02	1871.984827146	2.29𝐸−02	2092.771150715	8.36𝐸−03	2331.156479206	3.56𝐸−04	4216.942888298	3.99𝐸−03	1979.170306260	2.51𝐸+00
DE	2	2608.610778507	1.82𝐸−12	1627.909172752	0.00𝐸−00	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	3.64𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.162093432	8.31𝐸−03	1760.103018395	2.27𝐸−13	1994.535269293	7.26𝐸−03	2220.372641501	1.36𝐸−12	4112.631097687	4.55𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.261305066	2.80𝐸−03	1828.860328016	1.30𝐸−02	2059.865271461	6.85𝐸−03	2295.380095430	1.48𝐸−03	4180.883976390	7.41𝐸−03	1955.085619462	7.65𝐸+00
	5	2890.971346990	2.05𝐸−02	1871.976701063	2.34𝐸−02	2092.766907541	2.71𝐸−02	2331.156479206	3.56𝐸−04	4216.942888298	3.99𝐸−03	1979.170306260	2.51𝐸+00
CS	2	2608.610778507	1.82𝐸−12	1627.909172752	0.00𝐸−00	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	3.64𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.163280467	2.27𝐸−12	1760.103018395	2.27𝐸−13	1994.536306242	1.59𝐸−12	2220.372641501	1.36𝐸−12	4112.631097687	4.55𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.261511717	2.45𝐸−03	1828.864376614	1.59𝐸−12	2059.866280428	1.36𝐸−12	2295.380469158	2.27𝐸−12	4180.886161109	0.00𝐸−00	1957.017965982	0.00𝐸−00
	5	2890.976540127	4.85𝐸−04	1871.990230213	2.70𝐸−03	2092.775817560	1.03𝐸−03	2331.155240485	4.76𝐸−03	4216.943583790	9.09𝐸−13	1980.651043072	1.16𝐸−02
FA	2	2608.610778507	1.82𝐸−12	1627.909172752	0.00𝐸−00	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	3.64𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.163280467	2.27𝐸−12	1760.103018395	2.27𝐸−13	1994.536306242	1.59𝐸−12	2220.372641501	1.36𝐸−12	4112.631097687	4.55𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.262131671	4.55𝐸−13	1828.864376614	1.59𝐸−12	2059.866280428	1.36𝐸−12	2295.380469158	2.27𝐸−12	4180.886161109	0.00𝐸−00	1957.017965982	0.00𝐸−00
	5	2890.976609405	3.64𝐸−12	1871.990616316	0.00𝐸−00	2092.773515829	3.57𝐸−03	2331.156597921	2.27𝐸−12	4216.943583790	9.09𝐸−13	1980.656737348	9.09𝐸−13
BA	2	2608.610778507	1.36𝐸−12	1627.909172752	2.27𝐸−13	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	4.09𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.163280467	1.36𝐸−12	1760.103018395	2.27𝐸−13	1994.536306242	1.14𝐸−12	2220.372641501	1.36𝐸−12	4112.631097687	3.64𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.262131671	4.55𝐸−13	1828.864376614	2.27𝐸−12	2059.866280428	9.09𝐸−13	2295.380469158	2.27𝐸−12	4180.886161109	0.00𝐸−00	1957.017965982	2.27𝐸−13
	5	2890.976609405	2.73𝐸−12	1871.990616316	0.00𝐸−00	2092.772750357	3.78𝐸−03	2331.156597921	2.27𝐸−12	4216.943583790	3.64𝐸−12	1979.513584665	2.29𝐸+00
IBA	2	2608.610778507	1.36𝐸−12	1627.909172752	0.00𝐸−00	1863.346730649	0.00𝐸−00	2069.510202452	4.55𝐸−13	3974.738214185	4.09𝐸−12	1808.171050536	2.27𝐸−13
	3	2785.163280467	1.36𝐸−12	1760.103018395	2.27𝐸−13	1994.536306242	1.14𝐸−12	2220.372641501	1.36𝐸−12	4112.631097687	3.64𝐸−12	1905.410606582	1.14𝐸−12
	4	2856.262131671	4.55𝐸−13	1828.864376614	2.27𝐸−12	2059.866280428	9.09𝐸−13	2295.380469158	2.27𝐸−12	4180.886161109	0.00𝐸−00	1957.017965982	0.00𝐸−00
	5	2890.976609405	2.73𝐸−12	1871.990616316	0.00𝐸−00	2092.775965336	1.36𝐸−12	2331.156597921	2.27𝐸−12	4216.943583790	3.64𝐸−12	1980.656737348	9.09𝐸−13