Mathematical Problems in Engineering

Research Article

Improved Glowworm Swarm Optimization Algorithm for Multilevel Color Image Thresholding Problem

Table 4

Optimal thresholds and objective values obtained by IGSO and GSO algorithms using Otsu’s method.


	IGSO				GSO
				(×10³)				(×10³)

Airplane
2	120,177	94,166	124,181	5.15456	120,177	94,166	124,181	5.15456
4	83,126,169,199	66,116,164,201	112,150,180,203	5.48484	83,126,169,199	66,116,164,201	112,150,180,203	5.48484
6	68,99,129,162, 187,204	57,98,132,167, 193,209	102,134,156,176, 195,207	5.58695	68,100,130,162,187,204	55,98,133,167, 193,207	102,136,156, 176,196,209	5.58690
8	64,92,114,140, 163,184,198,209	47,80,107,132,159, 183,200,212	56,102,132,152, 170,188,201,211	5.63154	63,93,116,141, 166,186,199,210	47,81,108,134,161,184,202,214	57,104,134,154, 173,190,202,211	5.63124

Couple
2	35,83	30,81	27,76	2.64122	35,83	30,81	27,76	2.64122
4	17,42,71,109	16,39,74,122	17,39,72,117	2.91159	17,42,71,109	16,39,74,122	17,39,72,117	2.91159
6	13,32,52,73,97,131	13,31,51,81,123, 176	11,26,46,77,119, 177	2.99013	15,33,52,75,97,131	13,32,54,81,123, 176	13,27,46,77,119, 178	2.99009
8	12,28,45,62,81, 104,135,204	10,23,37,54,78, 104,138,200	9,22,38,56,80, 108,142,180	3.02731	12,29,43,61,78, 100,131,200	10,24,40,60,73,86, 106,135,201	9.20,34,55,74,102, 133,176	3.02709

Flower
2	101,190	53,129	73,151	10.35564	101,190	53,129	73,151	10.35564
4	42,92,154,209	44,84,132,188	32,68,108,163	11.25529	42,92,154,209	44,84,132,188	32,68,108,163	11.25529
6	41,76,119,160,194, 226	32,56,84,121,162, 206	26,55,86,114,152, 199	11.38993	41,76,118,159, 193,225	32,54,82, 121,163,206	26,55,83,114, 152,198	11.38990
8	35,53,78,109,142, 173,201,229	30,54,77,102,129, 157,189,222	20,38,55,76,96, 118,154,200	11.47485	34,53,76,109,142, 172,200,228	31,54,77,101,138, 162,193,220	24,40,59,72,91, 117,161,209	11.47454

Girl
2	69,124	34,88	31,81	4.34647	69,124	34,88	31,81	4.34647
4	37,69,106,155	25,58,92,129	24,52,81,117	4.84594	37,69,106,155	25,58,92,129	24,52,81,117	4.84594
6	35,62,88,112,140, 179	25,57,89,124,194, 208	23,44,67,94,124, 190	4.93170	34,62,89,114,140, 179	22,57,89,123,194, 208	23,48,67,94,124,190	4.93167
8	27,44,64,83,104, 125,151,187	16,34,52,72,92, 115,138,169	13,29,47,67,88, 110,134,163	5.02842	26,45,65,87,112, 130,160,192	12,31,50,67,88, 110,136,172	12,25,40,65,84, 103,131,167	5.02814

Monarch
2	114,176	79,142	62,122	5.19253	114,176	79,142	62,122	5.19253
4	89,127,162,198	63,90,125,175	55,86,122,164	5.63990	89,127,162,198	63,90,125,175	55,86,122,164	5.63990
6	77,105,129,149, 174,204	45,64,83,103,134, 180	40,60,85,113,144, 177	5.77439	79,105,129,150, 174,206	48,64,83,104,134, 181	40,60,85,113, 141,178	5.77434
8	63,85,109,130,148, 166,191,212	12,45,63,81,98, 119,149,186	38,54,70,86,108, 131,156,184	5.83061	68,90,103,123,145,160,187,208	21,46,63,81,98, 119,149,186	35,49,63,80,101,127,149,182	5.83002

