Page 57 - Dynamic Vision for Perception and Control of Motion

2.1 Three-dimensional (3-D) Space and Time 41

inversion. Since each row of the Jacobian matrix contains the first-order sensitivity
elements of the relation, how the feature measured depends on each state variable,
spatial interpretation may become (at least partially) possible even with monocular
vision, if either the object or the observer is moving. This will be discussed further
down. Temporal embedding thus alleviates image interpretation despite the higher
data rates. Temporal continuity conditions and attention control can counteract
these higher data rates.
In addition, the eigenvalues of the transition matrix A represent characteristic
time scales of the process. These and the frequency content of control inputs and of
perturbations determine the temporal characteristics of the motion process.
In the framework of mission performance, other timescales may have special
importance. The time needed for stabilizing image sequence interpretation is cru-
cial for arriving at meaningful decisions based on this perception process. About a
half second to one second are typical values for generating object hypotheses and
having the transients settle down from poor initialization. Taking limited rates of
change of state variables into account, preview (and thus prediction) times of sev-
eral seconds seem to be reasonable in many cases. Total missions may last for sev-
eral hours.
With respect to flawless functioning and maintenance of the vehicle’s body,
special timescales have to be observed, which an autonomous system should be
aware of. All these aspects will be briefly discussed in the next section together
with similar multiple scale problems in the spatial domain. To be flexible, an
autonomous visual perception system should be capable of easy adjustment to
temporal and spatial scales according to the task at hand.

2.1.4 Multiple Scales

The range of scales in the temporal and spatial domains needed to understand pro-
cesses in the real world is very large. They are defined by typical sensor and mis-
sion dimensions as well as by the environmental conditions affecting both the sen-
sors and the mission to be performed.

2.1.4.1 Multiple Space Scales

In the spatial domain, the size of the light sensitive elements in the sensor array
may be considered the lower limit of immediate interest here. Typically, 5 to 20
micrometer (Pm) is common today. Alternatively, as an underlying characteristic
dimension, the typical width of the electronic circuitry may be chosen. This is
about 0.1 to 2 Pm, and this dimension characterizes the state of the art of micro-
processors. Taking the 1-meter (m) scale as the standard, since this is the order of
magnitude of typical body dimension of interest, the lower bound for spatial scales
í7
then is 10 m.
As the upper limit, the distance of the main light source on Earth, the orbital ra-
11
dius of the planet Earth circling the Sun (about 150 million km, that is 1.5 ·10 m),
may be chosen with all other stars at infinity. The scale range of practical interest