Mathematical Problems in Engineering

Research Article

Improved Glowworm Swarm Optimization Algorithm for Multilevel Color Image Thresholding Problem

Table 5

Optimal thresholds and objective values obtained by APSO and SaDE algorithms using Otsu’s method.


	APSO				SaDE
				(×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	71,102,130,164,190,204	59,99,134,169, 194,211	104,136,157,179, 196,207	5.58678	69,101,131,163, 188,204	57,100,133,167, 192,210	102,135,158,177, 196,203	5.58683
8	63,90,110,134,160, 180,197,209	45,79,105,129, 154,180,199,207	52,97,125,150, 168,186,200,210	5.63107	64,91,111,136, 161,182,197,209	46,79,105,130, 156,181,198,208	53,99,127,150, 169,188,201,210	5.63113

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	16,34,52,76,99,136	15,32,56,84,126, 179	13,32,48,78,122, 178	2.98998	14,33,53,75,98, 133	14,33,55,82,127, 177	14,27,46,79,121, 179	2.99003
8	13,30,48,67,87, 110,142,205	10,24,40,56,82, 113,149,206	10,24,41,64,90, 122,146,187	3.02679	13,30,48,66,85, 109,139,204	10,23,39,55,83, 109,143,202	11,23,40,62,88, 119,147,185	3.02687

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	42,77,123,163,196, 224	35,59,90,122,165, 208	26,57,86,116, 156,197	11.38983	41,74,117,159,191,225	34,56,86,123,159, 203	27,55,84,112, 150,200	11.38986
8	34,54,79,115,149, 176,203,230	32,55,81,110,139, 167,192,225	24,44,63,81,100, 121,155,202	11.47416	35,54,78,112,146, 176,202,230	31,54,78,106,137, 158,192,226	22,43,60,81,100, 120,153,201	11.47424

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	37,60,85,108,138, 178	28,59,93,125,196, 210	27,45,69,96,127, 195	4.93159	35,65,89,113,141, 179	24,59,90,127,196, 209	26,46,69,95,126, 192	4.93162
8	29,47,67,89,110, 131,155,190	17,36,58,81,102, 123,130,164	16,34,51,73,92, 116,139,167	5.02802	27,46,66,87,107, 127,156,192	17,35,55,74,95, 119,139,175	15,32,50,71,91, 114,137,165	5.02796

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	78,109,133,151, 176,205	46,66,84,105,137, 183	42,61,87,116, 146,180	5.77425	79,104,130,153, 175,205	46,62,82,101,132, 179	40,62,87,114, 145,178	5.77428
8	62,82,104,123,144, 162,189,217	13,49,67,88,100, 123,158,192	38,55,70,90,116, 141,166,186	5.82961	62,84,105,125,145 ,164,187,210	17,46,68,84,101, 121,153,191	39,56,73,93,105 ,135,160,184	5.82970

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	46,72,94,121,158, 196	38,66,89,116,153, 193	35,62,91,117, 152,199	10.78625	44,71,91,122,158,197	37,64,87,116,153,192	33,63,88,116, 153,199	10.78627
8	42,64,82,104,126, 158,185,209	30,53,74,95,120, 151,177,202	29,55,79,100, 122,151,183,215	10.86558	40,62,81,101,126, 154,184,208	30,50,71,92,116, 145,174,201	30,55,78,98, 122,148,182,214	10.86549

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	61,91,120,141,168, 191	22,47,84,127,166, 194	22,48,69,94,128, 171	9.45348	59,93,121,142, 167,191	24,48,81,126,164,193	20,49,72,96,130, 172	9.45350
8	49,77,102,122,141,162,183,198	19,45,71,107,138, 165,185,203	13,32,54,74,89, 114,147,184	9.52933	53,79,104,124, 143,161,179,198	20,42,71,105,137, 162,187,202	12,35,51,71,90, 111,145,183	9.52941

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	44,78,110,139,158, 193	32,60,87,112,136, 175	30,59,84,106, 133,178	8.15211	45,76,111,137, 159,192	31,59,88,114,136, 176	28,58,84,107, 134,178	8.15213
8	46,68,90,119,137, 158,176,199	28,51,75,102,118, 136,163,199	27,51,70,91,110, 134,162,202	8.22550	40,65,92,118,138, 155,174,200	27,50,76,98,116, 136,165,195	25,48,71,89, 109,133,163,198	8.22559

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	51,79,102,129,160, 194	48,73,96,127,158, 185	39,60,83,114, 145,180	8.10924	51,76,99,126,159, 193	45,71,95,123,159, 186	41,63,86,113, 149,182	8.10927
8	48,70,91,110,137, 164,185,210	41,72,89,112,132, 165,186,203	39,56,77,98,120, 154,176,202	8.17762	47,71,89,109,133, 161,187,209	43,69,91,109,133, 163,184,201	37,57,75,96,121 ,150,177,197	8.17770

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	46,76,103,132,160, 183	49,84,114,141, 169,189	29,57,85,114, 142,176	9.98324	45,77,105,132, 159,185	47,80,110,139, 168,190	27,56,86,116, 145,175	9.98326
8	42,65,90,112,134, 163.181,198	26,45,66,83,101, 126,151,175	25,49,70,95,109, 142,165,189	10.00592	41,66,87,111,135, 160,178,195	25,49,68,86,103, 128,150,177	27,51,758,98,12 0,141,166,188	10.00601