Farhad Samadzadegan
new ideas based on fuzzy reasoning for feature detection and matching. To deal with imprecise knowledge in the
reasoning system the fuzzy logic concept is used. The advantage is that no yes/no decisions are necessary in an early
stage of reasoning. The long-term objective of our development is to improve the interpretation related capability of the
algorithms, for example, by combining given uncertain prior information about smoothness of a surface with hints
about discontinuities or other textural information extracted from the images.
2 OUTLINE OF THE MAJOR PROCESSING MODULES
Coarse-to-fine procession using image pyramids and multi-resolution modelling of DTMs are well-known conceptual
aspects of DTM generation procedures. By introducing a fuzzy inference system for DTM acquisition the established
modules are taken over and used as a basis of the system. As mentioned before fuzzy logic can be beneficially blended
with proven concepts and modules of DTM generation.
The major components of the proposed approach are the following. Detection and matching procedures are started on
the top level of the image pyramids. A corresponding rough approximation of the terrain surface might be given or
derived using existing ground control points. This surface defines the coarse layer of the DTM pyramid. Projection of
the DTM nodes into image space using the given collinearity equations is carried out for the left and the right feature
pyramid. This information is used to initiate the matching process and delimit the location and search space for
establishing conjugate features. The detection of features as well as feature correspondence are taken into account by
employing fuzzy rules. The aspects of fuzzy inference are discussed in detail in the next section.
Transfer of conjugate feature points into object space is carried out by spatial intersection. The calculated object co-
ordinates of feature points are used to interpolate a regular grid terrain model based on robust finite element (FE)
modelling. Matching and DTM interpolation are executed using coarse-to-fine processing. This results in a progressive
densification of the DTM which finally is generated with its highest grid point density.
A refinement of the DTM interpolation process can be developed by taking fuzzy knowledge about the relation of
image features and object space modelling into account. A fuzzy rule which relates to all edge points may state that
"corresponding edges of the images might be spatial discontinuities in 3D". Obviously this is not true in all cases
because there might be more edges which originate from texture, land use, etc. than 3D discontinuity lines. Therefore a
further rule stating "if the parallax on one side of an edge is similar to parallax on the other side then this edge will not
correspond to a 3D surface discontinuity" may contribute for clarification. These rules which are obviously of fuzzy
nature have to be processed by applying fuzzy operators, proper implication methods and aggregation of the outputs.
The task of fuzzy reasoning is to work out the different possibilities in an integrative manner. Reasoning and matching
have to be re-iterated with 3D FE modelling of the surface. If fuzzy reasoning indicates 3D discontinuities this can
directly be taken into account within the FE model by relaxing the continuity constraints for the corresponding
locations. Because fuzzy reasoning between image space and object space as indicated above is not fully worked out so
far we focus in the following on image space processes based on fuzzy logic and only shortly outline the object space
processes based on robust FE modelling. This reflects the current development state of the implemented software.
3 IMAGE SPACE PROCESSES BASED ON FUZZY LOGIC
Image space processing can be assigned to two separate stages: feature extraction and feature matching. In the first
stage key points have to be detected and in the second stage key points are matched to obtain conjugate points in two or
more images. Because the focus is laid on fuzzy inference processes for extraction and matching some basic ideas on
fuzzy reasoning will be reviewed first. Examples of fuzzy inference relating to the implemented detection and matching
processes will be presented afterwards.
3.1 Fuzzy Reasoning
Fuzzy inference is the actual process of mapping from a given input to an output using fuzzy logic. The process
involves membership functions, fuzzy logic operators, and if-then rules (Zimmermann, 1993). Since the terms used to
describe the various parts of a fuzzy inference process are far from standard and the idea is not to explain them all in
detail here we try to be as clear as possible about the different terms. A fuzzy reasoning processes may be composed by
five parts:
1- Fuzzification of the input variables. For each input variable the degree is determined to which it belongs to
each of the appropriate fuzzy sets via membership functions. The fuzzy set is a ‘container’ of elements
800 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
32 |
Key 1
promi
extrac
to be
