# Analysis of Random Dynamics of Cell Segmented by a Modified Active Contour Method
## 3 Results & Discussion
### Comparison of Image Analysis Methods  
Before the discussion about random dynamics of particles and cells analyzed by the localization methods, we explain how each method detects the local point from the bright field microscopy image using the cPMS image. Figure 3a shows the intensity distribution of a cPMS image of 121 by 121 pixels, localized by three methods, namely radial symmetry [18], circular Hough transform [36], and modified active contour. First, the radial symmetry method localizes the target image based on local intensity gradient. At the outset, it defines the midpoint of each grid in the entire image \((x_{k},\,y_{k})\)[18]. At the defined midpoint, the intensity gradient across the grid is calculated. The whole intensity gradient of the cPMS image in Figure 3a is shown in Figure 3b. The intensity gradients have large magnitudes at the bright center region and at the boundary of the particle and point to the center point of the particle. The center point is that where the weighted sum of the distance to the lines of all midpoints is minimal. Figure 3: (**a**) The intensity distribution of a cPMS image. (**b–d**) The illustration of the 3 different localization methods; (**b**) radial symmetry, (**c**) circular Hough transformation and (**d**) modified active contour method. (**e–h**) The representative trajectory of MCF-7 cell using different localization method; (**e**) manual localization, (**f**) radial symmetry, (**g**) circular Hough transformation and (**h**) modified active contour method. In the weighted sum process, the weighting factor is proportional to the magnitude of the intensity gradient, so that the longer vectors toward the center in Figure 3b have a greater effect in determining the center point than do the smaller ones. Radial symmetry is very useful when the resolution of the image is low or the target image is small. On the other hand, when the size of an image is so large that the intensity variation of the target image could possibly affect the overall intensity distribution, it could be treated as noise. Moreover, if the size of the target image was relatively so small that the background represents a large portion of the image, background noise could influence the overall intensity distribution. Second, the circular Hough transform (CHT) embedded in MATLAB 2018b is used to characterize the center point of the circular particle. First, the peripheral edge of an object in the whole image is detected through an edge gradient threshold automatically chosen using the graythresh function, which determines the threshold that minimizes intraclass variance of the selected black and white pixels following [PERSON]'s method [42], embedded in MATLAB 2018b. On the determined edge in the image, the circular Hough transform considers and counts all circles on the expected circumference. Figure 3c shows possible candidates of the circle in the range of radii. The probable center point is the position of the maximum counting point. The circular Hough transform is simple in detecting circular objects with relatively strong edges. However, for a suspended cell, which is not perfectly circular and has an irregular shape, it is hard to automatically detect a strong edge. Lastly, the modified active contour method is a segmentation technique with energy forces and constraints for discrimination of the pixels of interest from the image for further analysis. It does not depend on limited information because it considers the information obtained in the surrounding space as well as the brightness change in expressing the boundary part in the image, as shown in Figure 3d. This method considers the intensity of local edges obtained in the image to search for projected areas such as edges, lines, and subjective judgments in the image. In addition, it makes available a wider range of data by considering the internal relationship of the active contour. Since the conventional active contour method is sensitive to the initial boundary, we modified this method to overcome it.