Table 1 Area calculation and error rate comparison of 2D system and our method (RA = real area, AC = area calculation, AE = absolute value of relative error, MAPE = mean absolute percent error, var = variance)

1

2.02

2.1456

1.9641

6.22

2.77

60

0.78

0.8173

0.7533

4.78

3.43

2

0.27

0.1544

0.2581

42.82

4.41

61

3.03

3.1793

2.9266

4.93

3.41

3

1.90

1.9257

1.8883

1.35

0.61

62

4.35

4.3271

4.3493

0.53

0.02

4

5.03

2.9112

5.2029

42.12

3.44

63

3.67

5.4157

3.5271

47.57

3.89

5

9.91

9.4237

9.9797

4.91

0.70

64

1.25

1.1972

1.2581

4.23

0.65

6

0.20

0.1820

0.2078

9.00

3.89

65

3.64

3.6731

3.6411

0.91

0.03

7

1.33

1.2343

1.3485

7.19

1.39

66

1.85

2.4991

1.8362

35.08

0.75

8

12.50

7.5514

13.2206

39.59

5.76

67

0.39

0.4435

0.3890

13.71

0.26

9

1.09

1.0202

1.1145

6.41

2.25

68

0.15

0.1520

0.1450

1.35

3.32

10

0.11

0.1015

0.1065

7.74

3.19

69

0.61

0.6762

0.5812

10.84

4.73

11

0.99

0.6230

1.0458

37.07

5.64

70

1.12

1.1793

1.1410

5.29

1.98

12

6.74

6.9441

6.6396

3.03

1.49

71

0.18

0.1984

0.1795

10.22

0.28

13

0.23

0.2195

0.2347

4.56

2.04

72

0.89

0.7812

0.9094

12.22

2.18

14

0.23

0.2355

0.2255

2.40

1.95

73

0.28

0.2810

0.2825

0.34

0.91

15

6.20

5.4769

6.3677

11.66

2.70

74

0.34

0.2691

0.3529

20.84

3.79

16

0.59

0.5509

0.6075

6.63

2.97

75

0.96

0.4828

0.9796

49.70

2.04

17

0.88

0.8151

0.9091

7.38

3.30

76

2.72

1.6988

2.8421

37.54

4.49

18

3.99

4.0891

3.9113

2.48

1.97

77

1.48

0.8552

1.5444

42.22

4.35

19

0.72

0.8002

0.7487

11.14

3.99

78

3.05

4.0327

2.9880

32.22

2.03

20

2.98

3.0852

2.9614

3.53

0.62

79

1.61

0.9655

1.5669

40.03

2.68

21

1.80

2.7304

1.7449

51.69

3.06

80

0.36

0.1964

0.3722

45.45

3.39

22

2.04

1.9410

2.0404

4.85

0.02

81

2.79

2.2028

2.8371

21.05

1.69

23

2.47

2.6954

2.4928

9.13

0.92

82

2.20

1.3042

2.3150

40.72

5.23

24

5.96

5.0697

6.0596

14.94

1.67

83

1.66

1.6802

1.6637

1.22

0.22

25

3.06

2.1524

3.1713

29.66

3.64

84

1.69

1.2231

1.7594

27.63

4.11

26

0.97

0.7183

1.0164

25.94

4.78

85

4.36

4.7699

4.1851

9.40

4.01

27

3.49

3.4324

3.4955

1.65

0.16

86

2.50

2.5650

2.5028

2.60

0.11

28

12.14

12.6043

12.1365

3.82

0.03

87

2.29

2.1020

2.3011

8.21

0.49

29

4.65

3.9788

4.7489

14.44

2.13

88

5.12

5.5105

5.0762

7.63

0.85

30

0.84

0.6692

0.8794

20.34

4.69

89

0.41

0.5473

0.3989

33.49

2.70

31

0.89

0.8189

0.9227

7.99

3.67

90

8.10

9.5860

7.9691

18.35

1.62

32

8.17

6.0788

8.5622

25.60

4.80

91

0.38

0.5559

0.3731

46.29

1.82

33

1.40

1.4173

1.3779

1.24

1.58

92

2.29

2.0965

2.2347

8.45

2.41

34

1.37

1.2933

1.3213

5.60

3.56

93

0.45

0.2244

0.4401

50.14

2.20

35

0.74

0.6854

0.7051

7.38

4.71

94

0.76

0.7058

0.7765

7.13

2.17

36

1.35

1.1543

1.4025

14.50

3.89

95

8.03

7.9612

8.1409

0.86

1.38

37

0.59

0.4972

1.6038

15.73

2.34

96

3.25

3.7312

3.2752

14.71

0.78

38

5.10

3.6088

5.3373

29.24

4.65

97

11.26

11.8617

11.2349

5.23

0.22

39

1.44

1.3620

1.4128

5.42

1.89

98

3.78

3.8444

3.7817

1.70

0.04

40

0.11

0.1249

0.1131

13.57

2.85

99

0.80

1.0795

0.7856

34.93

1.80

41

0.89

0.8149

0.9306

8.44

4.57

100

0.47

0.5556

0.4623

18.21

1.65

42

2.14

2.0095

2.1400

6.10

0.00

101

1.00

1.0367

1.0077

3.67

0.77

43

0.27

0.2066

0.2830

23.49

4.83

102

0.46

0.5045

0.4387

9.66

4.62

44

4.41

4.1795

4.5546

5.23

3.28

103

0.50

0.3250

0.5174

35.00

3.49

45

2.25

1.7818

2.2985

20.81

2.15

104

6.98

5.5115

7.0106

21.04

0.44

46

1.59

1.1074

1.6206

30.35

1.92

105

2.28

1.4454

2.3099

36.60

1.31

47

1.04

1.6420

1.0235

57.88

1.58

106

0.31

0.2947

0.3106

4.92

0.20

48

2.02

2.3111

1.9642

14.41

2.76

107

0.35

0.3352

0.3586

4.23

2.46

49

2.13

2.4079

2.0971

13.05

1.55

108

4.73

4.9577

4.5500

4.81

3.81

50

2.64

2.4554

2.6605

6.99

0.78

109

0.45

0.40.5

0.4575

10.33

1.66

51

0.15

0.2385

0.1383

59.03

7.83

110

0.22

0.2280

0.2019

3.66

8.23

52

0.23

0.1250

0.2439

45.66

6.03

111

0.50

0.4164

0.5394

16.72

7.87

53

0.57

0.5687

0.5419

0.24

4.93

112

0.64

0.9773

0.5563

52.71

13.08

54

1.11

0.8933

1.2041

19.53

8.47

113

1.36

0.9864

1.4244

27.47

4.74

55

1.59

1.2239

1.6628

23.02

4.58

114

1.62

2.4508

1.5403

51.28

4.92

56

1.67

2.3435

1.5873

40.33

4.95

115

2.30

1.3004

2.4115

43.46

4.85

57

2.34

2.9862

2.2232

27.61

4.99

116

3.13

4.1409

2.9426

32.30

5.99

58

3.49

4.4483

3.3186

27.46

4.91

117

4.18

3.3670

4.3813

19.45

4.82

59

6.91

7.8040

6.5722

12.94

4.89

118

8.53

7.4215

8.9107

12.99

4.46