Hierarchical Artificial Bee Colony Optimizer with Divide-and-Conquer and Crossover for Multilevel Threshold Image Segmentation

Table 9

Objective value, standard deviation, and PRI by the compared population-based methods on Otsu algorithm.

Image	M − 1	Objective values (standard deviation)/PRI
		HABC	ABC	PSO	CMA-ES	EGA
38092	2	2.50644 ()/; 0.74248	2.50644 ()/; 0.74248	2.50644 ()/; 0.74248	2.50474 (18.3953)/; 0.73305	2.50634 (0.2663)/; 0.74268
	3	2.52594 (0.0257346)/; 0.78598	2.52594 (0.0259)/; 0.78611	2.52594 (0.0462)/; 0.78546	2.52354 (39.6597)/; 0.77094	2.52564 (1.4455)/; 0.78657
	4	2.53454 (0)/; 0.7994	2.53454 (0.0192)/; 0.79932	2.53444 (0.8140)/; 0.80059	2.52764 (65.1685)/; 0.77711	2.53404 (2.0187)/; 0.79761
14037	2	7.53603 (0.00682035)/; 0.73621	7.53613 (0.0068)/; 0.73621	7.53613 (0)/; 0.73614	7.47303 (99.7498)/; 0.72324	7.53593 (0.2176)/; 0.73693
	3	7.65933 ()/; 0.8019	7.65933 (0)/; 0.8019	7.65923 (0.2069)/; 0.80121	7.60063 (47.7619)/; 0.76189	7.65673 (1.4649)/; 0.79826
	4	7.71513 ()/; 0.79968	7.71513 ()/  0.79968	7.71203 (2.7500)/; 0.79803	7.67293 (57.4010)/; 0.78318	7.71103 (2.3737)/; 0.79919
24077	2	2.11334 ()/; 0.68224	2.11334 ()/; 0.68224	2.11334 ()/; 0.68224	2.11254 (7.4668)/; 0.6775	2.11334 (0.2056)/; 0.68234
	3	2.14114 ()/; 0.73976	2.14114 ()/; 0.73976	2.14114 (0.0720)/; 0.73931	2.14044 (9.8471)/; 0.73678	2.14094 (1.1128)/; 0.73934
	4	2.14994 ()/; 0.7637	2.14994 (0.0337)/; 0.76374	2.14974 (1.9265)/; 0.76223	2.14824 (11.1739)/; 0.7604	2.14954 (2.4823)/; 0.76263
163085	2	7.83653 (0)/; 0.61394	7.83653 (0)/; 0.61394	7.83653 (0)/; 0.61394	7.81563 (41.9717)/; 0.6188	7.83643 (0.1368)/; 0.6133
	3	7.90633 (0.0639873)/; 0.65094	7.90633 (0)/; 0.65081	7.90603 (0.7760)/; 0.64954	7.84573 (36.3918)/; 0.59472	7.90473 (1.4445)/; 0.64885
	4	7.94263 (0)/; 0.6706	7.94263 (0.0415)/; 0.67069	7.93983 (3.0506)/; 0.66165	7.91693 (21.5228)/; 0.6494	7.94023 (1.5929)/; 0.66836
101085	2	1.25594 ()/; 0.63896	1.25594 ()/; 0.63896	1.25594 ()/; 0.63896	1.25464 (31.8525)/; 0.63008	1.25594 (0.1912)/; 0.63819
	3	1.27884 (0.0338175)/; 0.70818	1.27884 (0)/; 0.70813	1.27874 (0.0692)/; 0.70822	1.27504 (54.4844)/; 0.68414	1.27854 (2.4630)/; 0.70652
	4	1.29044 (0.0274838)/; 0.73785	1.29044 (0.0466)/; 0.73806	1.29034 (1.6045)/; 0.73021	1.28854 (10.8032)/; 0.73136	1.28984 (3.2212)/; 0.73374
101087	2	2.85494 (0)/; 0.76849	2.85504 ()/; 0.76849	2.85504 ()/; 0.76849	2.84734 (186.3278)/; 0.74149	2.85494 (0.2269)/; 0.76852
	3	2.87154 (0.0071386)/; 0.81703	2.87144 (0.0077)/; 0.81703	2.87144 (0.0080)/; 0.81001	2.86844 (39.1601)/; 0.79675	2.87134 (0.9337)/; 0.81613
	4	2.87924 (0.0240985)/; 0.84197	2.87914 ()/; 0.84213	2.87914 (1.0312)/; 0.84132	2.87654 (30.3629)/; 0.83127	2.87884 (1.4238)/; 0.84142