## 2 Principles
### Image Processing Algorithm
In this study, the deviation value of 0.2 was used in a window with 32 \(\times\) 32 pixels. Because the parts detected on the image are stream lines with low temperatures, dark objects were extracted. After binarization, a mask method is used to delete data associated with the rod part, in which the seed is mounted, and the outer parts, which are not necessary for the measurement of stream lines on the surface of the melt. The region of interest is extracted from the original image using the mask method after binarization because the boundary line in the image may appear as data if binarization is performed after extraction. After the region of interest is extracted, noise elements, excluding the stream lines on the melt surface, are removed using a low-pass filter and pixel size. Figure 4 shows the image preprocessing process. The stream lines on the surface of the melt are distinguished through image preprocessing procedures. In the next image processing stage, the island position is traced using stream lines. Figure 4: Image preprocessing procedure: (**a**) acquiring image information; (**b**) extracting brightness information; (**c**) the binarization process; (**d**) extracting the region of interest; (**e**) removal of noise elements; (**f**) result of image preprocessing. First, through the Hough transform of the acquired pixel data, a straight line representative of each stream line is extracted. The Hough transform is illustrated in Figure 5. One point on the \(x\)-\(y\) coordinate system appears as one curve on the \(\varrho\)-\(\theta\) coordinate system, and one straight line on the \(x\)-\(y\) coordinate system is expressed as one point on the \(\varrho\)-\(\theta\) coordinate system. The region with the highest number of intersection points on the \(\varrho\)-\(\theta\) coordinate system is judged as a straight line in the \(x\)-\(y\) coordinate system, and a straight line in the image is detected in this way. Figure 6 shows the image processing procedure for detecting the position of stream-line intersection. Figure 6a shows an image that underwent the preprocessing procedure on the \(\varrho\)-\(\theta\) coordinate system. Figure 6b shows a histogram that represents the number of intersections of each curve. The region with a large number of intersections of curves on the \(\varrho\)-\(\theta\) coordinate system is actually expressed as a straight line on the \(x\)-\(y\) coordinate system. Thus, representative peak values are selected from each intersection region and moved to the \(x\)-\(y\) coordinate system region to generate straight lines as shown in Figure 6c. In particular, because too many straight lines are likely to appear, only points that have 100 or more intersections are transformed into straight lines, as shown in Figure 6c. Furthermore, the intersection count of curves on the \(\varrho\)-\(\theta\) coordinate system is assigned to each straight line as a weight value. Figure 6d shows the stage in which the coordinates of the island center are detected using the straight line data from the \(x\)-\(y\) coordinate system acquired in the previous stage. To scan the entire image, a circular region of 20 \(\times\) 20 pixels is created on the \(x\)-\(y\) coordinate. At this time, the intersections in the scanned region are detected and the sum of the weight values of the straight lines involved in the creation of each detected intersection is calculated. However, if the same straight line is included twice when summing the weights of straight lines, it is calculated only once. The region that has the largest sum of intersection weights in the inspected image is detected and the center of the intersections in that region is calculated; this is represented as the coordinate of the island center in the growth furnace melt material. Table 1 shows the parameter of image processing to find the center point of the spoke pattern.