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A developed computer vision algorithm [4] is used for dirt egg detection and determination of defected eggs size. Black and white images are used for egg defect ...
International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 11, November 2015)

Indirect Method for Egg Weight Measurement Using Image Processing Alikhanov D.1, Penchev S.2, Georgieva Ts.3, Moldajanov A.4, Shynybaj Z.5, Daskalov P.6 1,4,5

Kazakh National Agrarian University, Department of Energy Saving and Automation , Almaty, Kazakhstan 2,3,6 University of Ruse “Angel Kanchev”, Department of Automatics and Mechatronics,Ruse, Bulgaria

Abstract— An algorithm for indirect egg weight volume measurement using image processing is proposed. Regression analysis is used for approximation of relationship between egg weight and egg geometric parameters – perimeter, area, major and minor axis, shape coefficients and volume. The values of volume for each egg sample collected by image processing and traditional method based on water displacement were compared using percent differences between data. The experimental results show that the most significant parameters are egg area and volume with the following approximation - polynomial with order 3 with a value of R2=0,9439 and exponential regression with R2= 0,9235.

The objective of the study is to propose an algorithm for indirect measurement of egg weight using machine vision system and image analysis.

Keywords—egg weight, image processing, regression analysis, geometric parameters, shape coefficients.

A. Machine Vision System The components of machine vision system for egg grading shown on Fig. 1. include:  CCD camera VIDO AU CC540HDN - 1  Light source system – 2  Personal computer – 3  Work surface – 4.

II. MATERIALS AND METHODS The indirect method for egg volume measurement includes the following main steps: egg image acquisition using appropriate machine vision system, image analysis using appropriate image procedures for calculation of egg geometric parameters and statistical methods for determining the relationship between the weight of the eggs and their geometric parameters.

I. INTRODUCTION Main requirement in egg grading systems is weight eggs classification which is specified as per-egg weight ranges as shown in Table 1 [8]: TABLE 1 EGG WEIGHT RANGES

1 2 3 4

Egg Size XL-very large L-large M-medium S-small

Egg weight 73 g 63 g to 73 g 53 g to 63 g under 53 g

1 3

2

An analysis of literature for existing grading systems have shown that there are many automatic system for egg grading which are used mainly for defect detection [3,6] and for detecting internal blood spots and eggshell dirt [2,5]. Different methods such as optical, mechanical, spectral have also been used for classification of eggs using different classification criterion. In [7] near infrared spectroscopy is used for detection of blood spots in eggs. A developed computer vision algorithm [4] is used for dirt egg detection and determination of defected eggs size. Black and white images are used for egg defect detection [1].

5 4

Fig. 1. Machine vision system for egg grading

The technical data of the color CCD video camera used are the following: - Photo sensor - 1/3 "SONY Super HAD matrix with a resolution of 795 x 596 pixels;

30

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 11, November 2015) -

Resolution - 540 TVL; Video output - composite video with BNC connector; Electronic shutter - from 1/50 - 1/120000 sec; Spectral sensitivity - visible and infrared range (800 ÷ 1200 nm). The system provides illumination of the object in two different directions - over, to analyze the color characteristics and bottom, with the aim of radiographic object. LED lighting with white light and a color temperature of 3000K is used.

The coefficients KX and KY can be used to measure distances in a visual image, when the desired result should be in millimeters. For example, the distance between point A (XA,YA) and B (XB, YB) is obtained based on the Euclidean distance of the equation as follows:

DAB 

Input RGB Egg Image

2

Convert RGB to Gray Image

3

Convert Gray Image to Black/White Image

4

Calculation of Geometric Egg Parameters

b)

c)

d)

a) input RGB egg image, b) gray egg image, c) binary image, d) geometric parameters calculation

One of the main procedures for working with visual system is calibration procedure. Determined numbers of pixels correspond to the diameter of the object in horizontal and vertical direction. Identifying two coefficients Kx and Ky (mm/pix), provide millimeters corresponding to one pixel in X and Y direction: D, D, Ky  Px Py

a)

Fig. 3. Main steps of image processing algorithm

Fig. 2. Block diagram of the proposed method

Kx 

(2)

For converting the images in gray and then in black/white (binary) image are used functions in MATLAB. After receiving the gray image it is converted into a binary with two types of pixels - white (object pixels) and black (background pixels). This is done by standard procedure using threshold gray image segmentation. The calculated geometric egg parameters using images of the eggs are minor and major axis, area, perimeter and two shape coefficients.

