Indirect Method for Egg Weight Measurement Using Image Processing

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)

30

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.

Keywords—egg weight, image processing, regression

analysis, geometric parameters, shape coefficients.

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]:

TABLE1

EGG WEIGHT RANGES

Egg Size Egg weight

1 XL-very large 73 g

2 L-large 63 g to 73 g

3 M-medium 53 g to 63 g

4 S-small under 53 g

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].

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

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.

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.

1

2

3

[image:1.612.329.555.410.636.2]

4 5

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

[image:1.612.92.245.473.551.2]

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)

31

- 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.

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.

Input RGB Egg Image

Convert RGB to Gray Image

Convert Gray Image to Black/White Image

Calculation of Geometric Egg Parameters 1

2

3

[image:2.612.328.558.332.540.2]

4

Fig. 2. Block diagram of the proposed method

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:

x x

P D

K  ,

y y

P D

K  , (1)

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.

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:

















2

Y B A 2 X B A

AB X X K Y Y K

D      

,

mm. (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.

a) b)

c) d)

Fig. 3. Main steps of image processing algorithm a) input RGB egg image, b) gray egg image, c) binary image, d)

geometric parameters calculation

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.

S P K

2

1  and

B A

K2  , (3)

Where P is egg perimeter; S – egg area;

[image:2.612.95.244.347.537.2]

International Journal of Emerging Technology and Advanced Engineering

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The egg volume is calculated using the following equation:

AB 3 2 Vc



 , cm3 (4)

Where A is the minor axis;

B – major axis.

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.

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.

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.

TABLE2

EGG WEIGHT RANGES

Egg number

Weight, g

Perimeter, cm

Area, cm2

Major axis, cm

Minor axis,

cm K1 K2

c

V , cm3

WD

V ,

cm3

Percent differences

1 54,43 _{15,512 18,51 5,23 4,47} 13,00 0,85 _48,89 45 _7,96

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 _{15,221 17,47 5,40 4,13} 13,26 0,77 _46,69 45 _3,62

7 47,81 _{15,025 17,22 5,24 4,15} 13,11 0,79 _45,51 46 _1,07

8 62,56 17,015 21,53 6,27 4,37 13,44 0,70 57,32 60 4,67

9 57,49 16,574 20,81 5,93 4,47 13,20 0,75 55,43 56 1,04

10 63,73 16,504 20,89 5,74 4,64 13,04 0,81 55,68 56 0,57

11 45,61 14,704 16,54 5,04 4,20 13,07 0,83 44,29 42 5,17

12 61,09 _{16,219 20,07 5,63 4,57} 13,11 0,81 _53,80 53 _1,49

13 50,67 _{15,408 17,99 5,37 4,21} 13,19 0,78 _47,36 48 _1,35

14 60,28 16,274 20,13 5,72 4,45 13,16 0,78 53,28 50 6,16

15 53,52 15,886 18,92 5,69 4,18 13,34 0,74 49,79 47 5,61

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 15,517 18,48 4,99 4,61 13,03 0,92 48,14 50 3,86

21 55,64 _{15,759 18,91 5,46 4,36} 13,13 0,80 _49,80 50 _0,40

22 52,81 _{15,206 17,79 5,06 4,41} 13,00 0,87 _46,72 48 _2,73

23 50,52 14,991 17,25 5,06 4,31 13,03 0,85 45,69 47 2,87

24 52,60 15,542 18,29 5,37 4,33 13,20 0,81 48,63 46 5,40

25 54,80 15,527 18,42 5,23 4,49 13,09 0,86 49,09 51 3,90

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)

33

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:

,% 100 . V V V s difference Perecent C WD C

 (5)

The results of approximation with analytical model and

the values of R2 are shown on Fig. 4, 5, 6, 7, 8, 9 and 10.

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

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

y = -2,0957x2 _{+ 74,604x - 599,56} R2

= 0,8931

y = -0,7466x3 + 32,848x2

- 469,72x + 2222,3 R2

= 0,8956 y = 0,0215x2,8441

R2

= 0,8543 y = 3,1161e0,1816x R2 = 0,8427 30 35 40 45 50 55 60 65 70 75

14 14,5 15 15,5 16 16,5 17 17,5

[image:4.612.50.567.109.643.2]

P, cm W e ig h t, g Series1 Linear (Series1) Log. (Series1) Poly. (Series1) Poly. (Series1) Power (Series1) Expon. (Series1)

