# Stereo Digital Image Correlation in MATLAB
## 6 Conclusions
\begin{tabular}{l l} \(\lambda_{j}\) & Epipolar line of the \(j^{\text{th}}\) camera \\ \(M\) & \(3\times 3\) matrix \\ \(m\) & \(3\times 1\) vector \\ \([m]_{{}_{\times}}\) & Skew symmetric matrix of \(m\) \\ \(MAE\) & Mean of the absolute error \\ \(\mu_{w_{q}}^{true}\) & True displacement magnitude \\ \(\mu_{w_{q}}^{calc}\) & Calculated displacement magnitude \\ \(\Omega\) & Homography applied to projection matrices \\ \(\omega\) & Function to populate a square matrix with the shape \\ \(P\) & Shape function parameters \\ \(\Delta P\) & Iterative improvement of shape function parameters \\ \(P_{update}\) & Updated shape function parameters \\ \(\|\Delta P\|\) & Stopping criterion \\ \(\Phi\) & Function representing conversion of coordinate from projective space to Euclidean space \\ \(\Psi\) & Function representing the triangulation methods \\ \(\varphi_{1}-\varphi_{4}\) & Elements of the fundamental matrix for the polynomial \\ \(Q_{j}\) & Projection matrix of the \(j^{\text{th}}\) camera \\ \(Q_{c_{j}}\) & Projection matrix of the \(j^{\text{th}}\) camera in canonical form \\ \(q_{c_{j}}^{nt}\) & The \(n^{\text{th}}\) row of the canonical projection matrix of the \(j^{\text{th}}\) camera \\ Q & Number of subset pairs per image pair \\ \(R_{j}\) & Rotation matrix for pinhole camera model of the \(j^{\text{th}}\) camera \\ \(R_{j}^{pm}\) & rRotation matrix of the \(j^{\text{th}}\) camera for the polynomial \\ \(S\) & Matrix for the linear triangulation method \\ \(\sigma^{\delta}\) & Standard deviation of Gaussian function \\ \(\sigma\) & Standard deviation of the absolute error \\ \(T_{j}\) & Translation vector for pinhole camera model of the \(j^{\text{th}}\) camera for polynomial \\ \(T_{j}^{pm}\) & Translation matrix of the \(j^{\text{th}}\) camera for polynomial \\ \(t\) & Variable for parameterization of epipolar lines \\ \(\tau\) & Squared error distance threshold \\ \(u\) & Displacement in x-direction in the distorted sensor \\  & coordinate system \\ \(u_{x}\), \(u_{xx}\), \(u_{y}\), \(u_{yy}\) and \(u_{xy}\) & Derivatives of the x-direction displacement \\ \(\hat{u}_{w}\) & Displacement in x-direction in the world coordinate system \\ \(V_{j}\) & Extrinsic parameter matrix of the \(j^{\text{th}}\) camera \\ \(v\) & Displacement in y-direction in the distorted sensor \\  & coordinate system \\ \(v_{x}\), \(v_{xx}\), \(v_{y}\), \(v_{yy}\) and \(v_{xy}\) & Derivatives of the y-direction displacement \\ \(\hat{w}\) & Displacement in y-direction in the world coordinate system \\ \(W\) & Shape function \\ \(\frac{\partial W_{i}}{\partial P}\) & Jacobian of the shape function, in terms of the shape function \\ \(\hat{w}_{w}\) & Displacement in z-direction in the world coordinate system \\ \(\hat{\kappa}_{w}=\left[\begin{array}{cc}\hat{x}_{w}&\hat{y}_{w}&\hat{z}_{w} \end{array}\right]^{T}\) & Ideal coordinate in the world coordinate system \\ \(\hat{\kappa}_{s_{j}}=\left[\begin{array}{cc}\hat{\kappa}_{s_{j}}&\hat{y}_{s_ {j}}\end{array}\right]^{T}\) & Ideal coordinate in the ideal sensor coordinate system of the \\ \(\hat{\kappa}_{n_{j}}=\left[\begin{array}{cc}\hat{\kappa}_{n_{j}}&\hat{y}_{n_ {j}}\end{array}\right]^{T}\) & Normalized ideal image coordinates of the \(j^{\text{th}}\) camera \\ \(x_{n_{j}}=\left[\begin{array}{cc}x_{n_{j}}&y_{n_{j}}\end{array}\right]^{T}\) & Normalized distorted image coordinates of the \(j^{\text{th}}\) camera \\ \(x_{s_{j}}=\left[\begin{array}{cc}x_{s_{j}}&y_{s_{j}}\end{array}\right]^{T}\) & Coordinate in the distorted sensor coordinate system of the \(j^{\text{th}}\) camera \\ \end{tabular}   
\[\begin{array}{l}\textbf{x}_{l}^{true}=\left[ \begin{array}{cc}x_{l}^{true}&y_{l}^{ true}\end{array} \right]^{T}\\ \textbf{x}_{l}^{calc}=\left[ \begin{array}{cc}x_{l}^{calc}&y_{l}^{calc}\end{array}  \right]^{T}\\ \textbf{x}_{i}=\left[ \begin{array}{cc}x_{i}&y_{i}\end{array} \right]^{T}\\ \textbf{x}^{o}=\left[ \begin{array}{cc}x^{o}&y^{o}\end{array} \right]^{T}\\ \textbf{\Delta}\textbf{x}_{i}=\left[ \begin{array}{cc}\Delta x_{i}&\Delta y_{i} \end{array}