B. Image Processing Algorithm The proposed algorithm for egg image processing includes following main steps: RGB image acquisition (1), converting RGB to Gray image (2), converting Gray to Black/White image (3) and calculation of geometric egg parameters (4). The block diagram of the proposed method is shown in Fig 2. 1

X A  X B  K X 2  YA  YB  KY 2 , mm.

The geometric egg parameters are obtained as results of Matlab function regionprops. Other three parameters are also calculated – two coefficients of egg shape (K1 and K2) and egg volume.

K1 

(1)

P2 S

and

Where P is egg perimeter; S – egg area; A - minor axis; B – major axis.

Where D, mm is the diameter of the standard circular object; Px, Py - the number of pixels in the directions X and Y, corresponding to this diameter.

31

K2 

A , B

(3)

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 11, November 2015) The egg volume is calculated using the following equation:

Vc 

2 AB , cm3 3

Tools used for this purpose is regression analysis of the eggs weight and their geometric parameters. For this approximation a set of analytical models is performed and for each of them the coefficient of determination R2 is calculated.

(4)

Where A is the minor axis; B – major axis.

III. RESULTS AND DISCUSSION Results for calculated geometric parameters of eggs are shown in Table 2. The second column is egg weight which is measurement using precise electronic scale.

C. Indirect Method for Weight Egg Measurement The results are analyzed to determine the relationship between the weight of the eggs and their geometric parameters. TABLE 2

