Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am reading about homography in images and such. One thing pops up a lot:

$\mathbf{P} = [\mathbf{R}|\mathbf{t}]$

What does this mean?

Does this mean: If $\mathbf{R} = \begin{bmatrix}a & b\\\ c &d\end{bmatrix}$ and $ \mathbf{t} = \begin{bmatrix}x\\\ y\end{bmatrix}$, I get $ \mathbf{P} = \begin{bmatrix}a &b &x\\\ c& d& y\end{bmatrix}?$

share|improve this question
Could you mention what book are you looking at? –  J. M. Jul 21 '11 at 14:37
Yes, I think you got this right. Think of matrices $\mathbf{R}, \mathbf{S}$ as consisting of their columns. Then $[\mathbf{R}|\mathbf{S}]$ usually means the matrix consisting of the columns of $\mathbf{R}$ then $\mathbf{S}$ (assuming that $\mathbf{R},\mathbf{S}$ have the same number of rows. –  t.b. Jul 21 '11 at 14:38
@J.M. I am looking at Hartley & Zisserman, Multiple View Geometry (2000/2003) –  Unapiedra Jul 21 '11 at 14:53
Yes, if you read through the book carefully, you'll see that it's their notation for a "camera matrix". –  J. M. Jul 21 '11 at 15:01
Well, I only have access to the chapter posted on Zisserman's website. –  Unapiedra Jul 22 '11 at 8:46
add comment

2 Answers

up vote 1 down vote accepted

P denotes an augmented matrix (in this case a projection matrix) and your assumptions are correct about R and t.

share|improve this answer
I don't understand: projection matrix? –  t.b. Jul 21 '11 at 14:41
Projection matrix is the matrix P such that: x = P X. Where X is your 3D point in homogeneous coordinates and x is your 2D point on the image plane. –  Unapiedra Jul 21 '11 at 14:55
add comment

It called as the augmented matrix. Quite useful while solving linear equations. Please see:

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.