Improved Bat Algorithm Applied to Multilevel Image Thresholding

Table 3

Comparison of the mean values and standard deviations 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 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	12.668336540	5.33𝐸−15	12.405792709	1.64𝐸−04	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552015642	2.82𝐸−03	15.820679619	8.84𝐸−04	15.607747002	1.42𝐸−14	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.549612938	1.94𝐸−02	18.467328310	6.64𝐸−03	18.640100415	3.00𝐸−02	18.414173744	2.07𝐸−04	18.357505953	2.02𝐸−02	18.615899102	1.78𝐸−14
	5	21.241857967	6.71𝐸−03	21.131564234	2.18𝐸−02	21.392020144	4.12𝐸−02	21.099092699	1.28𝐸−04	21.015922726	4.40𝐸−02	21.192396874	5.44𝐸−02
DE	2	12.668336540	5.33𝐸−15	12.405985592	5.33𝐸−15	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552578874	3.03𝐸−04	15.820902860	8.88𝐸−15	15.607743578	2.40𝐸−05	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.556749938	1.51𝐸−04	18.470970822	3.16𝐸−04	18.655660844	1.64𝐸−04	18.603017275	1.78𝐸−03	18.365579671	2.79𝐸−04	18.615769177	6.36𝐸−04
	5	21.245566656	2.34𝐸−04	21.149062508	1.78𝐸−03	21.401458219	3.21𝐸−04	21.409946039	3.55𝐸−15	21.024780111	4.59𝐸−04	21.210411012	1.12𝐸−04
CS	2	12.668336540	5.33𝐸−15	12.405985592	5.33𝐸−15	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552622213	1.07𝐸−14	15.820902860	8.88𝐸−15	15.607747002	1.42𝐸−14	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.556786861	2.49𝐸−14	18.471055578	2.49𝐸−14	18.655733570	1.07𝐸−14	18.414197322	6.53𝐸−05	18.365636309	1.78𝐸−14	18.615899102	1.78𝐸−14
	5	21.245645311	1.42𝐸−14	21.149400604	1.64𝐸−03	21.401608305	7.11𝐸−15	21.099125539	6.59𝐸−05	21.024962923	5.95𝐸−05	21.210455499	1.78𝐸−15
FA	2	12.668336540	5.33𝐸−15	12.405985592	5.33𝐸−15	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552622213	1.07𝐸−14	15.820902860	8.88𝐸−15	15.607747002	1.42𝐸−14	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.556786861	2.49𝐸−14	18.471014902	2.85𝐸−04	18.655723798	4.79𝐸−05	18.414213765	2.13𝐸−14	18.365636309	1.78𝐸−14	18.615899102	1.78𝐸−14
	5	21.245645311	1.42𝐸−14	21.149483979	1.46𝐸−03	21.401583877	7.33𝐸−05	21.099138996	0.00𝐸−00	21.024982760	0.00𝐸−00	21.210455499	1.78𝐸−15
BA	2	12.668336540	5.33𝐸−15	12.405885825	1.52𝐸−04	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552622213	1.07𝐸−14	15.820902860	8.88𝐸−15	15.607747002	1.42𝐸−14	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.555593147	8.36𝐸−03	18.469796068	3.52𝐸−03	18.644796771	2.68𝐸−02	18.414213765	2.13𝐸−14	18.356346829	2.13𝐸−02	18.615899102	1.78𝐸−14
	5	21.245645311	1.42𝐸−14	21.133082528	1.59𝐸−02	21.399205241	7.12𝐸−03	21.099138996	0.00𝐸−00	21.024982760	0.00𝐸−00	21.210452617	2.02𝐸−05
IBA	2	12.668336540	5.33𝐸−15	12.405985592	5.33𝐸−15	12.574798244	1.42𝐸−14	12.546393623	7.11𝐸−15	12.520359742	5.33𝐸−15	12.538208248	1.78𝐸−15
	3	15.747087798	1.42𝐸−14	15.552622213	1.07𝐸−14	15.820902860	8.88𝐸−15	15.607747002	1.42𝐸−14	15.566286745	1.24𝐸−14	15.751881495	5.33𝐸−15
	4	18.556786861	2.49𝐸−14	18.471055578	2.49𝐸−14	18.655733570	1.07𝐸−14	18.414213765	2.13𝐸−14	18.365636309	1.78𝐸−14	18.615899102	1.78𝐸−14
	5	21.245645311	1.42𝐸−14	21.150302316	1.78𝐸−14	21.401608305	7.11𝐸−15	21.099138996	0.00𝐸−00	21.024982760	0.00𝐸−00	21.210455499	1.78𝐸−14