Notations

To enhance the readability the notations used throughout the text are summarized here.

For matrices bold face fonts are used (i.e. ${\bf A}$). 4-vectors are represented by ${\tt A}$ and 3-vectors by ${\tt a}$. Scalar values will be represented as $a$.

Unless stated differently the indices $i$, $j$ and $k$ are used for views, while $l$ and $m$ are used for indexing points, lines or planes. The notation ${\bf A}_{ij}$ indicates the entity ${\bf A}$ which relates view $i$ to view $j$ (or going from view $i$ to view $j$). The indices $i$,$j$ and $k$ will also be used to indicate the entries of vectors, matrices and tensors. The subscripts $P$, $A$, $M$ and $E$ will refer to projective, affine, metric and Euclidean entities respectively

${\bf P}$	camera projection matrix ($3 \times 4$ matrix)
${\tt M}$	world point (4-vector)
${\tt\Pi }$	world plane (4-vector)
${\tt m}$	image point (3-vector)
${\tt l}$	image line (3-vector)
${\bf H}^{\tt\Pi}_{i j }$	homography for plane ${\tt\Pi }$ from view $i$ to view $j$ ($3 \times 3$ matrix)
${\bf H}_{{\tt\Pi} i}$	homography from plane ${\tt\Pi }$ to image $i$ ($3 \times 3$ matrix)
${\bf F}$	fundamental matrix ($3 \times 3$ rank 2 matrix)
${\tt e}_{ij}$	epipole (projection of projection center of viewpoint $i$ into image $j$)
${\bf T}$	trifocal tensor ( $3 \times 3 \times 3$ tensor)
${\bf K}$	calibration matrix ($3 \times 3$ upper triangular matrix)
${\bf R}$	rotation matrix
${\tt\Pi }_\infty$	plane at infinity (canonical representation: $W=0$)
$\Omega$	absolute conic
	(canonical representation: $X^2+Y^2+Z^2=0$ and $W=0$)
$\Omega ^*$	absolute dual quadric ($4 \times 4$ rank 3 matrix)
$\omega _\infty$	absolute conic embedded in the plane at infinity ($3 \times 3$ matrix)
$\omega^*_\infty$	dual absolute conic embedded in the plane at infinity ($3 \times 3$ matrix)
$\omega$	image of the absolute conic ($3 \times 3$ matrices)
$\omega^*$	dual image of the absolute conic ($3 \times 3$ matrices)
$\sim$	equivalence up to scale ( $A \sim B \Leftrightarrow \exists \lambda \neq 0 : A = \lambda B$)
$\Vert {\bf A} \Vert _F$	indicates the Frobenius norm of ${\bf A}$ (i.e. $\sum_{ij} {a_{ij}^2}$)
${\bf F}( {\bf A} )$	indicates the matrix ${\bf A}$ scaled to have unit Frobenius norm
	(i.e. $\frac{\bf A}{\Vert {\bf A} \Vert}_F$)
${\bf A}^\top$	is the transpose of ${\bf A}$
${\bf A}^{-1}$	is the inverse of ${\bf A}$ (i.e. ${\bf AA}^{-1} = {\bf A}^{-1}{\bf A} = {\bf I}$)
${\bf A}^\dagger$	is the Moore-Penrose pseudo inverse of ${\bf A}$