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OPTIMIZED ALGORITHM FOR THREE DIMENSIONAL OBJECT 
RECONSTRUCTION 
Maria Luiza Reis 
Programa de Engenaria Nuclear - COPPE/UFRJ 
C.P.68509 - Rio de Janeiro - Brazil 
ABSTRACT 
WG III/2 
This paper presents the development of the mathematical concept of 
image reconstruction of three-dimensional object from silhouettes 
based on functional analysis. 
This concept leads to the formulation 
of an algorithm which is also described. The use of this algorithm 
with en additional optimization procedure eliminates the errors in 
positioning the camera or the object. 
the reconstruction to convex cross sectional objects although two or 
more convex objects can be reconstructed in the same scene using 
combinatorial methods. The complete method was used to reconstruct a 
lamp-shade from four silhouettes of images taken by a camera with good 
results. 
The use of silhouettes limits 
KEY WORDS: 3D-Reconstruction, Algorithm, Optimization 
INTRODUCTION 
The problem of reconstructing shapes of 
three-dimensional objects from two- 
dimensional images is one of the important 
goals of computer vision. Concerning to 
the reconstruction from silhouettes, the 
problem can be viewed as similar to 
computerized tomography, where the 
projection mapping used in analysis of 
interior densities is different from the 
silhouettes projection and thus, in order 
to solve the problem, an alternative 
mathematical analysis is required. 
For ‘many different uses the reconstruction 
of a real body in three dimensional space 
has become very important. In designing, 
remote sensing, computer animation, and 
any other field where an object should be 
analyzed visually in 3D, the 
reconstruction is of great interest. 
Some authors have written about this 
subject. (Pai et al., 1990), (Cyganski et 
al., 1990), (Cernuschi-Frias et al.,1989) 
and (Bolle et  al., 1991) developed 
algorithms and showed the importance of 
inference to solve the problem. 
In this paper, in order to introduce the 
algorithm, a mathematical description of 
the problem is done and is specially 
helpful for the optimized algorithm for 
incorrect centralization. 
The test using a real object using the 
complete algorithm are showed in section 
5. 
335 
1. EXPERIMENTAL DATA 
1.1 Data Acquisition 
The problem of three-dimensional object 
reconstruction consists essentially in the 
surface estimation from images taken from 
different positions. In this analysis the 
images are taken over a circumference 
around the object. 
Figure 1 shows a lamp shade to be 
reconstructed and a video camera connected 
to a microcomputer. The lamp shade is 
over a rotatory base. It is not necessary 
to the body stay at the center of the 
rotatory axis but the video camera should 
be fixed so that this axis appears at the 
same position in all the images. 
The rotatory base is positioned in a few 
different angles over Il rad. No images 
are taken in opposite directions, as two 
angles differing from M rad are 
symnetrical and together carry no more 
information for this algorithm. 
  
Figure 1