Camera Calibration for 3D Reconstruction and View Transformation - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 87

although more research needs be done to model other types of distortions with
high accuracy.
In Farid & Popescu (2001), large radial distortion is detected by analyzing the
correlation in the frequency-domain of a single image. The method, however,
may only work for certain types of scenes. Finding out what types of scenes are
suitable for this technique seems to be an interesting research topic.
Contrary to the nonlinear equations 11 and 13, the standard distortion model is
modified in Fitzgibbon (2001) to a projective linear, but equivalent, representation
assuming only radial distortion. Based on this, an efficient closed-form algorithm
is formulated that is guaranteed to estimate the fundamental matrix (Faugeras,
1993).
Passive Camera Calibration
The aim of passive camera calibration is to recover all camera parameters in p c
by fitting the camera model described in section 1 to a corresponding set of
reference points, called calibration control points , in the 3-D world and their
corresponding projections, called calibration feature points , on the image
plane.
Much work has been done on passive camera calibration ranging from the
classical nonlinear optimization approach (Slama, 1980) to closed-form solutions
(Tsai, 1987). Very recently attention has been paid to multi-step schemes that
attempt to combine both nonlinear optimization and linear closed-form solutions.
In the following, all important and representative approaches developed for
passive camera calibration are discussed. Major equations involved are recalcu-
lated and reformulated in a uniform way using the camera model introduced.
All algorithms are presented in detail so that they are directly applicable. Only
considering the linear imaging model, the simplest directed linear transformation
(DLT) approach is first described. Its geometrically valid variations are then
discussed. Nonlinear elements are introduced into the DLT approach to also
handle the camera distortion. However, the nonlinear system formed from this
idea is, in most cases, too complex to be solved efficiently and accurately.
Therefore, a method to avoid the possibly large optimization problem is pre-
sented. Because the method can only handle the radial distortion, a more general
approach, an iterative two-phase strategy, is discussed. Further, to ease the
tedious calibration-data-acquisition work, the 2-D planar pattern is introduced as
an alternative, but effective, calibration object. To recover the geometry of more
than one camera, the linear phase of the iterative two-phase strategy is modified.