Mathematical Problems in Engineering

Research Article

Improved Glowworm Swarm Optimization Algorithm for Multilevel Color Image Thresholding Problem

Table 8

Optimal thresholds and objective values obtained by APSO and SaDE algorithms using MCE.


	APSO				SaDE
				(×10²)				(×10²)

Airplane
2	109,168	72,153	120,180	28.75021	109,168	72,153	120,180	28.75021
4	73,117,162,197	53,100,146,191	109,147,178,203	28.7628	73,117,162,197	53,100,146,191	109,147,178,203	28.7628
6	63,95,123,156,185, 205	28,65,102,137,177, 208	54,109,144,169, 193,209	28.76701	64,95,123,155, 183,203	29,64,100,136,176, 203	58,107,143,169, 190,206	28.76702
8	58,82,101,123,147, 172,192,206	26,57,87,111,139, 171,194,209	48,94,120,144,162, 180,197,208	28.76895	59,84,103,126, 149,174,193,205	24,53,85,110,139, 170,194,210	53,95,119,145, 161,180,198,209	28.76897

Couple
2	26,78	21,74	22,71	3.97893	26,78	21,74	22,71	3.97893
4	12,30,57,93	8,22,42,81	8,21,40,78	4.02494	12,30,57,93	8,22,42,81	8,21,40,78	4.02494
6	10,30,56,85,127, 207	11,24,42,71,114, 235	10,22,42,76,138, 194	4.02987	9,29,54,83,127, 211	8,21,40,71,110, 234	8,20,42,75,137, 193	4.02988
8	7,20,31,46,63,89, 120,178	8,15,24,29,50,81, 125,234	8,6,14,29,3941,73, 106,175,214	4.03710	8,19,28,44,64,87, 116,180	7,12,24,41,55,82, 123,228	8,16,29,44,66, 105,174,221	4.03712

Flower
2	41,119	44,111	53,114	12.34354	41,119	44,111	53,114	12.34354
4	39,79,135,199	27,52,93,159	23,56,98,157	12.39484	39,79,135,199	27,52,93,159	23,56,98,157	12.39484
6	28,48,78,119,168, 214	25,41,59,87,131, 186	8,35,64,106,146, 191	12.40939	27,47,77,119,167, 213	22,41,61,87,128, 184	6,34,63,99,146, 192	12.40940
8	15,30,45,57,81,123, 179,218	25,39,58,82,106, 136,173,216	9,31,44,68,87,108,147,198	12.41604	18,29,44,58,82, 124,171,216	22,41,58,77,105, 136,166,205	6,27,45,65,91, 118,154,199	12.41606

Girl
2	41,90	22,72	26,80	7.65874	41,90	22,72	26,80	7.65874
4	33,65,102,149	11,31,62,109	11,28,56,101	7.70152	33,65,102,149	11,31,62,109	11,28,56,101	7.70152
6	22,46,67,100,134, 186	10,33,58,90,124, 183	14,26,57,100,146, 168	7.70993	23,44,68,98,132, 185	10,29,59,89,122, 182	11,26,55,95,144, 166	7.70994
8	21,39,55,67,88,103, 135,172	6,19,35,43,56,87, 110,154	12,44,50,134,141, 167,204,237	7.71551	18,36,52,71,90, 110,132,167	8,22,30,42,61,85, 117,153	11,45,51,128, 152,173,209,239	7.71553

Monarch
2	108,172	75,135	58,113	14.98290	108,172	75,135	58,113	14.98290
4	79,115,147,186	61,86,119,169	38,61,91,141	15.00562	79,115,147,186	61,86,119,169	38,61,91,141	15.00562
6	64,86,112,141,166,202	42,65,82,101,133,179	34,47,69,92,123, 164	15.01302	61,85,112,139, 165,199	44,63,83,102,130, 175	38,50,68,89,119, 163	15.01303
8	55,73,92,111,136, 154,177,207	39,54,66,86,99,120, 148,190	36,49,63,75,92,116, 146,175	15.01597	61,77,93,110,132, 148,176,200	33,53,62,83,97, 124,143,182	39,47,59,74,90, 118,143,170	15.01599

