Graphics Reference
In-Depth Information
frame (time
t
= 0), the relative distance between the two cars is approximately
7m. The velocity of approach is uniform and approximately 1m/time unit.
A B-spline snake is initialized in the center of the windshield and expands
out until it localizes the closed contour of the edge of the windshield. The
snake then automatically tracks the windshield over the sequence. For uniform
translation along the optical axis, the relationship between area and time is
given (from equations 5.48 and 5.60) as
dt
(
a
(
t
)) =
2
U
.
Q
a
(
t
)
.
d
(5.64)
λ
Its solution is
a
(0)
a
(
t
)=
t
c
(0)
2
,
(5.65)
1
t
−
where
t
c
(0) is the initial estimate of the time to contact as given by
λ
(0)
U
.
Q
.
t
c
(0) =
(5.66)
This is in close agreement with the data. For uniform motion, this should
decrease linearly. For nonuniform motion, time to contact as a function of time
is important for braking and landing. Lee [102] provided a braking condition
for drivers that states
d
dt
(
t
c
(
t
))
≥−
0
.
5
.
(5.67)
This ensures that vehicles will decelerate uniformly and to avoid collision.
Thus, the divergence of the image velocity field provides sucient information
to control over braking.
If the translational motion has a component parallel to the image plane,
the image divergence is composed of two components. The first term deter-
mines time to contact, while the other term occurs due to image foreshortening
when the surface has a non-zero slant. The two effects can be computed sep-
arately by measuring the deformation. The deformation also helps to recover
the surface orientation. The only assumption of Cipolla and Blake [38] is of
uniform motion and known direction of translation.
5.9 Concluding Remarks
B-spline has widespread applications in image processing and vision problems.
The application of B-spline in machine vision problems discussed in this chap-
ter shows its importance. Based on the original philosophy, different solutions
have been suggested to render the snake more stable and to yield faster con-
vergence results. An alternative approach to snakes, which also circumvents
some of the problems, is to use a parametric B-spline representation of the
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