Given a set of $n$ line segments (\emph{allsegs}) that have been detected in the input image (usually by the \verb+align_mdl+ module), this module searches for convex regions $V$ in the image plane, which are met by the supporting lines of at least $k$ among the total of $n$ segments. The threshold $k$ depends on the shape and location of $V$ with respect to the image domain an is chosen in such a way that the expected number of occurrences (NFA) of the event ``at least $k$ among $n$ lines meet $V$'' is upper-bounded by $10^{-eps}$, if we assume the a-contrario model that lines are independent and randomly distributed in the image plane, and such that $n$ of them meet the image domain (see \cite{almansa.desolneux.vamech:vanish}, \cite{almansa:phd}).
\index{meaningful!vanishing points}
\index{vanishing point detection}

The regions $V$ are chosen from a set of tilings of the image plane at a range of dyadic angular precisions (16,32,...,512). The module only detects maximal regions, \emph{i.e.} regions $V$, such that for any other region $V'$ in the set of tilings, if $V'\cap V \neq \phi$ then we have $NFA(V)\leq NFA(V')$.

In order to avoid spurious vanishing regions that result from the accidental concurrence in the image plane of several sets of parallel lines in 3D, the exclusion principle (MDL) 
\index{Minimum Description Length}
is applied (unless the -a option is specified), by constraining each line to count for a single region, namely the most meaningful region it meets.

Once all maximal meaningful regions were detected, if we remove the corresponding segments (thus decreasing $n$), then further regions may become meaningful. Option -m allows to compute such vanishing regions that were ``masked'' by the overwhelming amount of lines belonging to other vanishing regions.

The output of this module is best visualized one vanishing region at a time by \verb+vpsegplot+ and \verb+fkview+.

