## 2 Materials and Methods
#### 2.1 2D Sensors  
Initial calibration of both 2D sensors is needed because it is only possible to state the relevant values for the sensed products successfully. We can achieve this by setting the 2D sensors values (calibration matrix, distortion factor) and \"mutual spacing and 2D sensors orientation\". Furthermore, epipolar geometry (which addresses two sensor issues) is needed for the statement of the number of 3D points that we can estimate based on the positions at 2D sensors [20]. During the determination of the search points \(m=[x^{\prime},y^{\prime},1]\) using the obtained picture, the following equation applies:  
\[m=P\times M \tag{2}\]  
where, the dot \"\(m\)\" is the picture of point \"\(M\)\"in the surface for screening (therefore, in the surface that is sensed by the camera system for capture). Value \"\(P\)\" for the projection matrix dimension has a state 3 \(\times\) 4 and shows the dependence of the actual dot with the sensed dot as:  
\[P=K\times[I,0] \tag{3}\]  
where, dimension calibration matrix \"\(K\)\" has a state of 3 \(\times\) 3 and describes the values of the environment and values of the 2d sensors. The followed matrix is \"\(I\)\", 3 \(\times\) 3 is the dimension, and \"0\" is zero columns.  
\[K=\left[\begin{array}{ccc}a_{x}&c&t_{x}\\ 0&a_{y}&t_{y}\\ 0&0&1\end{array}\right] \tag{4}\]  
\(a\)--trend is scaling in axes \"\(x\)\" and \"\(y\)\" related to the 2d sensors.  
\(t\)--intersection of sensed surface and visual surface.  
\(c\)--Distortion parameter (_usually_ = 0).  
Matrix \"\(P\)\" can be other than the higher mentioned and written representation for the value of translation and orientation to the coordinate system. Regarding this assumption, we can add the transformation matrix for the 2D sensor coordinate and environment surface:  
\[P=K\times[I,0]\times\left[\begin{array}{cc}R&RC^{\prime}\\ 0&1\end{array}\right] \tag{5}\]  
were,  
\(R\)--this is the matrix 3 \(\times\) 3 and explains the rotation.  
\(C^{\prime}\)--translation vector to the environment surface.  
In such a way, we can state the value between dot \"\(m\)\" from the first sensed product, allocating dot \"\(m\)\" from the second sensed product. In the case of these two dots, we propose the matrix \"\(F\)\" with 3 \(\times\) 3:  
\[{m^{\prime}}^{T}\times F\times m=0 \tag{6}\]  
In the next step, we suggest that one of the projection matrices is allocated at the start of the coordinate system, so that no additional activities are needed. The satisfactory result lies in the determination of the second matrix using the dual sensors:  
\[W=\left[\begin{array}{ccc}0&-1&0\\ 1&0&0\\ 0&0&1\end{array}\right] \tag{7}\]  
To achieve the success of this methodology, we need to test projection matrices at any dot and choose the correct one. This means our selected dot must be positioned in front of the 2D sensors. After this, we can state the coordinates of the dots (with help from the linear method for the triangulation) and the relevant equations:  
\[\left[\begin{array}{ccc}xp^{3T}&-p^{1T}\\ y^{3T}&-p^{2T}\\ x^{\prime}p^{3T}&-p^{\prime 1T}\\ y^{\prime}p^{\prime 3T}&-p^{\prime 2T}\end{array}\right] \tag{8}\]  
By using the least square methods, we can state a resultant 3\(D\) coordinate of point \"\(X\)\". Variable's \"\(x\)\" and \"\(y\)\" are a coordinate \"\(p\)\", which is an i-th row of matrix \"\(P\)\".  
A sensed product and its 3D position are crucial for picture transformation, and every individual dot realizes it compared with the same \"\(y\)\" coordinate. Therefore, after we found the corresponding dot and its row (for the second sensor), we were advised to firstly realize the preprocessing, and only after discovering the processing process of an obtained image [21].