# Application of Visual Radiographic Analysis of Quality Grade of Table Eggs
## 4 Discussion  
The principle of radiographic imaging is the result of the effect of the linear attenuation coefficient when ionizing radiation is applied to a non-uniform density material. The linear attenuation coefficient of the X-rays is proportional to the density of the material [28]. The performance of the gray-scale values of the images represents the image converted from every gray-scale matrix unit density value [29]. According to other studies, there is no direct correlation between the quality of the shell and the quality of the egg. The same results are shown in Figures 3-5. However,  
Figure 10: The results of the gray-scale density distribution curves from radiography visualization for the yolk and albumen of eggs of three different qualities in the axial plane directions. (**A**) Comparison of shell quality curves of eggs of three different qualities, (**B**) SO egg (Egg 1) (black line), (**C**) GO egg (Egg 2) (red line), and (**D**) CO egg (Egg 3) (green line). the thickness of the shell and the compressive strength indeed reduce the damage rate of the egg [30; 31; 32]. The shell is mainly composed of calcium carbonate (CaCO\({}_{3}\)) crystals. The quality of the shell is indeed directly related to the production of the eggs. The measurement of the quality of the shells is mostly achieved through destructive inspection methods, such as optical or electronic inspection methods, to measure the uniformity of shell thickness and determine the shell quality [33]. Radiography visualization is a non-destructive detection, where imaging is based on the principle that the density of the substances, the linear attenuation coefficient, and the absorption of ionizing radiation are different [34]. Figure 4B,C shows the stratification images of the inner egg and air chamber based on the segmented results using the multi-level Otsu thresholding methods. As the grayscale intensities of eggshell partially overlap with that of egg yolk (see Figure 1D), this makes it difficult to perfectly perform image segmentation between eggshell and inner egg using the intensity-based segmentation method. Therefore, the stratification images in Figure 4C retain some eggshell structure. The segmentation error may affect the quantification analysis; however, we consider the effect is small because the grayscale value of the eggshell is small relative to the inner egg. Further improvement can be investigated by using advanced segmentation methods such as K-means segmentation algorithm. Figures 7 and 8 show the results of the comparison of shell qualities, which were obtained through the median and axial plane DICOM gray-scale images of eggs of three different qualities. The gray-scale density values of SO eggshell in the median plane direction are significantly higher than GO and CO eggs. The trend is similar to the results observed in [PERSON] et al. [35]. They found that the eggshell tendency to break increased as the egg quality decreased (from good quality to rotten and defective eggs). The yolk and albumen are mainly composed of ovomucin and a variety of amino acids and vitamins [36]. Among them, the structure of ovomucin is directly related to the egg quality. Although the United States Department of Agriculture also has established a quality standard for yolk thickness [2], there are many ways to evaluate the in-egg quality. Taking the regression detection of destructive detection and spectrophotometer detection of albumen height, egg weight, and absorbance between HU values (Haugh values) as the evaluation standard of thickness [37], the difference in consistency is directly related to the internal density of the substance. The quality of an egg is determined by the saturation and thickness of the yolk and albumen after the egg is broken. The density under high saturation and thickness is also relatively high, and correspondingly, the grayscale value in the radiography is also relatively high, the results shown in Figures 9 and 10. The two gray-scale density peaks of the yolk and albumen decrease with the quality of the egg.