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Symmetry: This relation has drawn remarkably less attention in the pattern recognition community then in psychology. 
Gestaltists usually found it to be very important in figure-background discrimination. Maybe this lack of interest is just 
another fear for difficulties, because searching a data set for axis of symmetry is a very non-local task involving 
correspondence hypothesis, and thus may again demand high computational complexity. 
3 PROBLEMS 
Transferring such ideas of perceptual grouping as they are presented by psychologists into code that will run in 
admissible time and with satisfying results on non-trivial data is difficult. So following list of problems is not meant to 
be complete and the reader is invided to add his or her own items from their own experience. Also the order does not 
necessarily reflect our assessment on the impact of the problems. 
1. 
Likelihood of Appearance of Modelled Features: Usually polyhedrons are used for the geometric aspect of the 
models and straight line segments are extracted from the image data. There are a couple of questionable 
assumptions in the match or identification or correspondence between these. Some of the modelled features will 
appear, but if they do, they do it for different reasons: 1) A figure-background contour will appear, if the 
reflectivity of the background is different from that of the object, or if there is shadow cast on the background and 
not on the object. The left hand side of Fig. 2 exemplifies that such contours are frequently missed. 2) Inner 
contours will appear, if there is a change either in reflectivity or in reflection (mostly due to different surface 
orientation with respect to the lighting). The former is relatively rare with buildings. Usually a difference in 
reflectivity is assumed in road recognition — although it is quantitatively unknown. The later will fail for both 
complete rows in Fig. 2 if the sun is perpendicular to them. Existing geometric models of objects of interest such as 
buildings or vehicles have often been assembled for different purposes - not for visual recognition. They tend to fail 
because many of the features modelled do not appear in image (e. g. if free-formed surfaces are modelled by 
triangles). 
Insertion of Unpredictable Objects: In nearly every aerial image You'll find surprising objects You'd never 
thought about. Every person modelling a scene will also be able to name several object classes neglected by the 
model. In Fig. 2 for example also trees, garages, cars e.c. appear, although the model only captures simple gabled 
houses and roads. Usually the majority of the features will not origin from the objects modelled. Some of the 
objects not modelled but present in the scene might be similar to parts of the model. 
Occlusiuon: Many Features demanded by a model based recognition algorithm may not appear in the data because 
they are occluded or partially occluded by other objects. This is extremely difficult with oblique views. But also in 
example like Fig. 2 partial occlusion is evident. Especially large portions of the road contour are hypothesised 
instead of measured. 
Determination of an Adequate Feature Subset: From problems 1 and 2 we learned, that usually only a subset of 
the features are present and we do not know which. Since we need e. g. some 20 features for discrimination from 
arbitrary background the Model should have some 50 features. The set of all subsets of between 20 and 30 elements 
of a set of 50 elements is astronomically large. It is not sufficient to specify a threshold for the percentage or 
absolute number of features, because for instance a small number of ‘the right’ features will be enough to stabely 
infer the presence of a modelled object, whereas a larger number of ‘unimportant’ features will not do. 
3D-2D Invariance: Many properties of geometric models such as angles, measures, topology, are not invariant 
under perspective projection. Usually one geometric model may either be used for matching with 3D-features 
gathered by stereo methods or it may be transformed via hidden line or any other rendering into many appearances 
or aspects, which are used for 2D matches. Then a single 3D model generates possibly hundreds of 2D appearance 
models. Matching become instable with such many templates. For this reason we prefer working with 3D-models 
and with 3D-features (like in Fig. 2). Doing this on aerial images demands correctly calibrated, overlapping image 
sets. Also correspondence errors may lead to wrong 3D-features. 
Erroneous Early Decisions: Often there are alternatives in the correspondence choice between a certain model 
part and a certain subset of the features. For instance in situations like in Fig. 2 there will often be more then one 
line that fit — together with some other already identified lines - into the model of a rectangular part of a roof. One 
might be tempted to only accept the ‘best’. But at this stage of analysis this will be a local criterion. Later, when the 
house-row is established, another line might fit better. Moreover if such early decisions are made on local criteria, 
the whole outcome of the search depends on the features and models it used in the begin. Often the correct solution 
will not be found. On the other hand, if every alternative is kept, the computational effort and demand for memory 
will grow very badly with the size and hierarchical depth of the model. The following problem point clarifies this. 
Combinatorial Growth: Let us again consider the house-row example: Let the probability for missing lines be 
0.25 and the probability for the presence of two competing line instantiations be as well 0.25. So each rectangle 
will in the average have one segment missing and one double. This gives 2 alternatives for each rectangle and little 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 579