Fig. 4. Approximation of the weight from the perimeter

y = 3,9345x - 19,343 R2

= 0,9204

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

y = -0,2777x2

+ 14,102x - 111,72 R2 _{= 0,9394} y = -0,0775x3

+ 3,9647x2

- 62,811x + 349,92 R2

= 0,9439 y = 0,8558x1,4162

R2 _{= 0,925}

y = 12,718e0,0772x R2 = 0,906 30 35 40 45 50 55 60 65 70

13 15 17 19 21 23

A,cm2 W e ig h t, g Series1 Linear (Series1) Log. (Series1) Poly. (Series1) Poly. (Series1) Power (Series1) Expon. (Series1)

Fig. 5. Approximation of the weight from the area

y = 13,218x - 18,669 R2

= 0,3582

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

= 0,3582

y = -0,9691x2 _{+ 23,962x - 48,343} R2 _{= 0,3585} y = -28,394x3

+ 476,3x2

- 2641,8x + 4900 R2

= 0,3886

y = 5,0756x1,3842 R2

= 0,3293

y = 13,528e0,2504x R2 _{= 0,3286} 30 35 40 45 50 55 60 65 70

4,50 5,00 5,50 6,00 6,50

Major axis, cm

[image:4.612.324.566.121.270.2]

W e ig h t, g Series1 Linear (Series1) Log. (Series1) Poly. (Series1) Poly. (Series1) Power (Series1) Expon. (Series1)

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

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

R2 _{= 0,8247}

y = -0,6351x2 _{+ 29,79x - 63,335} R2 _{= 0,8255} y = -13,296x3 _{+ 165,37x}2 _{- 658,97x + 886,22}

R2 _{= 0,827} y = 2,6391x2,0534

R2 _{= 0,8509} y = 6,3893e0,4902x

R2 _{= 0,8474}

30 35 40 45 50 55 60 65 70

3,50 3,70 3,90 4,10 4,30 4,50 4,70

M inor axis, cm

[image:4.612.49.288.292.661.2]

W e ig h t, g Series1 Linear (Series1) Log. (Series1) Poly. (Series1) Poly. (Series1) Power (Series1) Expon. (Series1)

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

y = -21,556x + 337,21 R2

= 0,2817

y = 36,774x3 - 1513,7x2

+ 20723x - 94319 R2

= 0,319 y = -285,21Ln(x) + 788,55

R2 = 0,2805

y = -49,859x2

+ 1300,8x - 8429,4 R2 _{= 0,3185} y = 2E+08x-5,9576

R2 = 0,313

y = -2865,9x4 + 152162x3

- 3E+06x2

+ 3E+07x - 9E+07 R2 = 0,36 30,00 35,00 40,00 45,00 50,00 55,00 60,00 65,00 70,00

12,90 13,00 13,10 13,20 13,30 13,40 13,50 13,60

K1

We

igh

t,

[image:4.612.50.288.333.470.2]

g

[image:4.612.323.563.355.627.2]

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)

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y = 35,711x + 24,304

Ry = -1726,5x2 _{= 0,0883}

3 _{+ 4024,9x}2 _{- 3075,9x + 821,97} R2 _{= 0,0996}

y = 28,66Ln(x) + 59,336 R2 _{= 0,0902}

y = -138,37x2 _{+ 256,6x - 63,45} R2 _{= 0,0951} y = 60,43x0,6261

R2 _{= 0,1101}

y = 111486x4 _{- 362813x}3 _{+ 441177x}2 _{- 237531x + 47822} R2 _{= 0,138}

30,00 35,00 40,00 45,00 50,00 55,00 60,00 65,00 70,00

0,65 0,70 0,75 0,80 0,85 0,90 0,95

K2

We

igh

t,

[image:5.612.50.288.144.393.2]

g

Fig. 9. Approximation of the weight from K2

y = 0,6224x + 15,719 R2 _{= 0,9085} y = 31,156Ln(x) - 74,75

R2 _{= 0,8903}

y = 0,0006x3 _{- 0,0844x}2 _{+ 4,4645x - 40,829} R2 _{= 0,9196} y = 0,0075x2 _{- 0,1489x + 35,226}

R2 _{= 0,9165} y = 3,66x0,6522

R2 _{= 0,9128}

y = 24,395e0,013x R2 _{= 0,9235}

35,00 40,00 45,00 50,00 55,00 60,00

30 35 40 45 50 55 60 65 70

Vc, cm3

W

e

igh

t,

g

Series1 Linear (Series1) Log. (Series1) Poly. (Series1) Poly. (Series1) Power (Series1) Expon. (Series1)

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.

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.

IV. CONCLUSION

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.

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