. 2020 Oct 29;167:114142. doi: 10.1016/j.eswa.2020.114142

Table 7.

Comparison of different segmentation methods with the $β$ index values (Highlighted values denotes the acceptable values).

Image Id	Algorithm	No. of Clusters
Image Id	Algorithm	3	5	7	9
$I_{001}$	robust modified GA (Shayeghi et al., 2007)	1.08030166	2.54577616	3.22490003	2.347810386
	modified PSO (Sedghi et al., 2013)	0.12896068	1.0972991	2.50810354	3.105269436
	modified ACO (Zhu & Wang, 2016)	0.95460335	1.10476818	1.52963416	2.744418936
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	3.67130847	1.32872736	2.13048943	1.894271413
	SuFMoFPA (Proposed)	0.39961555	2.05274396	3.95434278	2.433800915
$I_{002}$	robust modified GA (Shayeghi et al., 2007)	1.60888678	2.52923119	2.17984335	0.17301238
	modified PSO (Sedghi et al., 2013)	3.4656689	0.7370578	1.34864831	1.062931572
	modified ACO (Zhu & Wang, 2016)	0.75240613	2.52461831	1.90775524	2.708374815
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.28630694	2.71348371	1.84906597	2.303622357
	SuFMoFPA (Proposed)	1.25105943	1.26202883	3.56707587	1.50230463
$I_{003}$	robust modified GA (Shayeghi et al., 2007)	0.85462328	1.13172637	2.44214648	2.332910353
	modified PSO (Sedghi et al., 2013)	0.05850133	1.54902953	2.48389261	2.474018521
	modified ACO (Zhu & Wang, 2016)	1.15553341	0.11922888	2.25133489	0.96989777
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.62117707	1.22497331	1.46286087	2.202865732
	SuFMoFPA (Proposed)	2.01391643	3.60499596	2.54503349	2.478372258
$I_{004}$	robust modified GA (Shayeghi et al., 2007)	−0.323756	2.1072883	1.53166572	1.130117436
	modified PSO (Sedghi et al., 2013)	2.52282579	2.99556638	3.05567925	2.597314922
	modified ACO (Zhu & Wang, 2016)	3.84312474	1.46517086	1.77834996	1.627108032
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.40700832	1.9367675	1.96927611	2.334228243
	SuFMoFPA (Proposed)	2.22061779	2.9231381	4.04870654	0.389403893
$I_{005}$	robust modified GA (Shayeghi et al., 2007)	0.90736785	1.09738243	1.1964885	1.965702243
	modified PSO (Sedghi et al., 2013)	2.70120004	3.10898795	2.83360465	0.799582251
	modified ACO (Zhu & Wang, 2016)	2.80200617	2.25668212	1.80455619	0.565179198
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	1.24901793	2.9797685	4.00365635	3.211382077
	SuFMoFPA (Proposed)	2.50442646	3.45505346	3.95273903	1.710608254
$I_{006}$	robust modified GA (Shayeghi et al., 2007)	1.48932711	2.64378217	1.61909543	2.715290484
	modified PSO (Sedghi et al., 2013)	2.18962706	3.19300694	2.23155991	2.6998225
	modified ACO (Zhu & Wang, 2016)	1.17775759	1.6740792	2.82040535	2.854924226
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.46858705	3.25291566	2.55103456	2.180550543
	SuFMoFPA (Proposed)	0.19171251	3.04508239	4.83691179	1.876129512
$I_{007}$	robust modified GA (Shayeghi et al., 2007)	1.03190965	0.92863533	1.70238882	2.033984423
	modified PSO (Sedghi et al., 2013)	2.66441796	1.84029684	3.02041233	3.328463297
	modified ACO (Zhu & Wang, 2016)	1.01154939	1.77237091	2.61272764	0.885098898
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	4.31950134	4.03012854	2.61867249	1.208037556
	SuFMoFPA (Proposed)	0.90437179	3.99787823	2.42973167	1.957067206
$I_{008}$	robust modified GA (Shayeghi et al., 2007)	3.38371626	2.6349559	2.25267573	1.651698877
	modified PSO (Sedghi et al., 2013)	1.30299086	1.53569527	1.21467864	0.931970088
	modified ACO (Zhu & Wang, 2016)	1.26054601	2.10699216	1.89587126	2.524847925
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	3.17034431	3.80187904	3.4724212	2.526850986
	SuFMoFPA (Proposed)	2.60614501	4.9605439	2.39995219	2.92391514
$I_{009}$	robust modified GA (Shayeghi et al., 2007)	0.71399444	2.14788247	2.72756786	2.616832182
	modified PSO (Sedghi et al., 2013)	2.44888085	0.52143725	1.7003886	1.505823292
	modified ACO (Zhu & Wang, 2016)	3.0116282	3.45612248	2.40811288	2.035794501
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.59708775	2.17195911	2.00127627	3.378663995
	SuFMoFPA (Proposed)	2.83994234	1.92787401	5.00456648	3.639328475
$I_{010}$	robust modified GA (Shayeghi et al., 2007)	1.81960457	2.35468121	3.5681476	1.597325231
