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292 6 Feature-based alignment

(a) (b)

Figure 6.10 Single view metrology (Criminisi, Reid, and Zisserman 2000) c 2000 Springer: (a) input image
showing the three coordinate axes computed from the two horizontal vanishing points (which can be determined
from the sidings on the shed); (b) a new view of the 3D reconstruction.

6.3.3 Application: Single view metrology

A fun application of vanishing point estimation and camera calibration is the single view
metrology system developed by Criminisi, Reid, and Zisserman (2000). Their system allows
people to interactively measure heights and other dimensions as well as to build piecewise-
planar 3D models, as shown in Figure 6.10.
The first step in their system is to identify two orthogonal vanishing points on the ground
plane and the vanishing point for the vertical direction, which can be done by drawing some
parallel sets of lines in the image. (Alternatively, automated techniques such as those dis-
cussed in Section 4.3.3 or by Schaffalitzky and Zisserman (2000) could be used.) The user
then marks a few dimensions in the image, such as the height of a reference object, and
the system can automatically compute the height of another object. Walls and other planar
impostors (geometry) can also be sketched and reconstructed.
In the formulation originally developed by Criminisi, Reid, and Zisserman (2000), the
system produces an affine reconstruction, i.e., one that is only known up to a set of indepen-
dent scaling factors along each axis. A potentially more useful system can be constructed by
assuming that the camera is calibrated up to an unknown focal length, which can be recov-
ered from orthogonal (finite) vanishing directions, as we just described in Section 6.3.2. Once
this is done, the user can indicate an origin on the ground plane and another point a known
distance away. From this, points on the ground plane can be directly projected into 3D and
points above the ground plane, when paired with their ground plane projections, can also be
recovered. A fully metric reconstruction of the scene then becomes possible.
Exercise 6.9 has you implement such a system and then use it to model some simple
3D scenes. Section 12.6.1 describes other, potentially multi-view, approaches to architectural
reconstruction, including an interactive piecewise-planar modeling system that uses vanishing
points to establish 3D line directions and plane normals (Sinha, Steedly, Szeliski et al. 2008).