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A | / 
Matching in 2D 
Symbolic image description 
Reconstruction in 3D 
v dy 
3D description of the object E | 
Fig. 1 Deriving 3D information of an object 
a. Classical approach 
b. The matching in 2D is replaced by two steps 
rules of the inverse perspectivity for deriving 3D attributes 
from image data and hypothesis about the object’s shape. 
SUGIHARA (1986) probably has presented the most 
consistent theoretical framework for the geometrical 
interpretation of line drawings. The reasoning is based on line 
drawings which are labeled according to HUFFMANN (1971) 
and CLOWES (1971), deriving a set of linear constraints for 
the parameters of the object’s faces with the exception of a few 
form parameters (>=4) which have to be derived by other 
means. The approach is not able to handle incomplete sketches 
or even non linked edge images, thus assumes the labeling of 
edges to be complete. 
The approach presented in the following aims at the 
geometrical interpretation of perspective and orthogonal 
images. The sketch, derived from an image, may be incomplete 
and inaccurate, without any apriori information about the 
object's orientation or about the exterior orientation of the 
images as well. The approach tries to link the features of the 
procedures mentioned above. The process of interpreting 
single images is devided into several steps. As the kind, 
number and order of these steps of the process are dependent 
on the input data, on the kind of object and on the image, there 
are several ways to solve the task. Therefore the steps are 
formulated as rules, organized by the control modul of a rule- 
based system, finding one possible short way to the solution. 
Chapter 2 gives an overview of the approach, chapter 3 
contains the geometric reasoning process. The rule-based 
system is described in chapter 4, illustrated by some examples. 
815 
Images L] L] y 
Edge eio grouping 
i 
Sketches 5 [1 [-] 
hoc peus 
Geometric Reasoning 
jl | 
Single 3D models [ ] m [-] 
Ari. 17 
Matching in 3D 
17 
3D description of the object [1 
b. 
2 Overview of the approach 
The vision system for Interpreting Single Images of Polyhedra 
(ISIP) uses four levels for the representation of data (Fig. 2). 
The first level is the original image, a single black and white or 
color one. Methods of noise cleaning or image restauration 
being edge preserving may be applied for preprocessing. 
As primitives, like extracted straight line segments and 
detected regions with similar intensity (blobs), the data 
original image 
I 
edge detection 
J 
extracted line segments, blobs 
| 
grouping 
+ 
2D features (points, lines, planes) 
+ incidence relation 
I 
geometric reasoning 
J 
3D structures (vertices, edges, surfaces) 
+ incidence relation 
Fig. 2 Four levels for the representation of data