INTERPRETING SINGLE IMAGES 
OF POLYHEDRA 
Carola Braun 
Institute of Photogrammetry 
University of Bonn, FRG 
abstract 
The paper presents a concept of a rule-based system for 
deriving the 3D structure of polyhedral objects in perspective 
projections using known geometrical constraints. The system 
may supply a complete reconstruction of objects, especially of 
buildings in aerial images, by matching the results of 
individual image interpretation in space. 
As buildings can be simplified to polyhedra, the procedures 
first are developed for polyhedral objects. Many real objects 
have groups of parallel and orthogonal lines and rectangular 
corners. The presented system uses this information for 
reconstructing polyhedral objects with the aim of a 
geometrically correct shape description. The geometric 
reasoning process, implemented in the system, is able to 
automatically determine the structure of the object step by step, 
asking the operator to provide information about geometrical 
constraints if necessary. Examples illustrate the applicability of 
the approach. 
keywords 
rule-based system, inverse perspectivity, perceptual grouping, 
geometric reasoning, image analysis 
1 Introduction 
The concept of a rule-based system is presented for deriving 
the geometrical shape of polyhedral objects in perspective 
projection using known geometrical constraints. The system is 
intended to be used for a complete reconstruction of buildings 
in aerial images, matching the results of individual image 
interpretations in space. 
The system is part of a long term project for the development 
of procedures for the recognition and reconstruction of 
buildings. 
As man-made objects like buildings may reasonably well be 
514 
described by their geometric structure and this structure can be 
approximated by a polyhedra (skyscrapers, terrace houses), the 
procedures of the system first are developed for polyhedral 
objects in single images. It is also possible to extend the 
interpretation process for buildings, consisting not only of 
planes but of cylindrical surfaces or cones (castles, churches, 
congress halls). 
There are two possibilities for deriving the 3D information of 
an object. The classical approach first applies point or edge 
detection and possibly also grouping procedures to get a 
symbolic description of the images (Fig. 1.a). This description 
is either based on pixels, attributes and/or relations. Matching 
the image descriptions of several images and determining the 
object points in space by a spatial intersection allows a 3D 
reconstruction of the object. The other approach applies edge 
detection and grouping procedures in order to get sketches of 
the object (Fig. 1b). A reasoning process then infers from the 
2D features of the sketches to single 3D models of the object 
which can easier be matched in space in order to get a 3D 
description of the object. The advantage of this aproach is that 
the problems involved in the step "matching in 2D" are 
avoided, however replaced by the additional interpretation step 
of sketches. Thus, in contrast to most existing approaches, the 
matching process will take place in object space after the 3D 
interpretation of the individual images. 
Researchers have used various techniques for interpreting 
sketches or line drawings. In their Mosaic image understanding 
system HERMAN and KANADE (1984) implemented several 
strategies to extract 3D information about houses from single 
aerial images by exploiting the special structure of the houses 
(vertical lines, flat roofs) and the special orientation of aerial 
images. MULGAONKAR and SHAPIRO (1985) have 
presented a PROLOG-based reasoning system which allowed 
to interprete perspective line drawings. It contains a large 
number of rules of the inverse perspectivity and of grouping 
processes. The system is able to interpret even images basing 
only on extracted line segments by means of these rules, but 
seems to be inefficient for interpreting sketches of even rather 
simple objects. HARALICK (1989) has collected a number of 
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