EGG WEIGHT RANGES

1

54,43

15,512

18,51

5,23

4,47

13,00

0,85

48,89

2

52,36

15,567

18,38

5,42

4,28

13,18

0,79

48,51

46

5,18

3

48,66

15,344

17,62

5,43

4,09

13,36

0,75

46,41

45

3,05

4

43,70

14,625

15,97

5,12

3,98

13,39

0,78

42,67

40

6,26

5

43,68

15,089

16,79

5,51

3,86

13,56

0,70

44,54

41

7,95

6

49,14

4,13

13,26

0,77

46,69

45

3,62

7

47,81

4,15

13,11

0,79

45,51

46

1,07

8 9 10 11 12

62,56 57,49 63,73 45,61 61,09

13,44 13,20 13,04 13,07 13,11

0,70 0,75 0,81 0,83 0,81

57,32 55,43

60 56 56 42 53

4,67 1,04

13 14 15

50,67 60,28 53,52

15,408 16,274

17,99 20,13

5,37 5,72

4,21 4,45

5,69

4,18

49,79

48 50 47

1,35 6,16

18,92

0,78 0,78 0,74

47,36 53,28

15,886

13,19 13,16 13,34

16

42,75

14,548

15,83

5,10

3,93

13,37

0,77

41,92

44

4,95

17

56,55

15,836

19,02

5,51

4,34

13,17

0,79

50,09

47

6,19

18

58,83

15,832

19,15

5,36

4,54

13,09

0,85

50,84

49

3,61

19

37,22

14,208

14,91

5,17

3,65

13,54

0,71

39,53

39

1,35

20

55,67

4,61

13,03

0,92

48,14

50

3,86

21

55,64

4,36

13,13

0,80

49,80

50

0,40

22 23 24 25 26

52,81 50,52 52,60 54,80 58,75

13,00 13,03 13,20 13,09 13,06

0,87 0,85 0,81 0,86 0,84

46,72 45,69

48 47 46 51 51

2,73 2,87

15,221 15,025

Area, cm2

17,47 17,22

Major axis, cm

Minor axis, cm

K1

K2

Vc , cm3

Percent differences

VWD , cm3 45

Egg Weight, Perimeter, number g cm

5,40 5,24

17,015 16,574

21,53 20,81

6,27 5,93

4,37 4,47

16,504 14,704

20,89 16,54

5,74 5,04

4,64 4,20

16,219

20,07

5,63

4,57

15,517 15,759

18,48 18,91

4,99 5,46

15,206 14,991

17,79 17,25

5,06 5,06

4,41 4,31

15,542 15,527

18,29 18,42

5,37 5,23

4,33 4,49

15,884

19,31

5,39

4,55

32

55,68 44,29 53,80

48,63 49,09 51,28

7,96

0,57 5,17 1,49

5,61

5,40 3,90 0,54

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 11, November 2015) Columns from third to seventh are calculated from egg images. The last column for egg volume is obtained using water displacement method for volume measurement as a reference method for assessment the accuracy of volume calculation using equation 4. The values of volume for each egg sample collected by image processing and traditional method based on water displacement were compared. The percent difference between two data points was calculated as the ratio between the absolute value of the difference between the two values and the expected value:

70 65 y = 13,218x - 18,669 R2 = 0,3582

60

Series1

Weight, g

55

Linear (Series1)

y = 73,004Ln(x) - 70,301 R2 = 0,3582

50

Log. (Series1) Poly. (Series1) Poly. (Series1)

45 40 35

Power (Series1)

1,3842

y = 5,0756x R2 = 0,3293 y = -28,394x3 + 476,3x2 - 2641,8x + 4900 R2 = 0,3886 y = -0,9691x2 + 23,962x - 48,343 R2 = 0,3585

30 4,50

5,00

Expon. (Series1)

y = 13,528e0,2504x R2 = 0,3286

5,50

6,00

6,50

Major axis, cm

differences 

Perecent

VC  VWD VC

(5)

.100 ,%

Fig. 6. Approximation of the weight from the major axis 70

The results of approximation with analytical model and the values of R2 are shown on Fig. 4, 5, 6, 7, 8, 9 and 10.

65 60

75 70

Weight, g

Series1

y = 145,06Ln(x) - 345,03 R2 = 0,8692

55

Weight, g

60

2,0534

y = 2,6391x R2 = 0,8509

55

y = 9,2803x - 91,411 R2 = 0,8607

65

y = 24,461x - 52,196 R2 = 0,8254 y = 102,22Ln(x) - 95,956 R2 = 0,8247

Linear (Series1)

50

Series1 Linear (Series1)

0,4902x

y = 6,3893e R2 = 0,8474

Log. (Series1) Poly. (Series1) Poly. (Series1)

45

Power (Series1)

Log. (Series1)

Expon. (Series1)

Poly. (Series1)

50

y = -2,0957x2 + 74,604x - 599,56 R2 = 0,8931

45

y = -0,7466x3 + 32,848x2 - 469,72x + 2222,3 R2 = 0,8956

40 y = 0,0215x2,8441 R2 = 0,8543

35

14,5

15

15,5

16

16,5

y = -0,6351x2 + 29,79x - 63,335

Power (Series1)

2

R = 0,8255

35

Expon. (Series1)

y = -13,296x3 + 165,37x2 - 658,97x + 886,22 2

30 3,50

y = 3,1161e0,1816x R2 = 0,8427

30 14

40

Poly. (Series1)

R = 0,827 3,70

3,90

4,10

4,30

4,50

4,70

Minor axis, cm

17

17,5

P, cm

Fig. 7. Approximation of the weight from the minor axis

Fig. 4. Approximation of the weight from the perimeter

70,00

y = -21,556x + y337,21 = -285,21Ln(x) + 788,55 R2 = 0,2817

65,00

R2 = 0,2805

70 y = 3,9345x - 19,343 R2 = 0,9204

60,00

y = 71,881Ln(x) - 156,02 R2 = 0,9319

60

Weight, g

65

Series1

Weight,g

55

Linear (Series1)

1,4162

y = 0,8558x R2 = 0,925

50

Log. (Series1)

