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Table 1 Results of error of area and perimeter for various sizes of test circle images

From: New parameter of roundness R: circularity corrected by aspect ratio

Width of test circle image (pixel)

A I

P I

r

A

P

ΔA (%)

ΔP (%)

Area measured by ImageJ (pixel)

Perimeter measured by ImageJ (pixel)

Major and minor axis length measured by ImageJ

Area calculated by p·r 2

Perimeter calculated by 2·p·r

1

1

2.828

1.128

0.999328

3.543716

0.067260

−20.196760

2

4

5.657

2.257

4.000856

7.090573

−0.021393

−20.218015

3

9

9.657

3.385

8.999267

10.634289

0.008145

−9.189979

4

12

11.314

3.909

12.001102

12.280483

−0.009184

−7.870074

6

32

19.314

6.383

31.999226

20.052782

0.002417

−3.684186

8

52

24.971

8.137

52.001806

25.563134

−0.003472

−2.316360

11

97

34.627

11.113

96.995686

34.912512

0.004447

−0.817792

16

208

52.284

16.274

208.007222

51.126268

−0.003472

2.264456

23

421

75.598

23.152

420.985191

72.734138

0.003518

3.937439

32

804

104.569

31.995

803.996244

100.515236

0.000467

4.032985

45

1581

147.196

44.866

1580.973153

140.950667

0.001698

4.430865

64

3196

211.48

63.791

3196.013548

200.405295

−0.000424

5.526154

90

6320

296.735

89.704

6319.946608

281.813369

0.000845

5.294863

128

12,796

422.96

127.642

12796.081336

400.999086

−0.000636

5.476550

181

25,565

597.47

180.417

25564.935720

566.796604

0.000251

5.411711

254

51,104

842.607

255.084

51104.156942

801.369854

−0.000307

5.145832

360

102,252

1193.97

360.82

102251.807881

1133.549225

0.000188

5.330229

510

204,520

1690.871

510.297

204520.017549

1603.144973

−0.000009

5.472121

722

408,932

2391.253

721.574

408932.420696

2266.891106

−0.000103

5.486011

1020

818,196

3381.743

1020.666

818195.500707

3206.516140

0.000061

5.464712

1442

1,636,024

4893.536

1443.278

1636024.391899

4534.190619

−0.000024

7.925238

  1. p = 3.141592