# Analysis of Random Dynamics of Cell Segmented by a Modified Active Contour Method
## 4 Conclusions  
The random dynamics of a cPMS particle and MCF-7 cell recorded at a frame rate of 25 hz were measured, and sub-pixel resolution analyses were performed using three localization methods, the radial symmetric method, circular Hough transform method, and modified active contour method. To understand the effects of different image analysis methods in localizing the position of a cell in an image for random dynamics analysis, the trajectory, MSD, and VACF of the measured objects were compared, and we found that the modified active contour method presented the smallest localization error compared to the other two methods considered. In addition, the effect of denoising on the stochastic dynamics of the MCF-7 cell was discussed for different image analysis methods. An iterative fitting-based localization method has been used in single-particle tracking, where the considered particle size is on the order of a nanometer so that the image can be approximately modeled as a point spread function such as a Gaussian function. The radial symmetry method, however, determines a direction of center from every pixel by calculating the gradient of the point spread function at each pixel instead of using Gaussian fitting. When it is applied to the image of a nanosized object or of an object that is radially symmetric and has a clear gradient about the centroid, the radial symmetry method is appropriate for tracking. As shown in Figure 2 for cPMS, the radial symmetry method found the center of the cPMS and reported the MSD and VACF with little localization error, even though the size of the particle was on the micron scale. When studying cellular dynamics or migration, the size of the target object is on the micron scale; in our study, it was approximately 14.32 \(\upmu\)m. Additionally, unlike a particle image, cellular images contain many irregular components such as non-circular shapes and small signal to noise ratios. Due to such weak radial symmetric properties, the radial symmetric method is not suitable for detecting the center point of a cellular image and has an enhanced likelihood of generating localization errors for algorithms detecting an object based on a circular shape. The localization error from the circular Hough transform method was the largest among the methods considered, as shown in Figure 4. The circular Hough transform method finds the center point, assuming that the object is circular. The non-circular shape of the cell and unclear edges of cell images can be major sources of localization errors. In addition to non-circularity, there are many dynamic noise sources in the interior of the cell. The morphology of the cell is inhomogeneous due to diverse cellular components such as the nucleus, ER, and mitochondria. As time elapses, these cellular components move freely within the cellular membrane. As discussed, both the radial symmetry method and the circular Hough transform method can be influenced by noise inside and/or outside of a cell; in particular, the radial symmetry method can be significantly influenced by background noise. Therefore, it could be useful to consider only the boundary of the cell for cellular localization in a dynamic cellular image. The modified active contour method employed in this study considers the boundary of the cell and calculates the center based on this boundary, decreasing the possibility of localization errors. After the denoising process was applied to the bright field image, the boundaries of the cells became clear, and the cell outline detection was more effective than in the images without denoising. This preprocessing could reduce localization error through analysis of MSD and VACF, as shown in Figure 6. Thus, we conclude that it is helpful to employ a denoising process on a bright field image and/or to analyze the position using the modified active contour method to minimize the effects of localization error in cellular dynamics measurements.