# U-Net-Based Semi-Automatic Semantic Segmentation Using Adaptive Differential Evolution
## 2 Proposed Method
### Windowing by jDE  
DICOM is an international standard format for medical images such as CT and MRI DICOM has various parameters consisting of personal information such as name, gender, and hospital, as well as image composition information such as CT number, window size, and tone level. The CT number is the value of the X-ray absorption coefficient of the tissue captured by CT, with 0 for water and \(-1000\) for air. The values range from \(-1000\) to \(4000\) and must be converted to a range from 0 to 255 when outputting images. If all CT numbers are projected in the image output, the tissue irrelevant to the diagnosis is also included in the image. Thus, it is necessary to use only the CT number ranges that match the target tissue. This conversion is called windowing. Windowing uses two parameters, window center (WC) and window width (WW), to specify the center and width of the target area, respectively. Figure 2 shows an example of the distribution of CT numbers in body tissues. More detailed observations become possible by setting the window conditions according to the target tissue. In our proposed method, the U-net is applied for semantic segmentation, but image preprocessing affects the final performance of the segmentation. As mentioned above, windowing parameters are sensitive and require a real-value optimization. To estimate appropriate windowing parameters, in this paper, we optimize them using adaptive differential  
Figure 2: CT number distribution. evolution (jDE). jDE [31] is a kind of DE and is a real-value optimization method that applies an evolutionary computation algorithm to perform a multipoint search. DE is usually applied to nonlinear and nonconvex optimization problems that cannot be differentiated. Compared to other real-value optimization approaches, it is faster and more robust because it does not require complex computations and differentiation and has few operating parameters. The parameters that need to be set in DE are the number of generations, scaling factor, and crossover probability. The \"number of generations\" indicates the number of searches, while the \"scaling factor\" is a parameter that manipulates the range of searches. The crossover probability is a parameter used for inheriting elements from the original individual in a crossover. The jDE algorithm is as follows:  
* Generate an initial population set \(\mathbf{X}=\{\mathbf{x}_{1},...,\mathbf{x}_{N}\}\) with a random uniform distribution within feasible regions. * \(g\gets 1\)
* Select three individuals \(\mathbf{x}_{r1},\mathbf{x}_{r2},\mathbf{x}_{r3}\) for individual \(\mathbf{x}_{i}\), where (\(r1\
eq r2\
eq r3\)). * Generate the mutant vector \(\mathbf{v}_{i}=\mathbf{x}_{r1}+F_{i}^{g}(\mathbf{x}_{r2}-\mathbf{x}_{r3})\), where \(F[0,1]\) is a scaling parameter. * Select \(j\) randomly from \([1,\,n]\), where \(n\) is the dimension of each \(\mathbf{x}_{i}\). * Cross over between the mutant vector \(\mathbf{v}_{i}\) and the parent vector \(\mathbf{x}_{i}\) using the following equation, \[u_{i,j}= \begin{cases}v_{i,j}&\text{if }\ (\text{rand}[0,1)\leq CR_{i}^{g})\vee(j= \text{rand}[1,n]),\\ x_{i,j}&\text{otherwise},\end{cases} \] where \(CR\) represents the crossover rate. * Apply D-1 to D-4 to generate a population of trial vectors \(\mathbf{U}=\{\mathbf{u}_{i};i=1,...,N\}\). * Evaluate \(\mathbf{U}\) and update the solution set. * Update \(F_{i}^{g}\) and \(CR_{i}^{g}\) by the following equations \[F_{i}^{g+1}= \begin{cases}F_{l}+\text{rand}[0,1)\cdot F_{u}&\text{if }\ (\text{rand}[0,1)\leq\tau_{1},\\ F_{i}^{g}&\text{otherwise},\end{cases} \] \[CR_{i}^{g+1}= \begin{cases}F_{l}+\text{rand}[0,1)&\text{if }\ (\text{rand}[0,1)\leq\tau_{2},\\ CR_{i}^{g}&\text{otherwise},\end{cases} \] \[\textbf{D-9}\ \ g\gets g+1\] **D-10**: Repeat D-1 through D-9 for a certain period. Using the jDE, we optimized the windowing parameters \(\mathbf{w}_{i}=\{wc_{i},ww_{i}\}\), where \(wc\) is a window center and \(ww\) is a window width.