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Visual Guidance for Autonomous Vehicles 21

The Chauffeur II demonstration features large trucks driving in convoy
on a highway. The lead vehicle is driven manually and other trucks equipped
with the system can join the convoy and enter an automatic mode. The system
incorporates lane tracking (lateral control) and maintaining a safe distance to the
vehicle in front (longitudinal control). This is known as a “virtual tow-bar” or
“platooning.” The Chauffeur II demonstration is highly structured in the sense
that it was implemented on specific truck models and featured inter-vehicle
communication. Active IR patterns are placed on the rear of the vehicles to aid
detection, and radar is also used. The PATH demonstration (UCLA, USA) used
stereo vision and ladar. The vision system tracks features on a car in front and
estimates the range of an arbitrary car from passive stereo disparity. The ladar
system provides assistance by guiding the search space for the vehicle in front
and increasing overall robustness of the vision system. This is a difficult stereo
problem because the disparity of features on the rear of car is small when viewed
from a safe driving separation. Recently much of the research work in this area
has concentrated on the problems of driving in urban or cluttered environments.
Here, there are the complex problems of dealing with road junctions, traffic
signs, and pedestrians.

1.3.4.2 A road camera model
Road- and lane-following algorithms depend on road models [29]. These mod-
els have to make assumptions such as: the surface is flat; road edges or markings
are parallel; and the like. We will examine the camera road geometry because,
with caution, it can be adapted and applied to less-structured problems. For
simplicity and without loss of generality, we assume that the road lies in the
plane Z = 0. From Equation 1.1, setting all Z coordinates of X to zero is equi-
valent to striking out the third column of the projection matrix P in Equation 1.2.
There is a homographic correspondence between the points of the road plane
and the points of the image plane which can be represented by a 3 × 3 matrix
transformation. This homography is part of the general linear group GL 3 and as
such inherits many useful properties of this group. The projection Equation 1.1
becomes

x = HX: H ∈ R 3×3 (1.7)
2
As a member of the group, a transformation H must have an inverse,
so there will also be one-to-one mapping of image points (lines) to points
(lines) on the road plane. The elements of H are easily determined (calib-
ration) by finding at least four point correspondences in general position on

2
The exception to this is when the road plane passes through the camera center, in which case H
is singular and noninvertible (but in this case the road would project to a single image line and the
viewpoint would not be of much use).

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c001” — 2006/3/31 — 16:42 — page 21 — #21