Jorge Brito
The strategy of using iterative orthophoto refinements to correct DEM’s has been applied by Norvelle (1992). Li,
Wang, and Li (1996) have presented a methodology for automatic quality diagnosis in DEM generation by digital
image matching techniques. These researchers use the same principle of associating parallaxes in digital orthoimages
either to errors in the DEM or to occlusions.
There is, however, a main drawback to the approaches mentioned. These approaches are deterministic, since they do not
take into account errors associated with the planimetric positions of points in the digital orthoimages. Those errors are
present in digital orthoimages by the error sources and their error propagation through the photogrammetric process.
Therefore, the uncertainties in the planimetric coordinates of digital orthoimage pixels need to be taken into account in
some way. This constraint suggests that a probabilistic approach would be more appropriate for detecting occlusions in
digital images. Such an approach will be implemented using Bayesian networks, the principles of which are explained
in the next sub-heading.
1.2 Bayesian Networks
Bayesian Networks have been used in many areas of knowledge since the late 1970s, particularly in artificial
intelligence applications and knowledge representation and reasoning. In the context of spatial data, however, it remains
a largely unexplored area, with few available references. An exception is a Doctoral dissertation entitled “Bayesian
Networks for Inference with Geographic Information Systems,” which uses a Bayesian Network for modeling the
problem of assessing the risk of desertification of some burned forests in the Mediterranean region (Stassopoulou,
1996). Judea Pearl (Pearl, 1988), one of the most active, contemporary researchers in this area, defines Bayesian
Networks as directed acyclic graphs, in which the nodes represent random variables (regardless of the discrete or
continuous domain), and the links represent causal influences among these variables. A detailed description of
Bayesian Networks goes far beyond the scope of this paper. Those who are searching for literature in this topic will find
also a comprehensive survey by Charniak (1991) in addition to the references mentioned above. For the purposes of
this research, it is sufficient to summarize the principles of Bayesian Networks as. follows:
e the nodes of the network represent random variables;
e asetof directed links connects pairs of related nodes;
e each non-root node (i.e., each node with parents) has a conditional probability matrix that quantifies the effects of
the parents in the node;
each root node (i.e., node with no parents) has a prior probability distribution, and
* the graph has no directed cycles (hence it is a directed, acyclic graph).
1.3 Statement of the Problem
Occlusion is a relationship of visibility, in the image space, along a given direction “6”, among the image perspective
center and two points. It is caused by the relative position of those points mentioned above on the ground (object space).
Figure 1 depicts an example of occlusion caused by relief displacement in a central perspective image.
Dorn (1991) stated how an occlusion can be detected along a single radial line in ideal images. He considered the
relationship between the radial distances of two points in the object space and in the image space (i.e., points “A” and
"B," and "a" and “b," respectively, in figure 1.
In the situation showed, point “B” is occluded by point “A” because its radial distance in the object space (Rg) is greater
than (R,), and the opposite situation is observed in the image space ( ry, < r,).
The problem stated above could easily be implemented in
a deterministic approach. To do so, the following d
assumptions would be implicit:
e the images are ideal, which means they have no errors
but relief displacement; rl
e the planimetric coordinates of ground points are Image —
assumed to be errorless, and
e the DEM from which the height of the ground points A
is interpolated is errorless.
Unfortunately the assumptions stated above are valid only
theoretically. In real-world photogrammetric mapping
b
“Ta — es
projects, there are always errors in the computation of the Ground B
coordinates of the perspective center "p" and in the ^ . t RA cuo J
projections of points “A” and «p? onto the image space. utem Ie ER. mn
The uncertainties in the coordinates propagate according 2 nut
to the photogrammetric process. This characteristic Figure 1. Occlusion along a single radial line
suggests the use of a probabilistic approach to solve the in a vertical mage.
102 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
