Image Processing Reference
In-Depth Information
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Fig. 13.10. (
Left
) The result of 3D position estimation for a sparse set of points. The planes
interpolate linearly between the estimated 3D points. (
Right
) The set of points in the right
camera view, for which the 3D positions have been estimated
the world. Fig. 13.8 illustrates a result of the camera calibration for the stereo cam-
eras shown in Fig. 13.4. The positions of the checkerboards as well as the positions
ofthetwocamerasobservingthemaremarked.Thecameraswerestaticallthetime,
whereas the world coordinates attached to the checkerboard were displaced.
As in the linear symmetry direction estimate case discussed in Chap. 12, the
eigenvalues of the matrix
A
T
A
can be sorted and used in various combinations to
provide an estimate for the quality of the fitted plane, normal whose now represents
the sought position in the triangulation problem. Examples include
λ
4
,
λ
3
− λ
4
,or
the dimensionless certainty measure:
C
t
=
λ
3
−
λ
4
λ
3
+
λ
4
(13.92)
where
λ
4
is the least significant eigenvalue.
Example 13.3. Fig. 13.9 shows the images registered by the left and right cameras
showninFig.13.4.Thecameraswerecalibrated,i.e.,theextrinsicaswellasintrinsic
parametersareknown.InFig.13.10thetriangulationisillustratedbyusingthestereo
imagepairofFig.13.9. Theresultoftriangulation forasetofpointsisshown on the
left. The surfaces are planes that interpolate between the 3D points, whereas color
modulates height. Because their 3D positions are known, the object defined by the
