Camera Calibration for 3D Reconstruction and View Transformation - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 86

accurately aligned. The recovered distortion corrections from this projec-
tive base are then interpolated across the whole image (Brand, Courtney,
Paoli & Plancke, 1996).
Linear fundamental matrix embedded in a stereo set-up: A stereo (or
triple-camera) setup can also be used for distortion estimation. First, an
initial guess of the distortion coefficients is used to calculate the undistorted
image point coordinates. These are then used to calculate the so-called
fundamental matrix (or tri-linear tensors). Based on this matrix (or tensors),
the correspondence error is calculated. This error is then reduced by
adjusting the values of distortion coefficients and the process is repeated
until a certain optimal point is reached. The optimal values for distortion
coefficients are finally estimated independently (Stein, 1997).

In the last three approaches, stereo correspondences or correspondences
between 3-D points and their projections are needed. Traditionally, these
correspondences are obtained manually. To automatically search for them, view
and illumination changes have to be taken into consideration together with the
distortion coefficients (Tamaki, Yamamura & Ohnishi, 2002).
Which linear property or invariant is most resistant to noise is still not clear. This
needs to be addressed in future work.

Other techniques

In addition to using linear projective geometry, three other interesting techniques
have also been proposed for distortion estimation, each of them with their own
limitations.
In Perš & Kova 11 (2002), by labeling the camera distortion as an inherent
geometry property of any lens, the radial distortion defined in equation 11 is
remodeled by the following non-parametric equation:

2

r r

( )

2

( )

2

im im

xx ˆ −+− =⋅ yy ˆ f ln ++ 1

,

0 0

2

f f

where r was as defined in equation 10 and f is the focal length.
This model is much simpler than the one defined in equation 10 and the model in
equation 12. Reasonable results have been obtained in Perš & Kova 11

(2002),