Page 248 - Innovations in Intelligent Machines

Toward Robot Perception through Omnidirectional Vision 241
In order to dewarp an omnidirectional image to a bird’s eye view, notice
that the azimuthal coordinate of a 3D point is not changed by the imaging
geometry of the omnidirectional camera. Therefore, the dewarping of an omni-
directional image to a bird’s eye view is a radial transformation. Hence, we
can build a 1D look up table relating a number of points at different radial
distances in the omnidirectional image and the respective real distances. The
1D look up table is the radial transformation to be performed for all directions
on an omnidirectional image in order to obtain the bird’s eye view.
However, the data for building the look up table is usually too sparse.
In order to obtain a dense look up table we use the projection model of
the omnidirectional camera. Firstly, we rewrite the projection operator, P ρ
in order to map radial distances, ρ ground measured on the ground plane, to
radial distances, ρ img , measured in the image:

ρ img = P ρ (ρ ground ,ϑ) (16)

Using this information, we build a look up table that maps densely sampled
radial distances from the ground plane to the image coordinates. Since the
inverse function cannot be expressed analytically, once we have an image
point, we search the look up table to determine the corresponding radial
distance on the ground plane.
Figure 6 illustrates the dewarpings of an omnidirectional image to obtain
the Bird’s Eye and Panoramic Views. Notice that the door frames are imaged
as vertical lines in the Panoramic view and the corridor guidelines are imaged
as straight lines in the Bird’s Eye view, as desired.
As a final remark, notice that our process to obtain the look up table encod-
ing the Bird’s Eye View, is equivalent to performing calibration. However, for

Fig. 6. Image dewarping for bird’s eye and panoramic views. (Top-left) original
omnidirectional image, (top-right) bird’s eye view and (bottom) panoramic view