Graphics Reference
In-Depth Information
c) What if both the scanner vehicle and the truck travel at ten meters per
second?
Note that these phenomena can be viewed as a type of spatial aliasing.
Scanner
vehicle
3 m
10 mps
Figure 8.41.
A laser stripe scanner mounted on a vehicle (white dot) moves forward at 10 mps
while the truck moves forward at a different speed.
8.16 Following Figure
8.25
, sketch examples in which a patch that projects to a
square region in one image
a) projects to a skinny region in another image
b) projects to a wide region in another image
c)
is partially occluded in another image by another piece of the scene.
8.17
Show that the normalized cross-correlation is unchanged if the values of
one vector in Equation (
8.10
) are subjected to an affine transformation
ˆ
,
n
.
8.18 Provide a sketch to showwhy the image pairs
u
i
=
au
i
+
b
,
i
=
1,
...
(
i
,
j
)
and
(
j
,
i
)
produce different
contributions to the cost function in Equation (
8.11
).
8.19 Mathematically formalize these two descriptions of how to compute a unit
normal at a 3D point
p
of a triangular mesh:
a) Compute the normal of a plane fit to all the points within a radius
r
of
p
using principal component analysis.
b) Compute a weighted average of the normals to all the triangles that
have
p
as a vertex, where the weight for each triangle is proportional to
its area.
8.20
If the radii of a spin image descriptor are given by the increasing sequence
{
r
i
}
and the levels of the normal bins are given by the increasing sequence
th
bin.
8.21 Determine the 3D transformation defined by 3 point matches in 3D given
by
{
(
{
z
j
}
, then compute the volume of the
(
i
,
j
)
X
i
,
Y
i
,
Z
i
)
. Why are 2 matches insufficient?
8.22 Reformulate the VRIP fusion Equation (
8.21
) so that it can be computed
incrementally by merging the component scans one at a time. Does the
incremental result depend on the order of merging?
X
i
,
Y
i
,
Z
i
)
,
(
,
i
=
1,
...
,3
}
