Graphics Reference
In-Depth Information
5.26 Explain the effects of increasing
K
in the Pottsmodel, and
β
in the intensity-
adaptive Potts model.
5.27 Provide a counterexample to show that the truncated quadratic function is
not a metric (in particular, that it does not satisfy the triangle inequality).
5.28 The grid graph structure common to many computer vision problems
(including stereo) is bipartite. That is, we can partition the vertices
V
into
disjoint sets
V
1
and
V
2
such that
V
=
V
∪
V
2
and each edge in
E
connects a
1
vertex in
V
1
to a vertex in
V
2
.
is the usual set of all 4-neighbors.
b) Show how the belief propagation algorithm in this case can be sped up
by a factor of two, since only half the messages need to be computed in
each iteration (see [
138
]).
5.29 Given a segmented region of roughly constant-intensity pixels, determine
the linear least-squares problem to estimate the disparity plane parameters
a
i
,
b
i
,
c
i
in Equation (
5.56
).
5.30 Compute the parallax (in the sense of Equation (
5.59
)) for the pair of
correspondences
a) Determine the sets
V
1
and
V
2
when
E
.
5.31 Explicitly derive the position of the striped dot in Figure
5.20
. That is, show
how the quadratic's parameters are obtained using a linear-least-squares
problem and determine its minimizer.
5.32 Explicitly determine the affine transformation between image planes
induced by a single line segment correspondence
{
(
−
2, 5
)
,
(
−
9, 7
)
}
and
{
(
−
1, 4
)
,
(
−
7, 6
)
}
p
,
q
)
}
{
(
p
,
q
)
,
(
in field
morphing.
5.33 Show that field morphing produces a different dense correspondence field
when theorder of the input images is switched. That is, create a simple coun-
terexample using two pairs of control lines in which the forward mapping
is not the inverse of the backward mapping.
5.34 Describe how to modify the cross-dissolve equation (
5.62
) so that the top
half of an image morphs more quickly to its destination than the bottom
half.
5.35 A simple way to show that morphing is not physically consistent is to con-
sider an image of a planar object; thus the dense correspondence is defined
by a projective transformation
H
. Show that the weighted average of corre-
spondences in the first and second images is not a projective transformation
of the first image plane, and thus that intermediate images are not physically
consistent.
5.36 Determine a two-camera configuration in which view morphing cannot be
applied (i.e., when does the rectification process fail?)
