Fig. 3 Image of a toy block 
a. Extracted line segments 
b. Sketch 
structure of level 2, are not sufficient to be connected with an 
object model, it is necessary to get a relational description 
between these primitives. 
Methods for finding relationships or groups of primitives with 
common properties are perceptual grouping procedures 
(MOHAN/NEVATIA 1987, STRAFORINI et al. 1990). These 
groups supply hypothesis about the possible appearance of an 
object, their common properties might be parallelity, 
collinearity, connectivity, symmetry or texture. 
The data structure of level 3 are 2D features, consisting of 
points, lines and planes, including a list of incidence relation 
(line is in plane), which is introduced as a hypothesis 
(VOSSELMANN 1991). In this case the result of the grouping 
is represented by groups of lines, each group belonging to a 
special plane. Sketches of the objects, being represented by the 
data of level 3, can be derived automatically or 
semiautomatically by the system in dependence of the input 
data. Approximately digitizing the toy block of Fig. 3 for 
example supplies initial values for a model. A best estimator 
then fits the model in the extracted line segments in order to 
get an input for the interpretation of sketches of polyhedra 
(SCHICKLER 1992). The geometric reasoning, being the 
internal part of the rule- based system, is then able to 
automatically determine the 3D shape of the object step by 
step, asking the operator to provide information about further 
geometrical constraints if necessary. 
The 4th level finally consists of 3D structures, i.e. vertices, 
edges and surfaces, derived from the 2D features of the 3rd 
level. The result of the interpretation process is the 
reconstructed object, represented by a 3D geometric model 
composed by the 3D structures and the incidence relation. 
  
3 Geometric Reasoning 
3.1 Motivation and Task 
The human visual system is able to interpret the geometry of 
an objet from one perspective line drawing without any 
additional information about the object (Fig. 4). For a 
computer line drawings are only simple collections of lines in a 
plane, therefore special algorithms are needed for deriving the 
scene structure. It is shown how some aspects of the human 
interpretation process can be transferred to a computer by 
applying some of the assumptions the human visual system 
obviously has implicitly made about the object, e.g. 
assumptions about the existence of parallel and perpendicular 
lines of the house in Fig. 4. 
Fig. 4 Example of a line drawing and one of its possible 
interpretations 
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