## 3 Proposed Methodology
### License Plate Character Segmentation
\begin{array}{l}1\text{ \emph{GI} }(x,y)<\frac{\sum_{i=x-m/2}^{x+m/2}\sum_{j=y-m/2}^{y+m/2}GI \text{ (}i,j)}{max}\\ 0\text{ \emph{GI} }(x,y)\geq\frac{\sum_{i=x-m/2}^{x+m/2}\sum_{j=y-m/2}^{y+m/2}GI \text{ (}i,j)}{max}\end{array} \right. \tag{9}\]  
\[Ns=2*floor(size(I)/16)+1 \tag{10}\]  
Figure 6 shows the effect of prior knowledge of foreground polarity. In Figure 6a, the LP with dark foreground is well thresholded while in Figure 6b, the LP with bright foreground is well thresholded. So, for multinational vehicle LPs, we must have prior knowledge of foreground polarities in order to separate foreground from background as multinational VLPs have different backgrounds and foregrounds polarities. After getting binary image, we change its background polarity to bright if needed by using (11). \[B_{I}(x,y)=\left\{ \begin{array}{l}\frac{B_{I}(x,y)}{B_{I}(x,y)}\text{ \emph{if} }FP=Dark\\ \frac{B_{I}(x,y)}{B_{I}(x,y)}\text{ \emph{if} }FP=Bright\end{array} \right. \tag{11}\]The next step is to extract the ROI which contains only required characters by discarding redundant area of license plate. Let I be a given set of objects of 2 types, then required region \((R_{R})\) can be extracted as  
\[R_{R}=\left\{ \begin{array}{c}R\mid R\text{ {is the maximal connected}}\\ \text{ {set of type 1 in I}}\end{array} \right\} \tag{12}\]  
where type 1 and type 2 represent the white and black objects respectively. The character height estimation is also one of the most important and difficult tasks to accomplish the character's segmentation for multinational LPs as different countries LPs have different character size. It also uses further for skew correction and to eliminate the other remaining redundant objects. Until this step, we have already discarded a lot of redundant area of LP by extracting the required background region. To accomplish this task, we propose an adaptive way to estimate the character's height, which can be estimated as  
\[H_{O_{hi}}=\left\{O_{hi}\mid h_{i}=\pm 20\%\text{ {of }}h_{max}\text{ ; }i=1,2, \ldots n\right\} \tag{13}\]  
The \(H_{O_{hi}}\) is a set that is used to keep the objects of specific height. Where, \(h_{max}\) is the maximum height among all detected bounding boxes in extracted region (\(R_{R}\)) of license plate. The \(O_{hi}\) is the targeted object that is selected based on the criteria of height \(h_{i}\). The next bounding box object is compared with \(h_{max}\), if its height is \(\pm 20\%\text{ {of }}h_{max}\) then it will be considered as required object. If it does not fulfil the criteria then the previous bounding box with maximum height will be discarded and a recent one will be considered as maximum height object for further processing. This process will be continued until all required objects are extracted. By following this approach, all larger and smaller objects are eliminated automatically and only required objects, i.e., license plate characters are left. After finding the heights of required objects, we use this information for skew correction by using (14). The skew detection and correction problem is also addressed in an efficient and accurate way, as it helps to enhance the system performance at segmentation as well as at recognition stage. \[CA_{LP}=\text{ {tan}}^{-1}\Bigg{(}\frac{y_{RM(O_{hi})}-\text{ {y}}_{LM(O_{hi})}}{x_{RM(O_{hi})}-\text{ {x}}_{LM(O_{hi})}}\Bigg{)} \tag{14}\]  
where \(O_{hi}\)\(H_{O_{hi}}\), \(y_{RM(O_{hi})}\) and \(y_{LM(O_{hi})}\) is y-axis values of right most and left most detected objects while \(x_{RM(O_{hi})}\) and \(x_{LM(O_{hi})}\) is x-axis values of right most and left most detected objects of _hi_. The border touched characters are separated by using the information of upper and lower boundaries of objects in set \(H_{O_{hi}}\) as shown in Figure 8c. The final step is to remove the remaining redundant information and to get bounding boxes on our required objects that are LP characters, so, this task is done by using (15)  
\[FI=\left\{