Pen
2	61,133	48,125	49,136	13.20604	61,133	48,125	49,136	13.20604
4	45,76,112,169	34,66,101,157	29,63,102,166	13.25261	45,76,112,169	34,66,101,157	29,63,102,166	13.25261
6	38,57,82,109,144, 189	28,48,73,98,136, 184	21,42,66,98,124, 180	13.26477	35,55,77,104,141, 187	26,50,71,96,134, 184	22,43,72,97,128, 183	13.26478
8	33,50,64,88,106, 135,168,201	26,41,59,75,102, 120,152,196	19,30,56,73,94, 119,151,200	13.27000	31,48,67,85,105, 132,165,202	24,42,60,78,97, 123,155,192	17,32,54,76,96, 115,154,201	13.27001

Pepper
2	87,153	22,104	21,74	16.40133	87,153	22,104	21,74	16.40133
4	62,102,137,174	10,39,85,156	15,52,83,133	16.45113	62,102,137,174	10,39,85,156	15,52,83,133	16.45113
6	49,82,108,133,164, 191	11,34,62,100,152, 185	6,26,55,84,115, 166	16.46414	51,82,113,135, 163,190	9,35,65,104,149, 189	8,30,56,81,116, 172	16.46415
8	48,72,99,118,136, 157,178,197	9,25,44,69,101,126, 170,201	10,28,45,64,84,110, 160,189,196	16.46921	44,73,98,113,130, 156,177,198	5,22,45,68,94, 132,161,194	6,25,42,65,83, 120,170,192	16.46923

Soccer
2	64,126	42,97	42,113	13.11371	64,126	42,97	42,113	13.11371
4	43,79,123,165	30,63,105,155	25,60,99,150	13.15363	43,79,123,165	30,63,105,155	25,60,99,150	13.15363
6	39,62,94,127,160, 191	22,45,72,97,125, 169	21,48,79,104,141, 193	13.16533	38,62,91,125,156, 187	23,43,67,96,126, 168	22,46,77,104,140, 192	13.16534
8	35,55,71,96,124, 145,166,198	19,38,59,79,106, 121,145,177	16,30,50,65,87, 105,133,173	13.17064	33,49,72,95,125, 146,165,196	21,39,60,82,103, 123,142,176	15,29,44,67,86, 106,123,169	13.17066

Test
2	80,137	83,140	67,132	16.22951	80,137	83,140	67,132	16.22951
4	55,88,122,167	40,70,97,143	39,65,100,155	16.25759	55,88,122,167	40,70,97,143	39,65,100,155	16.25759
6	41,70,90,124,158, 190	37,65,95,119,152, 185	33,50,69,92,126, 169	16.26695	43,70,95,123,157, 192	38,66,90,116,151, 182	30,51,68,91,127, 170	16.26696
8	38,64,78,98,110, 134,164,198	37,60,72,90,104, 127,155,188	30,46,63,83,106, 132,159,184	16.27101	39,62,77,95,113, 128,165,199	35,56,75,91,112, 133,162,190	28,48,63,82,104, 128,157,185	16.27103

Yacht
2	60,133	55,125	53,127	15.87338	60,133	55,125	53,127	15.87338
4	44,80,119,166	28,56,92,139	25,55,99,154	15.91058	44,80,119,166	28,56,92,139	25,55,99,154	15.91058
6	31,51,83,112,141, 179	26,51,77,97,128, 170	21,43,68,94,126, 164	15.92185	30,52,82,108,141, 178	25,48,74,95,126, 167	20,41,64,90,122, 162	15.92186
8	30,43,66,95,114, 135,162,187	23,42,63,83,102, 122,148,178	22,31,52,78,99, 125,150,180	15.92641	28,48,70,89,110, 137,162,186	22,40,53,80,98, 121,145,171	18,34,53,74,92, 124,148,179	15.92644