Image Processing Reference

In-Depth Information

Figure 3.1:
Correspondences between a reference image and an input image. The point-to-point cor-

respondences are shown as red lines going from the first image to the second one.

to explicitly exhibit its underlying ambiguities. More specifically, in the
weak perspective
case,

which will be defined below, a third of the degrees of freedom is unconstrained. By contrast, in

the
full perspective
case, there theoretically is only a scale ambiguity. However, for most realistic

scenarios, the same number of degrees of freedom as before are so poorly constrained as to be

unconstrained for all practical purposes.

Shape-from-shading techniques
Horn and Brooks
[
1989
] offer an alternative to shape-from-

correspondences for monocular shape recovery. However, despite many generalizations of

the original formulation to account for more realistic shading effects, such as interreflec-

tions
Forsyth and Zisserman
[
1991
],
Nayar
et al.
[
1991
], specularities
Oren and Nayar
[
1996
], shad-

ows
Kriegman and Belhumeur
[
1998
], or non-lambertian materials
Ahmed and Farag
[
2006
], the

resulting solutions are only valid in specific environments. As a consequence, we will only discuss

techniques that rely on shading in conjunction with texture.

3.1.2 CAMERAMODELS

In the following analysis, we will assume the internal camera parameters to be known and, as indicated

above, we will distinguish between the behavior under the weak and full perspective camera models.

We therefore define them below.

Under the weak perspective model, the projection of a 3D point
q
i
can be written as

d
u
i

v
i

A
Rq
i
+

t
,

=

(3.1)

where
A
is the 2

2 matrix of camera internal parameters,
R
contains the first two rows of the full

camera rotation matrix,
t
is the 2

×

1 camera translation vector, and
d
is a scalar. In general,
d
is the

same for all the considered 3D points. In the case of the projection of a mesh, we can define a more

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