Page 264 - Innovations in Intelligent Machines

Toward Robot Perception through Omnidirectional Vision 257
In [79] Sturm uses an omnidirectional camera based on a parabolic mirror
and a telecentric lens for reconstructing a 3D scene. The user specifies rele-
vant points and planes grouping those points. The directions of the planes are
computed e.g. from vanishing points, and the image points are back-projected
to obtain parametric representations where the points move on the 3D pro-
jection rays. The points and the planes, i.e. their distances to the viewer, are
simultaneously reconstructed by minimizing a cost functional based on the
distances from the points to the planes.
We build 3D models using omnidirectional images and some limited user
input, as in Sturm’s work. However our approach is based on a different recon-
struction method and the omnidirectional camera is a generalised single pro-
jection centre camera modelled by the Unified Projection Model [37]. The
reconstruction method is that proposed by Grossmann for conventional cam-
eras [43], applied to single projection centre omnidirectional cameras for which
a back-projection model was obtained.
The back-projection transforms the omnidirectional camera to a (very
wide field of view) pin-hole camera. The user input is of geometrical nature,
namely alignment and coplanarity properties of points and lines. After back-
projection, the data is arranged according to the geometrical constraints,
resulting in a linear problem whose solution can be found in a single step.

4.1 Interactive Scene Reconstruction

We now present the method for interactively building a 3D model of the envi-
ronment. The 3D information is obtained from co-linearity and co-planarity
properties of the scene. The texture is then extracted from the images to
obtain a realistic virtual environment.
The 3D model is a Euclidean reconstruction of the scene. As such, it may
be translated and rotated for visualization and many models can be joined
into a single representation of the environment.
As in other methods [50, 79], the reconstruction algorithm presented here
works in structured environments, in which three orthogonal directions, “x”,
“y” and “z” shape the scene. The operator specifies in an image the location
of 3D points of interest and indicates properties of alignment and planarity.
In this section, we present a method based on [42].
In all, the information specified by the operator consists of:
– Image points corresponding to 3D points that will be reconstructed,
usually on edges of the floor and of walls.
– Indications of “x−”, “y−” and “z =constant” planes as and of alignments
of points along the x, y and z directions. This typically includes the floor
and vertical walls.
– Indications of points that form 3D surfaces that should be visualized
as such.