## 2 Principles
### Image Processing Algorithm  
The sapphire growth process of the Ky method consists of the following stages: the heating stage, in which alumina is put into the crucible and heated; the melting stage, in which the alumina is molten; the seed preparation stage, in which the temperatures of melted alumina, stream lines, and island position are observed to prepare for seeding; and the seed descending stage. Seed cleaning occurs through the first contact between the seed and the melt, and the second contact between the seed and the melt for sapphire growth. The process observed in this study is the seed preparation stage. In this process, the worker generally monitors the surface of the melt in the growth furnace through a view point with the naked eye. Convection becomes activated from the heater around the crucible after the internal alumina is fully molten. At this time, stream lines begin to form in areas where the temperature is lower than the surrounding areas on the surface of the melt, and a spoke pattern can be observed as a result. When the melt material temperature inside the growth furnace is stabilized, the convection of the alumina melt is also stabilized, and the island, is located at the center of the growth furnace crucible. Then, when the island size grows to 10-20 mm, seeding begins. To detect the seeding point accurately, a technique is required for automatic detection of island size and the time when the center of the island coincides with the center of the crucible. To measure the melt surface inside the growth furnace using an image, a charge coupled device (CCD) camera is installed at a view point on the top of the growth furnace. However, due to the location and size of the view point, only a portion of the actual melt material surface can be measured as shown in Figure 2.  
Therefore, an algorithm was developed to measure the shape of the spoke pattern from a limited field of vision, to detect stream lines using various data obtained from the surface of the melt, and to measure the island, or the intersection point of the stream lines  
The image processing procedure is divided into the image preprocessing stage, in which the collected images are binarized, and the image processing stage in which the center point of the island is traced through binarized data, as shown in Figure 3.  
Figure 1: Spoke patterns on the surface of the melt according to temperature distribution in the crucible. Image preprocessing is not only important for acquiring accurate stream-line data, but is also related to the accuracy of the measured data. The luminance plane is extracted to obtain information related to the brightness of the melt surface, which is obtained from the CCD camera images. The extracted image goes through a binarization process that distinguishes particles (stream lines) from non-particles (background). Global binarization, which is one of the image binarization methods that uses threshold values, provides the advantage of minimal computation. However, both the surface temperature distribution and brightness of the extracted image are irregular. It is difficult to obtain accurate stream-line data through global binarization alone. Hence, the Niblack binarization algorithm is used to overcome this condition. Niblack binarization takes threshold values by region and then performs binarization. The Niblack binarization equation is shown below:  
\[(x,y)=m(x,y)+k\cdot s(x,y) \tag{1}\]  
In this equation, \(m(x,y)\) and \(s(x,y)\) denote the average and standard deviation in a regional window, and \(k\) denotes the user defined variable for binarization. Niblack binarization determines the critical value using the average and standard deviation of pixel values inside the regional window, and the parts above the threshold value are extracted by comparing the critical value with the original image; these parts are then binarized. Figure 3: Image processing procedure to find the center point of the spoke pattern. Figure 2: Comparison of the spoke pattern and observed pattern on the surface of the melt.