Camera Calibration for 3D Reconstruction and View Transformation - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 105

~ ~

K T is called the Image of Absolute Conic ( IAC ), which has been
applied successfully in self-calibration (Hartley & Zisserman, 2000). Once the
IAC of a camera is located, the geometry of this camera has been determined.

− K − 1

where

~ −

Equations 48 and 49 thus provide two constraints for the intrinsic matrix

1

with

K

~ K has four DOFs (ref. equation 32), if two frames (which
means two different H ) are available,

1

one frame. Since

~ −

1

K (and all four intrinsic parameters) can

then be recovered.
Once

~ K is determined, r 1 , r 2 , and t can be calculated directly from equation
47 under the constraint ( r 1 ) T r 1 = ( r 2 ) T r 2 = 1. It follows that r 3 can then be computed
as r 3 = r 1 ×

1

r 2 . Here it is obvious that, if r 1 and r 2 are solutions of equation 47, r 1 ' = -r 1 and
r 2 ' = -r 2 also satisfy equation 47. Again, the correct solutions can be verified by
means of the oriented projective geometry.
In the single-camera case, without loss of generality, it can be assumed that
I

o . However, in a multiple-camera
configuration, which is discussed in the next section, things are not so simple.

R

w
c

= and t

w
c

= 0 . Then R

w
o

= R and t

w

= t

Conclusions

Using the planar pattern as the calibration object may ease the calibration-data-
acquisition work quite a lot. The corresponding calibration method is simple and
efficient. However, the algorithm described above only holds for a single-camera
case. If multiple cameras need to be calibrated in one system, the calibration
algorithm should be modified for obtaining higher accuracy (Slama, 1980). This
issue is discussed next.

Multiple Camera Configuration Recovering

Suppose that there are n cameras ( n > 1) and m frames ( m > 1) for which the

relative poses among all cameras are to be recovered.
In the general situation, let us assume that each frame can be viewed by every
camera. The whole camera and frame set in this configuration is called
complete . By applying the linear geometry estimation techniques discussed, the
relative pose between camera i and frame j can be computed as:

()

T

w
ci

w
oj

Orientation: R = R ⋅ R ,

ij