[CT404]: Complete Camera Calibration lab

year4/semester1/CT404: Graphics & Image Processing/labs/1. Camera Calibration/latex/assignment.tex

@@ -76,7 +76,55 @@
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-\section{\textit{P}–Matrix Estimation Using Provided Code}
+\section{\textit{P}-Matrix Estimation Using Provided Code}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/1.1.png}
+    \caption{ Command window output showing he computed camera matrix $P$, the intrinsic matrix $K$, \& the rotation matrix $R$ }
+\end{figure}
 
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/1.2.png}
+    \caption{ The 3D plot showing the camera center, the world points, \& the principal axis }
+\end{figure}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/1.3.png}
+    \caption{ The image with projected 3D points \& vanishing lines }
+\end{figure}
+
+\section{Using Your Own Image from Your Camera for \textit{P}-Matrix Estimation}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/2.1.png}
+    \caption{ Command window output showing he computed camera matrix $P$, the intrinsic matrix $K$, \& the rotation matrix $R$ }
+\end{figure}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/2.2.png}
+    \caption{ The 3D plot showing the camera center, the world points, \& the principal axis }
+\end{figure}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=\textwidth]{./images/2.3.png}
+    \caption{ The image with projected 3D points \& vanishing lines }
+\end{figure}
+
+\section{Experiment \& Reflect}
+\subsection{How does increasing the number of points affect the accuracy \& stability of the \textit{P}-matrix estimation?}
+As the number of control points increased, the accuracy and stability of the estimated P Matrix improved. With 12 points, we observed discrepancies in the back-projected 3D points, while results with 40 points were far more consistent. The intrinsic and rotation matrices derived from the P Matrix appeared less sensitive to noise with more points, enhancing the reliability of the calibration.
+
+\subsection{Is there a noticeable difference in the accuracy of the back-projection when using fewer points versus more points?}
+Using fewer points (e.g., 12) resulted in higher deviations in back-projected points compared to their actual image locations. With 40 points, the back-projection closely matched the real-world setup, minimizing errors.
+
+\subsection{What challenges did you encounter when manually selecting points \& entering 3D world coordinates?}
+The primary challenge that we faced when manually entering selecting the points was the precision: it was extremely difficult to precisely select the correct points due to the imprecision of the mouse as a selection device, human error, and a lack of fine-grain zoom control in the MATLAB UI.
+\\\\
+We also found the process of manually entering the points very time-consuming and error-prone.
+If we mis-clicked a point or accidentally entered in the wrong world coordinate, it would greatly damage the accuracy of the entire calibration and we would be forced to start over again.
 
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