International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
the iterative least squares adjustment. | 1
In order to evaluate the precision of the reconstruction and | a
measurement system, 25 distances between lines and planes on | I
sheetmetal parts are measured by callipers and compared with | 2
which computed by the reconstructed CAD model (Figure 12). | 5
The distance between a line and a plane is defined as the mean | S
of two distances from the two end points of a line to the plane | e
determined by all points in it. Coordinates of points are V
obtained from the reconstructed CAD model. Distances |
between lines, planes are defined in a similar way. "Producing |
imprecision” means distances between lines, planes or line to |
plane measured by callipers subtracting the corresponding |
designed distances. “Computed imprecision” means distances
computed with the reconstructed CAD model subtracting the |
corresponding designed distances. |
0.6 mm
0.4
0.2
00 —
-0.2
-0.4
x +
£x
—$— Producing imprecision —#-- Computed imprecision |
-0.6 |
mm
E wed / . 5 a Ea A ti i
00 - 5 i d B 3 Jt EE jm |
3 11 13 15 Taf 19 A 23 25 |
-0.2 |
0.4 |
—&— Producing imprecision —#— Computed imprecision |
-0.6 |
Figure 12. Measuring results of the two parts
It can be seen from top of Figure 12 that the largest “producing |
imprecision” of the first part is about 0.5mm, i.c., the maximum |
difference between the real part and the designed CAD model is |
0.5mm. Note that all imprecision larger than 0.1mm can be |
detected accurately by the proposed system. Measured distances
of the second part are very close to that of CAD data, i.e., the |
producing imprecision is nearly zero. Deviations of computed |
imprecision show a well normal distribution (bottom of Figure |
12). The RMS error of deviation is 0.070mm and 0.067mm for |
the two parts, respectively. The relative precision, which can be
calculated as the ratio of RMS against the distance between |
camera and part, are both higher than 1/8000 (0.07mm/600mm |
= 1/8570), which shows the precision of the proposed system
when manually measured distances are treated as errorless. |
Actually, distances measured by callipers cannot be errorless, |
so precision of the proposed system should be higher than |
1/8000. |
The proposed circle reconstruction approach is also tested with
several real image data. Top of Figure 13 shows two projections
of a circle with CAD designed data and camera parameters
obtained from hybrid point-line photogrammetry. As can be
seen, there are many rusts on the circle. The reconstructed
projections (bottom of Figure 13) are well fitted with actual
image ones. The diameter of reconstructed circle is 9.948mm,
very close to the real value 10.00mm measured by callipers. \
Figure 11. Reconstructed 3D view of the two parts
The system can generate final CAD model for each industrial
part within 3 minutes (including image acquiring) in a PIV
personal computer. Results of reconstruction are displayed with
OpenGL (Figure 11) and can be used to measure the producing
e ©
imprecision and deformation automatically or interactively.
