Eckart Michaelsen
2 GROUPING
To capture our topic more precisely, we have to explain, what is meant by the term * grouping'. Two important aspects
are the part-of hierarchy and the topological and geometric relations.
2. Choosing a Decomposition
If an object of concern may be understood as conglomerate of elementary parts, then we have to consider the space of
all possible sub-set decompositions for an appropriate part-of hierarchy. There are very many different strategies in
decomposing object aggregates of considerable size into object parts. A simple parallelogram shape may for instance be
constructed from a pair of parallel line pairs, an angle pair, a quadrupel of lines e. c.. The choice of the decomposition
may have tremendous impact on the search performance resulting. For instance if the decomposition uses parallel line
pairs, and the model is used on image data from a rural area with ploughed fields, the search may need to consider many
meaningless groupings, and we would have been better off with modelling angles. Usually the choice of the
decomposition is left to the applicator. He or she will prefer decompositions that seam natural with the objects under
concern. The simple example already showed, that these might not be optimal for the recognition task.
2.2 Perceptual Grouping
In perceptual psychology people have investigated the rules that human vision presumably uses for composing complex
objects for nearly hundred years now [Wertheimer 1912]. We refer to the terms of Gestaltist psychologists, when we list
the relations used as follows:
Proximity: Spatial neighbourhood is the most important relationship for all non-local pattern recognition. Usually there
is at least one parameter accompanied with this relation: The size of the region that is declared to be within the
proximity of an object. The choice of a definite value for such a parameter is again left to the applicator, and he or she
may again not be aware of the consequences that a somehow reasonable choice with respect to the objects of concern
may have on the search effort. Compared to these difficulties the choice of the metric, i. e. the shape of the search
region, is of less impact. For the sake of rotational invariance, which seams desirable for many applications, Euclidian
metrics are preferred. Sometimes this is traded for performance, when a maximum metric gives much better search
performance.
Good Continuation: This property is usually captured geometrically as location of the parts on a curve. It may
therefore be sub-classified algebraically into linear, quadratic, cubic e. c. Traditionally pattern recognition handles such
relations by Hough-transforms, with the known difficulties of parameter space tessellation. We would like to mention,
that if the parameters of a curve are estimated by means of least squares method, they depend on the choice of a subset
of objects in the image or scene, and are sensitive to the inclusion of outliers. Such outliers can only be identified after
the parameter estimation. Here the search process itself is confronted with a power-set problem.
Similarity: This relation may be viewed as proximity in the attribute space of the objects. For example houses, that fit
into a parameterised model of the type ‘simple gabled’, might be viewed as similar, if they have similar height, length,
width and roof angle. Also the orientation might be included. Fig 1 shows an example of successful successive
exploitation of a combination of the relations continuation and similarity. In such cases also similar inter-house spacing
will be demanded, so that the final parametric description of the instance ‘house-row’ contains much less and much
more significant information, than the descriptions of the instances ‘house’ in sum.
Fig. 1: Grouping a 3D-House-Row using the relations similarity and linear continuation.
(3D-House-Instances generated from FLAT stereo benchmark)
578 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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