Note: That depends on what coordinates you use in the resized image. I am assuming that you are using zero-based system (like C
, unlike Matlab
) and 0 is transformed to 0. Also, I am assuming that you have no skew between coordinates. If you do have a skew, it should be multiplied as well
Short answer: Assuming that you are using a coordinate system in which $u' = \frac{u}{2} , v' = \frac{v}{2}$, yes, you should multiply $a_x,a_y,u_0,v_0$ by 0.5.
Detailed answer The function that converts a point $P$ in world coordinates to camera coordinates $(x,y,z,1)->(u,v,S)$ is:
$$ \left( \begin{array}{ccc}
a_x & 0 & u_0 \\
0 & a_y & v_0 \\
0 & 0 & 1 \end{array} \right)
\left( \begin{array}{ccc}
R_{11} & R_{12} & R_{13} & T_x \\
R_{21} & R_{22} & R_{23} & T_y \\
R_{31} & R_{32} & R_{33} & T_z \\
0 & 0& 0 & 1
\end{array} \right)
\left( \begin{array}{ccc}
x \\
y \\
z \\
1
\end{array} \right)
$$
Where $(u,v,S)->(u/S,v/S,1)$, since the coordinates are homogenous.
In short this can be written as
$ u= \frac{m_1 P}{m_3 P} , v = \frac{m_2 P}{m_3 P}$
where $M$ is the product of the two matrixes mentioned above, and $m_i$ is the i'th row of the matrix $M$. (The product is scalar product).
Re-sizing the image can be thought of:
$$ u'=u/2, v'=v/2 $$
Thus
$$ u' = (1/2) \frac {M_1 P} {M_3 P} \\
v' = (1/2) \frac {M_2 P} {M_3 P}
$$
Converting back to matrix form gives us:
$$
\left( \begin{array}{ccc}
0.5 & 0 & 0 \\
0 & 0.5 & 0 \\
0 & 0 & 1 \end{array} \right)
\left( \begin{array}{ccc}
a_x & 0 & u_0 \\
0 & a_y & v_0 \\
0 & 0 & 1 \end{array} \right)
\left( \begin{array}{ccc}
R_{11} & R_{12} & R_{13} & T_x \\
R_{21} & R_{22} & R_{23} & T_y \\
R_{31} & R_{32} & R_{33} & T_z \\
0 & 0& 0 & 1
\end{array} \right)
\left( \begin{array}{ccc}
x \\
y \\
z \\
1
\end{array} \right)
$$
Which is equal to
$$ \left( \begin{array}{ccc}
0.5 a_x & 0 & 0.5 u_0 \\
0 & 0.5 a_y & 0.5 v_0 \\
0 & 0 & 1 \end{array} \right)
\left( \begin{array}{ccc}
R_{11} & R_{12} & R_{13} & T_x \\
R_{21} & R_{22} & R_{23} & T_y \\
R_{31} & R_{32} & R_{33} & T_z \\
0 & 0& 0 & 1
\end{array} \right)
\left( \begin{array}{ccc}
x \\
y \\
z \\
1
\end{array} \right)
$$
For additional information, refer to Forsyth, chapter 3 - Geometric camera calibration.