Q1: Camera matrix P from 2D-3D correspondences

Implementation

For each image point, obtain two constraints where:

• $p$ is the 12 element linearized camera matrix $P$
• $x$ and $y$ are the image coordinates with homogeneous component $w$
• $\textbf{X}$ is the corresponding homogeneous 3D object point

$$\begin{bmatrix} \textbf{0} & -w\textbf{X}^\intercal & y\textbf{X}^\intercal \\ w\textbf{X}^\intercal & \textbf{0} & -x\textbf{X}^\intercal \\ \end{bmatrix} p = \textbf{0}$$

Solve for vector of coefficients based on these constraints using the smallest singular value from SVD. Reshape the 12 parameters into a $3 \times 4$ matrix to obtain $P$.

(a) Stanford bunny

Input image

Output image

(b) Cuboid

Input image

Output image