Jen-Jer Jaw
System
Redundancy
Case 1 0.11 | 0.12 0.09 0.000136 | 0.000416 | 0.000212 0.133 | 0.057 | 0.072 84
Case 2 0.11 | 0.10. | 0.08 0.000121 | 0.000428 | 0.000196 0.121 | 0.053 | 0.065 104
Case 3 0.10 | 0.10 | 0.07 0.000161 | 0.000407 | 0.000208 0.120 | 0.051 | 0.072 90
Case 4 0.08 | 0.12 0.08 0.000140 | 0.000365 | 0.000190 0.138 | 0.074 | 0.076 70
( X,,Y,, Z,, Ww, j,k }: exterior orientation parameters
(X, Y, Z) object point coordinates
Positional unit: meter; Angular unit: radian
Table 2. Accuracy assessment (R.M.S.E.) based on the ground truth
Note that the following common parameters were used in this test:
Focal length of the camera = 0.152764my
S.D. of photo point measurement = 7 micrometers;
S.D. of surface points in X component = 0.07m; Y=0.07m; Z=0.12m.
(S.D. Stands for Standard Deviation)
Variance component of photo measurement = 1; surface points = 1.
4.3 Analyses
! The system works without the necessity of employing control points, the ingredient of indispensable for traditional
aerial triangulation.
! In overall, the higher the system redundancy is, the higher the accuracy obtained.
! By comparing case 1 and case 2, the tie surface planes, adding the constraints into the adjustment increases the
system performance by higher redundancy, thus leading to the better parameter estimation both for the exterior
orientation and the object points.
! The tie surface planes, without knowing the orientation of the planes in the object space, show their importance in
tying models where known surface points are not available. The achieved accuracy does not deteriorate significantly
due to the lack of registering those points to the object space.
! Case4 involves none of the control surface or the tie surface observations, for that information-empty area shows the
worst accuracy overall for the object points due to the least favorable geometry among all cases. Therefore, the
contribution of the tie surface for the overall solution can not be neglected if observable.
! Even with the narrow strip, the unfavorable geometry by traditional aerial triangulation, the solution is not weakened
at all.
5 CONCLUSIONS
Aerial triangulation can be performed using the control surface rather than the control points, thus no identification of
measured surface points with respect to their object truth is necessary.
The control surface hypothesizing planes (first-order surface) in the object space may seem to oversimplify the surface
at the first glance. Yet with increasingly available surface collectors, such as laser range finder and INSAR, the denser
surface points data set would come into application field inevitably in the nearest future. Thus the available surface
information would be analyzed in a more local scale in which the first-order surface, namely the plane, seems to be the
most likely shape among all the others. Furthermore, for the residential area where artificial features dominate, the
surfaces of the buildings including the roofs and the side walls, the surfaces of the road and many other man-made
constructions provide abundant plane-like features not only in number but also in orientation, the proposed model
shows its potential for the application in this area.
The proposed model solves not only the newly added object points via photogrammetric methods but also has the
surface points adjusted through the registration of points from the photo space onto the object space. Thus the combined
data set, the solved object points and the adjusted surface points together with their variance and covariance matrix [Jaw,
1999], would provide a better surface description for the task of surface analyses or surface reconstruction especially
when image matching is to be exploited for the thorough surface generation. It is this author’s strongest emphasis for
450 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
