The column vectors of the camera matrix


Let the columns of a projective camera $ \tilde{\bf P}$ be $ {\bf p}_i$ for $ i = 1,\ldots,4$ . $ {\bf p}_i$ 's have geometric interpretations as special image points.

$ {\bf p}_1,{\bf p}_2,{\bf p}_3$ are the vanishing points of the world coordinates axes $ X$ , $ Y$ and $ Z$ respectively. For example, the $ X$ -axis has direction $ {\bf D} = (1,0,0,0)^T$ , which is imaged as

$\displaystyle {\bf p}_1 = \tilde{\bf P}{\bf D}

The column $ {\bf p}_4$ is the image of the world origin $ (0,0,0,1)^T$ .

Subhashis Banerjee 2008-01-20