update and the improvement of work efficiency. Using the
theory of generalized photogrammetry, it can be realized let
linear objects be the control. Figure 3a shows the projects of
linear objects on the image and corresponding generalized
points nearby, which can't be superposed. Figure 3a shows the
superposed result of the linear objects and image, after
orientation and rectification by the control of linear objects,
where the vector is better superposed.
a. Linear Objects & Image
b. Superposition
Figure 3. Superposition of Linear Objects & Image
3.3 Inspection of Sheet-metal Part
How to inspecting the parts in industrial production fast and
exactly is one of the keys for improving the industrial product
quality. The generalized point photogrammetry theory is
applied successfully into the inspection of the metal-sheet parts.
A rotated disk and CCD camera consist of the inspection
platform (Figure 4). The part is put on the disk, which rotation
is controlled by computer. The images are taken when the disk
is rotating. Usually 25 images are taken after the disk rotates
one circuit. By the bundle adjustment based on generalized
point photogrammetry theory, the precise and measurable
geometric model of the metal-sheet part is created (Figure 5).
Figure 5. Measurable
Geometric Model
Based on generalized point photogrammetry theory, not only
straight line but also the circle and the rectangle hole with arcs
in the corners can be measured accurately (Figure 6). Because
each pixel in the edge is participating in least squares matching,
the result with high precise can be insured, even if there is
much rust (Figure 6).
Figure 6. Measurement of circle and arc
[nternational Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004
3.4 Determination of Plane Pose by Contour Line Matching
Any mark point and line in a flying plane is hard to recognize,
and only its contour line can be extracted. The position of the
plane can be traced using the laser, and the image of the plane
can be acquired by photograph simultaneously. However, how
can the pose of the plane be determined?
Determining shape of an object by contour line is an important
research content (Li Li, Mao Shongde, 1996), and the pose of a
moving object could be measured by contour line also.
According to the coordinates traced by the laser and initial
value of the pose, a virtual plane could be projected to the
image (Figure 7). Then, based on generalized point
photogrammetry theory, the pose of flying object could be
determined using the co-linear equation (Table 1).
Table 1. Measurement of Flying Plane by Contour Line
9 (9) c (9) x (©)
True Value 15.99 -15.59 -31.19
Measured Value 15.92 215.33 234-17
Error -0.07 0.26 0.02
Real Contour Line
On Virtual Contour Line
Figure 7. Measurement of Flying Plane by Contour Line
4. CONCLUSION
The generalized point photogrammetry theory introduced in this
paper reduces the point, straight line, circle, arc, curve and
limitless point to one mathematical model: co-linear equation
and uniform adjustment. The theory discards the localization of
traditional and few feature points, the information can be
utilized adequately. The generalized point photogrammetry
theory has been successfully applied in 3D modelling of the
city, data update, measurement of industrial part, circle and arc,
and determination of the pose of flying plane. Consequently the
correctness and validity of the generalized point
photogrammetry theory are proved.
Acknowledgements
Thanks for the supporting from Natural Science Fund of P. R.
China (No. 40337055).
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