	modified PSO (Sedghi et al., 2013)	0.60991396	0.83944781	1.65777353	3.498810794
	modified ACO (Zhu & Wang, 2016)	0.76997978	1.37772079	0.71073799	2.016448483
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	4.0215901	1.64210239	3.31696429	1.34090451
	SuFMoFPA (Proposed)	0.22223857	2.30889269	3.95499191	1.228755654
$I_{011}$	robust modified GA (Shayeghi et al., 2007)	1.15289064	1.5291455	2.05372676	3.03432955
	modified PSO (Sedghi et al., 2013)	0.48630903	2.5296523	1.78686171	2.5096375
	modified ACO (Zhu & Wang, 2016)	1.18699733	1.08986712	2.34039959	1.006494197
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.36262768	0.8773631	0.75446494	1.701325217
	SuFMoFPA (Proposed)	1.05915599	2.96080359	2.2682372	3.215903931
$I_{012}$	robust modified GA (Shayeghi et al., 2007)	1.099847	1.95694211	1.26228229	1.294054493
	modified PSO (Sedghi et al., 2013)	1.33645051	2.65755194	3.91970296	2.117279192
	modified ACO (Zhu & Wang, 2016)	2.31398358	2.69638937	2.67147565	2.171889289
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	1.90548359	2.01335749	2.1705331	2.171304072
	SuFMoFPA (Proposed)	2.91573865	2.3324229	4.03121674	1.097428558
$I_{013}$	robust modified GA (Shayeghi et al., 2007)	1.3966156	1.89421075	0.62674073	2.074990828
	modified PSO (Sedghi et al., 2013)	3.09948678	2.80258726	3.01168379	0.417157951
	modified ACO (Zhu & Wang, 2016)	3.68787034	1.93767678	2.18609032	1.93744153
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.459167	2.51295226	4.05511791	4.112032152
	SuFMoFPA (Proposed)	3.09240172	4.6510254	3.39698465	2.503391612
$I_{014}$	robust modified GA (Shayeghi et al., 2007)	1.75901468	2.89057369	1.48593163	1.940841246
	modified PSO (Sedghi et al., 2013)	1.91261272	3.0947708	1.51191584	3.398500184
	modified ACO (Zhu & Wang, 2016)	1.01082091	1.71159966	3.14750022	2.67908343
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	3.22703421	2.71169602	3.68267574	2.413376839
	SuFMoFPA (Proposed)	1.23079627	2.75525092	4.22777124	2.234653012
$I_{015}$	robust modified GA (Shayeghi et al., 2007)	1.63630722	0.34174905	1.1411655	2.268922039
	modified PSO (Sedghi et al., 2013)	1.92343591	2.57740959	4.13875254	3.438041968
	modified ACO (Zhu & Wang, 2016)	1.32360399	1.15506857	1.85106544	1.451104932
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	3.6072077	4.77845301	3.77258317	1.23872438
	SuFMoFPA (Proposed)	0.29891733	4.14725366	1.69171125	1.261310612
$I_{016}$	robust modified GA (Shayeghi et al., 2007)	3.43809754	3.0480546	2.74492167	2.627967634
	modified PSO (Sedghi et al., 2013)	0.24807311	0.80150704	1.20288975	0.4368312
	modified ACO (Zhu & Wang, 2016)	2.0218355	2.05944617	2.27188204	1.973079218
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	3.90131485	3.44227838	3.10907189	3.029066541
	SuFMoFPA (Proposed)	1.50412711	5.06291945	2.6895786	2.641977937
$I_{017}$	robust modified GA (Shayeghi et al., 2007)	1.15958777	2.37983691	2.75183093	1.785976134
	modified PSO (Sedghi et al., 2013)	2.73704867	0.31549428	2.11261402	1.168603999
	modified ACO (Zhu & Wang, 2016)	3.5972623	3.40862177	2.19918987	1.847951785
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.4957426	1.80301025	2.82065921	3.476861333
	SuFMoFPA (Proposed)	2.83342366	2.13269299	4.28523577	3.113438599
$I_{018}$	robust modified GA (Shayeghi et al., 2007)	1.43661557	1.75386802	2.15887356	1.38820541
	modified PSO (Sedghi et al., 2013)	0.71616599	1.81928812	2.27493676	3.379698838
	modified ACO (Zhu & Wang, 2016)	1.02390364	1.03870838	1.30638805	3.652735604
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	4.28406919	1.17302868	2.1763827	2.444311055
	SuFMoFPA (Proposed)	2.41350136	1.44933675	4.2196256	1.040516042
Average	robust modified GA (Shayeghi et al., 2007)	1.42472	1.995318	2.037244	1.943332
	modified PSO (Sedghi et al., 2013)	1.697365	1.889783	2.334117	2.159431
	modified ACO (Zhu & Wang, 2016)	1.828078	1.830841	2.094082	1.98066
	modified cuckoo search (Chakraborty, Chatterjee, Dey, et al., 2017)	2.947476	2.46638	2.662067	2.398243
	SuFMoFPA (Proposed)	1.694562	3.057219	3.528023	2.06935