## Viewpoint estimation in three-dimensional images taken with
perspective range sensors

With the introduction of long range, wide angle, laser-based range
sensors, three-dimensional images are becoming more and more available
to the scientific community and to the general public. On the Internet
one can already find collections of three-dimensional models made of
polygons, or raw three-dimensional images consisting of a matrix of
3D points.
Sometimes these images merely consist of a point cloud arranged
as a matrix, so that neighbour relations exist, but there is no
information available about the sensor: field of view, angular
resolution, viewpoint, etc.
This latter information, the viewpoint, is probably the most
important one since, as we assume the 3D coordinates of the point
cloud and neighbourhood relationships between points in the 3D image
are known, knowing the viewpoint allows us to infer other information,
such as the aperture of the field of view, sensor orientation or
angular resolution. It also allows deduction of occlusion
relationships, rejection of outliers, etc.
3D images, like intensity images, are noisy \cite{Hebert92}.
For example the 3D coordinates
of the points may be computed by reading in information from the line
scanning device (which deflects the laser beam horizontally by
rotating a mirror), or from the tilt head (which modifies the azimuth
angle of the rotation mirror). If the readings from the motor encoders
are mistaken, it may result in a big angular drift of the points being
scanned. The depth may be correct, but the point location in space is
not.
If we know the viewpoint, we can predict the pan (tilt) angle of each
column (row) and discard or correct outliers, that is, put drifted
points back in place.
In this work we assume the 3D image has been taken with a central-projection,
that is, all rays starting from the centre of the mirror.