Image Processing Reference

In-Depth Information

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Figure 3.3:
Effective rank of matrix
M
. (a) 88-vertex mesh seen from the viewpoint used for reconstruc-

tion. (b) Singular values of
M
for the mesh of (a). Note how the values drop down after the 2
N
v
=

176
th

one. Although
M
was obtained with a full perspective model, this corresponds to the value predicted by

the weak perspective model of Section
3.3.1
. The small graph on the right is a magnified version of the

part of the graph containing the small singular values. The last one is zero up to the precision of the

Matlab routine used to compute it and the others are not very much larger.

(

(

(

Figure 3.4:
Visualizing vectors associated to small singular values. (a) Reference mesh and mesh to which

one the vectors has been added seen from the original viewpoint, in which they are almost indistinguish-

able. (b) The same two meshes seen from a different viewpoint. (c) The reference mesh modified by

adding the vector associated to the zero singular value. Note that the resulting deformation corresponds

to a global scaling.

that the global scale is directly related to the position of the vertices along the lines of sight, which

produces one fewer small singular value.

The fact that the depth of the mesh vertices is ill-constrained shows that 3D-to-2D corre-

spondences on their own are not sufficient to reconstruct the shape of a surface from a monocular

image. Therefore, additional knowledge must be introduced in the problem. This can be done by

taking into account other sources of image information, such as shading. However, as mentioned

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