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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}?$

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    Could you mention what book are you looking at?2011-07-21
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    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.2011-07-21
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    @J.M. I am looking at Hartley & Zisserman, Multiple View Geometry (2000/2003)2011-07-21
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    Yes, if you read through the book carefully, you'll see that it's their notation for a ["camera matrix"](http://en.wikipedia.org/wiki/Camera_matrix).2011-07-21
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    Well, I only have access to the chapter posted on Zisserman's website.2011-07-22

2 Answers 2

1

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

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    I don't understand: projection matrix?2011-07-21
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    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.2011-07-21
2

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