- #1

stephchia

- 1

- 0

## Homework Statement

If I have an affine camera with a projection relationship governed by:

\begin{equation}

\begin{bmatrix}

x & y

\end{bmatrix}^T = A

\begin{bmatrix}

X & Y & Z

\end{bmatrix}^T + b

\end{equation}

where A is a 2x3 matrix and b is a 2x1 vector. How can I form a matrix representing the linear mapping between the world point (X,Y,Z) and image point (x,y) if they are represented by homogeneous vectors?

## Homework Equations

NIL

## The Attempt at a Solution

I understand that for a camera perspective projection, the linear mapping between homogeneous coordinates where the equation is only up to a scale factor can be written as a 3x4 projection matrix that represents a map from 3D to 2D.

\begin{equation}

\begin{bmatrix}

x \\

y \\

w

\end{bmatrix}=

\begin{bmatrix}

f & 0 & 0 & 0 \\

0 & f & 0 & 0 \\

0 & 0 & 1 & 0

\end{bmatrix}

\begin{bmatrix}

X_c \\

Y_c \\

Z_c \\

1

\end{bmatrix}

\end{equation}

However, I am unclear as to how an affine camera differs and how to fit a linear mapping based on the above given governing equation.