A Global Multilevel Thresholding Using Differential Evolution Approach

Table 4

The average success rate (SR_HM) and ranks of the methods.

No		Multi-; thresh	FODPSO	DPSO	PSO	ABC	Rank-DE	DE	O(rand)R-DE	O(0.9)R-DE	O(0.8)R-DE	O(0.7)R-DE	O(0.6)R-DE	O(0.5)R-DE	O(0.4)R-DE	O(0.3)R-DE	O(0.2)R-DE	O(0.1)R-DE	O(0.0)R-DE
2	SRHM	0	0.977	1	1	1	1	1	1	0.999	1	1	1	1	1	1	1	1	1
	Rank	18	17	1	1	1	1	1	1	16	1	1	1	1	1	1	1	1	1
3	SRHM	0.000	0.635	0.972	0.991	0.979	0.998	1.000	0.997	0.986	0.993	0.999	0.997	0.998	0.999	1.000	1.000	1.000	1.000
	Rank	18	17	16	13	15	8	1	10	14	12	6	10	8	6	1	1	1	1
4	SRHM	0.000	0.379	0.742	0.934	0.833	0.987	0.995	0.986	0.897	0.945	0.972	0.971	0.986	0.993	0.992	0.991	0.998	0.997
	Rank	18	17	16	13	15	7	3	8	14	12	10	11	8	4	5	6	1	2
5	SRHM	0.000	0.185	0.391	0.767	0.706	0.936	0.977	0.960	0.782	0.878	0.874	0.944	0.950	0.959	0.968	0.960	0.985	1.000
	Rank	18	17	16	14	15	10	3	5	13	11	12	9	8	7	4	5	2	1
6	SRHM	0.000	0.000	0.187	0.433	0.453	0.863	0.968	0.900	0.601	0.706	0.826	0.878	0.934	0.922	0.944	0.935	0.970	0.999
	Rank	18	17	16	15	14	10	3	8	13	12	11	9	6	7	4	5	2	1
7	SRHM	0.000	0.000	0.000	0.153	0.164	0.696	0.884	0.835	0.366	0.561	0.675	0.741	0.840	0.851	0.883	0.914	0.949	0.998
	Rank	18	17	16	15	14	10	4	8	13	12	11	9	7	6	5	3	2	1
8	SRHM	0.000	0.000	0.000	0.000	0.000	0.300	0.458	0.530	0.105	0.256	0.351	0.502	0.592	0.628	0.724	0.757	0.838	0.972
	Rank	18	17	16	14	14	11	9	7	13	12	10	8	6	5	4	3	2	1
9	SRHM	0.000	0.000	0.000	0.000	0.000	0.495	0.695	0.681	0.083	0.274	0.372	0.548	0.721	0.725	0.769	0.815	0.852	0.999
	Rank	18	17	16	14	14	10	7	8	13	12	11	9	6	5	4	3	2	1
10	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.381	0.375	0.000	0.073	0.218	0.311	0.409	0.370	0.460	0.578	0.686	0.998
	Rank	18	17	16	14	14	12	6	7	13	11	10	9	5	8	4	3	2	1
11	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.271	0.267	0.000	0.000	0.000	0.144	0.407	0.316	0.424	0.584	0.704	0.999
	Rank	18	17	16	14	14	12	7	8	13	10	10	9	5	6	4	3	2	1
12	SRHM	0.000	0.000	0.000	0.000	0.000	0.090	0.270	0.423	0.000	0.000	0.089	0.177	0.400	0.407	0.501	0.641	0.810	1.000
	Rank	18	17	16	14	14	12	8	5	13	11	10	9	7	6	4	3	2	1
13	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.151	0.000	0.000	0.000	0.000	0.000	0.000	0.254	0.267	0.381	0.974
	Rank	18	17	16	14	14	12	6	5	13	10	10	6	6	6	4	3	2	1
14	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.102	0.000	0.000	0.000	0.000	0.000	0.110	0.000	0.253	0.494	0.993
	Rank	18	17	16	14	14	12	7	4	13	10	10	7	7	6	5	3	2	1
15	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.090	0.000	0.000	0.000	0.000	0.095	0.117	0.149	0.288	0.466	1.000
	Rank	18	17	16	14	14	12	8	4	13	10	10	8	7	6	5	3	2	1
16	SRHM	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.110	0.192	0.288	0.977
	Rank	18	17	16	14	14	12	6	4	13	10	10	6	6	6	5	3	2	1
Avg. for; 𝑛=2 to 16	𝑛0.5,; 𝑛max,; SRHM	<2,; <2,; 0.000	3,; 5,; 0.376	4,; 6,; 0.443	5,; 7,; 0.454	5,; 7,; 0.464	7,; 9,; 0.665	9,; 12,; 0.554	9,; 15,; 0.304	6,; 9,; 0.263	7,; 10,; 0.313	7,; 10,; 0.530	9,; 12,; 0.420	9,; 12,; 0.654	9,; 12,; 0.625	9,; 13,; 0.619	12,; 16,; 0.498	12,; 16,; 0.656	16,; 16,; 0.994
	Rank	18	17	16	15	14	12	8	4	13	11	10	9	6	7	5	3	2	1