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Toward Robot Perception through Omnidirectional Vision  239
                           This eliminates the need to built highly detailed environment representations,
                           thus saving computational (memory) resources.
                              In summary, both Visual Path Following and Topological Navigation rely
                           upon environmental perception (self-localisation) for regulating movement.
                           The main point here is that perception is linked to internal representations
                           of the world which are chosen according to the tasks at hand. We will now
                           detail Geometrical Representations for precise self-localisation, necessary for
                           Visual Path Following, and Topological Representations for global positioning
                           leading, necessary for Topological Navigation.


                           3.1 Geometric Representations for Precise Self-Localisation
                           Robot navigation in cluttered or narrow areas, such as when negotiating a door
                           traversal, requires precise self-localisation in order to be successful. In other
                           words, the robot has to be equipped with precise environmental perception
                           capabilities.
                              Vision-based self-localisation derives robot poses from images. It encom-
                           passes two principal stages: image processing and pose-computation. Image
                           processing provides the tracking of features in the scene. Pose-computation is
                           the geometrical calculation to determine the robot pose from feature obser-
                           vations, given the scene model.
                              Designing the image processing level involves modelling the environment.
                           One way to inform a robot of an environment is to give it a CAD model,
                           as in the work of Kosaka and Kak [52], recently reviewed in [24]. The CAD
                           model usually comprises metric values that need to be scaled to match the
                           images acquired by the robot. In our case, we overcome this need by defining
                           geometric models composed of features of the environment directly extracted
                           from images.
                              Omnidirectional cameras based on standard mirror profiles, image the
                           environment features with significant geometrical distortion. For instance, a
                           corridor appears as an image band of variable width and vertical lines are
                           imaged radially. Omnidirectional images must therefore be dewarped in order
                           to maintain the linearity of the imaged 3D straight lines.
                              Pose-computation, as the robot moves in a plane, consists of estimating a
                           2D position and an orientation. Assuming that the robot knows fixed points in
                           the environment (landmarks) there are two main methods of self-localisation
                           relative to the environment: trilateration and triangulation [5]. Trilateration
                           is the determination of a vehicle’s position based on distance measurements
                           to the landmarks. Triangulation has a similar purpose but is based on bearing
                           measurements.
                              In general, a single image taken by a calibrated camera provides only
                           bearing measurements. Thus, triangulation is a more “natural” way to calcu-
                           late self-localisation. However, some camera poses / geometries provide more
                           information. For example, a bird’s eye view image (detailed in the follow-
                           ing subsection) provides an orthographic view of the ground plane, providing
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