A Global Multilevel Thresholding Using Differential Evolution Approach

Table 5

The average of threshold value distortion (TVD) 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	TVD	74.153	2.217	0.000	0.000	0.000	0.000	0.000	0.000	0.050	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	Rank	18	17	1	1	1	1	1	1	16	1	1	1	1	1	1	1	1	1
3	TVD	163.333	41.753	2.968	7.424	1.510	0.150	0.000	0.270	1.004	0.519	0.075	0.246	0.171	0.075	0.000	0.000	0.000	0.000
	Rank	18	17	15	16	14	8	1	11	13	12	6	10	9	6	1	1	1	1
4	TVD	257.083	98.848	34.770	36.891	8.716	7.340	1.428	2.184	25.499	13.609	7.318	7.360	7.398	4.303	1.672	0.728	0.130	0.257
	Rank	18	17	15	16	12	9	4	6	14	13	8	10	11	7	5	3	1	2
5	TVD	516.582	148.344	97.216	62.319	21.565	5.373	1.864	3.241	20.441	10.064	10.422	4.584	3.904	3.289	2.441	3.385	1.195	0.000
	Rank	18	17	16	15	14	10	3	5	13	11	12	9	8	6	4	7	2	1
6	TVD	534.226	219.437	187.620	166.775	45.728	19.536	2.528	7.761	89.938	43.666	30.923	13.010	6.524	6.023	4.136	6.129	2.421	0.050
	Rank	18	17	16	15	13	10	3	8	14	12	11	9	7	5	4	6	2	1
7	TVD	599.250	265.029	242.194	285.862	66.259	58.877	27.976	35.481	125.040	75.011	49.851	44.610	28.039	29.841	26.075	17.950	4.776	0.150
	Rank	18	16	15	17	12	11	5	8	14	13	10	9	6	7	4	3	2	1
8	TVD	475.458	382.076	380.124	309.635	72.763	120.734	90.287	89.406	218.266	143.225	130.898	99.991	76.353	82.886	57.251	57.665	26.822	2.103
	Rank	18	17	16	15	5	11	9	8	14	13	12	10	6	7	3	4	2	1
9	TVD	862.458	394.744	375.229	410.710	113.892	82.099	44.407	46.539	250.470	154.662	96.417	68.197	44.223	35.333	26.627	23.406	12.757	0.780
	Rank	18	16	15	17	12	10	7	8	14	13	11	9	6	5	4	3	2	1
10	TVD	847.703	458.536	445.765	498.328	117.664	84.541	43.991	48.474	249.147	136.935	93.935	72.288	43.883	44.110	36.700	27.978	20.213	0.164
	Rank	18	16	15	17	12	10	6	8	14	13	11	9	5	7	4	3	2	1
11	TVD	977.976	536.258	528.329	531.211	137.941	87.267	44.944	44.973	296.513	152.195	104.092	75.115	44.461	47.564	34.944	26.231	18.782	0.083
	Rank	18	17	15	16	12	10	6	7	14	13	11	9	5	8	4	3	2	1
12	TVD	1070.300	592.750	589.931	605.280	157.169	174.580	109.138	101.282	388.491	258.312	196.098	150.932	101.112	82.365	79.966	51.281	23.429	0.000
	Rank	18	16	15	17	10	11	8	7	14	13	12	9	6	5	4	3	2	1
13	TVD	1142.808	567.442	579.495	711.382	183.451	204.665	147.251	123.438	466.508	299.040	216.656	178.394	114.244	114.491	96.104	81.076	52.578	1.975
	Rank	18	15	16	17	10	11	8	7	14	13	12	9	5	6	4	3	2	1
14	TVD	1148.641	632.482	660.908	770.319	205.714	218.408	141.431	116.716	524.783	325.936	241.997	177.121	113.426	104.073	88.593	65.908	39.647	0.564
	Rank	18	15	16	17	10	11	8	7	14	13	12	9	6	5	4	3	2	1
15	TVD	1245.529	707.835	722.126	816.158	256.477	307.873	219.556	182.464	605.623	428.370	343.439	261.522	174.700	166.309	138.710	100.296	62.940	0.000
	Rank	18	15	16	17	9	11	8	7	14	13	12	10	6	5	4	3	2	1
16	TVD	1182.989	768.714	835.747	828.004	249.042	279.753	211.614	195.676	605.790	416.711	311.314	251.408	174.118	167.316	133.922	113.776	76.661	2.539
	Rank	18	15	17	16	9	11	8	7	14	13	12	10	6	5	4	3	2	1
Avg. for; 𝑛=2; to 16	TVD	739.899	387.764	378.828	402.687	109.193	110.080	72.428	66.527	257.838	163.884	122.229	93.652	62.170	59.199	48.476	38.387	22.823	0.578
	Growth rate (𝛿)	86.86	55.25	61.13	67.98	19.25	21.76	15.61	13.48	48.43	32.25	23.91	18.93	12.52	11.86	9.99	7.69	4.94	0.09
	Rank	18	15	16	17	10	11	8	7	14	13	12	9	6	5	4	3	2	1