R2 = 0,319

55,00 50,00 45,00

y = 2E+08x -5,9576 y =2-49,859x 2 + 1300,8x - 8429,4 R = 0,313 2 R = 0,3185

Poly. (Series1)

40,00

Poly. (Series1) 45

Power (Series1)

2

y = -0,2777x + 14,102x - 111,72 2 R = 0,9394

40

3

35,00

Expon. (Series1)

2

30,00 12,90

y = -0,0775x + 3,9647x - 62,811x + 349,92 2

R = 0,9439

35

y = 36,774x 3 - 1513,7x 2 + 20723x - 94319

y = 12,718e 0,0772x

y = -2865,9x 4 + 152162x 3 - 3E+06x 2 + 3E+07x - 9E+07 R2 = 0,36 13,00

13,10

13,20

13,30

13,40

13,50

K1

2

R = 0,906 30 13

15

17

19

21

23

Fig. 8. Approximation of the weight from K1

A,cm2

Fig. 5. Approximation of the weight from the area

33

13,60

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 11, November 2015) 70,00

The relationship between egg weight and volume (Fig. 10) is approximated using exponential regression with R2 = 0,9235. The percent differences between data for egg volume calculated from digital egg image and the values obtained using water displacement method are less than 10%. This result shows that image analysis is appropriate for calculation of egg volume with values near to the reference.

y = 35,711x + 24,304 y = -1726,5x 3 + 4024,9x 2 - 3075,9x + 821,97 28,66Ln(x) + 59,336 R2y==0,0883 R2 = 0,0996 R2 = 0,0902

65,00

Weight, g

60,00 y = 60,43x 0,6261

55,00

R2 = 0,1101 50,00 45,00 y = 111486x 4 - 362813x 3 + 441177x 2 - 237531x + 47822 R2 = 0,138

40,00

IV. CONCLUSION

2

y = -138,37x + 256,6x - 63,45 35,00

An algorithm and procedure for indirect measurement of egg weight using egg digital images are developed and tested. The relationship between the egg weight and geometric parameters are approximated using regression analysis and coefficient of determination. The results show that perimeter, major and minor axes, shape coefficients K1 and K2 are insignificant for indirect measurement of egg weight using image analysis. Most significant parameters are area and egg volume with the following approximation - polynomial with order 3 with a value of R2 = 0,9439 and exponential regression with R2 = 0,9235.

2

R = 0,0951

30,00 0,65

0,70

0,75

0,80

0,85

0,90

0,95

K2 Fig. 9. Approximation of the weight from K2 60,00 y = 31,156Ln(x) - 74,75 R2 = 0,8903

y = 0,6224x + 15,719 R2 = 0,9085

55,00

Weight, g

Series1 Linear (Series1)

50,00 y = 3,66x 0,6522 R2 = 0,9128

y = 24,395e0,013x R2 = 0,9235

45,00

Log. (Series1)

REFERENCES

Poly. (Series1)

[1]

Poly. (Series1) Power (Series1)

y = 0,0075x 2 - 0,1489x + 35,226 R2 = 0,9165

Expon. (Series1)

40,00

[2]

y = 0,0006x 3 - 0,0844x 2 + 4,4645x - 40,829 R2 = 0,9196 35,00 30

35

40

45

50

55

60

65

70

Vc, cm3

[3] Fig. 10. Approximation of the weight from the volume

The results in Fig. 4 show that for the approximation of the dependence of weight on the perimeter, the good score were obtained by a polynomial of 4th order with a value of R2 = 0,8965. The results in Fig. 5 show that for the approximation of the dependence of weight on the area, the good score were obtained by a polynomial with order 3 with a value of R2 = 0,9439. The results in Fig. 6 show that the highest value of R2 = 0,3886 were achieved using polynomial with order 3. The relationship between the weight of the eggs and their minor axis is approximated with regression of type Power (Fig. 7) with value of R2 = 0,8509. The values of R2 for shape coefficients K1 and K2 (Fig. 8 and Fig. 9) are insignificant and do not show relationship between them and egg weight.

[4]

[5]

[6]

[7]

[8]

34

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