Hi,
I'm still a bit confused about the the vectorization. How did we convert from the affine the n6, 61 multiplication?
In the very first line, we have two equations, which we can expand as follows:
$x' = x * p_1 + y * p_2 + 1 * p_3$ $y' = x * p_4 + y * p_5 + 1 * p_6$
Next, for both equations, I can add in a few additional terms ($0 * p_k$):
$x' = x * p_1 + y * p_2 + 1 * p_3 + 0 * p_4 + 0 * p_5 + 0 * p_6$ $y' = 0 * p_1 + 0 * p_2 + 0 * p_3 + x * p_4 + y * p_5 + 1 * p_6$
Finally, by factoring out the vector $[p_1, \cdots, p_6]$, I get the first two rows of matrix $A$ (shown in the slide).
Every correspondence therefore gives us a $2\times6$ matrix. If we have $N$ correspondences, this produces a $2N\times6$ matrix $A$.
Thank you!
Hi,
I'm still a bit confused about the the vectorization. How did we convert from the affine the n6, 61 multiplication?
In the very first line, we have two equations, which we can expand as follows:
$x' = x * p_1 + y * p_2 + 1 * p_3$ $y' = x * p_4 + y * p_5 + 1 * p_6$
Next, for both equations, I can add in a few additional terms ($0 * p_k$):
$x' = x * p_1 + y * p_2 + 1 * p_3 + 0 * p_4 + 0 * p_5 + 0 * p_6$ $y' = 0 * p_1 + 0 * p_2 + 0 * p_3 + x * p_4 + y * p_5 + 1 * p_6$
Finally, by factoring out the vector $[p_1, \cdots, p_6]$, I get the first two rows of matrix $A$ (shown in the slide).
Every correspondence therefore gives us a $2\times6$ matrix. If we have $N$ correspondences, this produces a $2N\times6$ matrix $A$.
Thank you!