Pen
2	76,151	60,138	63,152	9.77709	76,151	60,138	63,152	9.77709
4	51,84,124,178	44,82,128,183	44,85,125,184	10.58262	51,84,124,178	44,82,128,183	44,85,125,184	10.58262
6	44,69,92,120,157, 195	36,63,86,114,151, 192	32,61,88,115,153, 201	10.78635	44,69,93,120,156, 194	36,63,85,114,152, 192	32,61,88,117, 155,201	10.78632
8	39,59,77,96,120, 149,179,206	29,50,70,89,110, 137,169,199	29,53,74,93,116, 142,177,212	10.86604	36,55,74,93,114, 141,171,202	28,48,67,85,106, 145,176,199	27,49,70,90,110,135,169,209	10.86570

Pepper
2	97,159	78,157	58,127	8.61756	97,159	78,157	58,127	8.61756
4	81,124,156,186	30,82,140,185	25,60,95,146	9.28037	81,124,156,186	30,82,140,185	25,60,95,146	9.28037
6	62,96,121,143,167, 191	20,46,81,125,163, 193	23,50,73,96,129, 172	9.45358	64,97,122,143,168,191	20,49,81,126,163, 194	20,50,73,96,129,171	9.45354
8	53,85,107,127, 145,164,183,199	17,42,69,100, 132,159,182,201	11,32,50,69,87, 108,140,177	9.53018	54,85,108,128, 145,165,184,200	17,40,64,92,122, 153,177,199	11,31,50,69,87, 108,140,179	9.52962

Soccer
2	86,149	71,138	55,126	7.27688	86,149	71,138	55,126	7.27688
4	57,103,144,180	41,83,120,166	38,77,113,166	7.96150	57,103,144,180	41,83,120,166	38,77,113,166	7.96150
6	44,75,109,137,160, 192	30,57,86,112,135, 175	27,56,82,105,133, 177	8.15225	44,75,108,136, 159,192	32,58,87,113,136, 176	27,55,82,105, 133,179	8.15218
8	40,63,86,113,135, 153,171,198	26,48,73,97,114, 133,158,192	23,46,68,86,105, 127,154,192	8.22619	36,58,79,110, 129,147,168,195	24,43,69,95,111, 129,151,186	22,45,67,86,104,126,155,192	8.22581

Test
2	89,148	86,144	82,150	7.43581	89,148	86,144	82,150	7.43581
4	61,92,127,171	57,90,126,165	55,88,127,172	7.94367	61,92,127,171	57,90,126,165	55,88,127,172	7.94367
6	52,78,100,127,161, 193	46,72,95,124,157, 185	40,62,86,114,147, 181	8.10926	51,77,100,127, 160,194	45,71,95,124,158, 185	40,62,86,1154,147,182	8.10922
8	45,68,87,104,129, 157,184,207	43,67,88,107,130, 158,180,198	33,52,69,90,115, 145,176,197	8.17834	40,63,78,99,124, 147,175,204	36,59,85,102,126, 153,172,196	35,51,67,86,106, 138,173,189	8.17792

Yacht
2	71,141	64,132	74,148	9.16339	71,141	64,132	74,148	9.16339
4	56,97,136,176	50,86,125,166	45,85,120,163	9.83344	56,97,136,176	50,86,125,166	45,85,120,163	9.83344
6	46,78,105,133,160, 185	48,81,111,141, 168,189	28,55,86,115,144, 176	9.98335	45,78,105,132, 159,185	48,80,109,140, 168,189	29,55,86,115, 143,176	9.98330
8	37,62,84,107,132, 155,173,190	29,53,74,92,110, 133,155,178	25,49,74,97,118, 139,162,185	10.00658	32,59,75,105,130, 146,162,185	29,51,74,92,110, 133,156,179	24,48,70,91,112,132,154,181	10.00622