# A Vision-Based Micro-Manipulation System
## 3 System Overview
### Image Enhancement  
Image enhancement plays a vital role in improving the image quality of living cells acquired from the microscope by emphasizing key features, reducing secondary characteristics, enriching information, and enhancing details. Fuzzy Automatic Contrast Enhancement (FACE) [5] is applied as a contrast enhancement technique for microscopic images of living cells. FACE changes the original pixel distribution to a less congested one while maintaining smoothness in the color distribution to prevent artifacts in living cell images. This approach utilizes a universal contrast enhancement variable (UCEV) to achieve better contrast enhancement automatically, without manually feeding parameters. The FACE technique utilizes a Fuzzy C-Means (FCM) method to classify pixels with similar colors together using clustering. The maximization of image entropy was automatically achieved through the use of UCEV. By utilizing FCM and UCEV, the image contrast was enhanced with good accuracy, without any artifacts or noise. The schematic diagram for FACE image enhancement is illustrated in Figure 2.  
Figure 1: Architecture of the proposed micro-manipulation system.  
In this method, it is assumed that there is an '\(n\)' set of image pixels \(x_{i}\) for \(i=1\ldots n\). These image pixels are arranged into \(k\) groups, whose centers are described by \(j=1\ldots k\). The presence of a \(i\)th pixel in \(j\)th cluster is indicated by \(u_{ij}\). When using K-means as an exact clustering method [45; 46], the value of \(u_{ij}\) can be either 0 or 1, where 0 represents inclusion and 1 represents exclusion. In contrast, FCM permits the representation of partial pixel inclusion within each cluster. According to FCM, \(u_{ij}\) will be a real number within a certain range of values from \([0,1]\). The definition of total in-group variance is shown in Equation (1).  
\[J=\sum\limits_{j=1}^{k}\sum\limits_{j=1}^{k}\left(u_{ij}^{m}\left\|x_{i}-c_{j} \right\|^{2}\right) \tag{1}\]  
The inclusion parameters suggested by different studies can range from 1 to 5. For this method, it is considered to be 5. To achieve optimal image segmentation, it is crucial to minimize the inclusion of \(J\) pixels, as this reduces in-group variations, leading to larger ones. We can formulate the Lagrangian Equation stated in Equation (2), where \(\lambda_{i}\) represents a Lagrangian multiplier determined by the minimization problem \(L\).  
\[L=\sum\limits_{j=1}^{k}\sum\limits_{i=1}^{n}\left(u_{ij}^{m}\left\|x_{i}-c_{j} \right\|^{2}+\lambda_{i}u_{ij}\right)-\sum\limits_{i=1}^{n}\lambda_{i} \tag{2}\]  
After solving the above equation to obtain the optimal fuzzy inclusiveness, the ideal parameter can be obtained as shown by Equations (3) and (4).  
\[c_{j}=\frac{\sum\limits_{i=1}^{n}u_{ij}^{m}x_{i}}{\sum\limits_{i=1}^{n}u_{ij}^{ m}} \tag{3}\]  
\[u_{ij}=\frac{1}{\sum\limits_{l=1}^{k}\left[\left\|\frac{\left\|x_{i}-c_{j} \right\|}{\left\|x_{i}-c_{l}\right\|}\right]^{\frac{2}{n-1}}} \tag{4}\]  
Equation (3) defines the center of the \(j\)th cluster, based on provided inclusiveness values, while Equation (4) determines the inclusiveness parameter \(u_{ij}\) based on the given cluster center points. The convergence of the value \(L\) persists as the parameterized process continues. In our approach, the parameterized technique is initiated with arbitrary assumptions denoted as \(u_{ij}\), and this approach consistently yields reliable results across multiple trials. It is noteworthy that the FCM typically delivers the most accurate identification outcomes when operating within the CIELAB color space, established by the Commission International d'Eclairage, where L signifies lightness, and AB represents the dimensions of color components.