Jen-Jer Jaw
the collection of the estimated object points and adjusted surface points, see Figure 1, would theoretically provide a
better surface points group from the data fusion point of view. However, the correlation between these two data sets due
to adjustment procedure should not be forgotten if the overall surface points are to be further processed, such as
interpolation or surface analyses. Based on the least squares solution, the fusion of the data sets and their variance-
covariance matrix can be further derived [Jaw, 1999].
A;
{) Estimated object point
X Adjusted surface point
Figure 1. Combined data set (estimated object points + adjusted surface points)
3.3 The extension of the Model
Although the above system is derived based on the assumption that the stochastic constraints in which the unknown
object points are registered with surface planes are employed. Yet for some applications where plane hypotheses are
confirmed by other information, such as the interpretation of the human operator or given scene knowledge, instead of
surface points, the associated stochastic constraints involved only parameters could be formulated taking the plane
measurements into account. In case the plane measurements are performed by overlapping models, an analogue to tie
points for traditional aerial triangulation, the “tie surface”, in this scenario, would tie the overlapping models together,
thus contributing to the estimations of both related exterior orientation parameters and object points (see Figure 2).
Without going into the detail, the stochastic constraints of this kind could be explained as following,
Given a set of plane measurements, p = {P PP }
P,, P, ,...P, are the points measured on p plane, thus one plane
constraint for every four points could be formulated in a similar way
as the author introduced in section three, the only difference is the
three surface points are replaced by three object points, therefore
formulating an "observation equation". The total number of -
independent constraints is (n-3). Since the similarity of the constraints )
the functional as well as stochastic model of “tie surface" can be
joined into the original stochastic constraints without losing the
generalization of the system towards the solution, the author would
not repeat the derivation of the system solution in this manner. Figure 2. Tie Surface Plane
4 EXPERIMENTAL RESULTS AND ANALYSES
The author conducted an experiment using an analytical plotter for collecting both the ground truth and the measuring
data. The measurements involving 4 consecutive stereomodels were performed by the Zeiss C120 Analytical Plotter in
the photogrammetric laboratory at the Department of Civil and Environmental Engineering and Geodetic Science, the
Ohio State University. The photographs with about 1/4000 scale were taken at Ocean City, Maryland in April, 1997.
The area of interest has been aerially triangulated by using highly accurate GPS site measurements as the control points.
Accordingly, the author treats the exterior orientation parameters as the true values for the collection of the object points,
then comparing them with the solved parameters in order to assess the empirical accuracy (root mean square error). The
coverage of the test area and the measured plane features, as marked, can be seen in Figure 3.
448 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
