Section 4 presents experimental results Finally, in Section 5 
conclusions are drawn and future work is outlined. 
2. ACQUISITION SYSTEM 
The acquisition system (Figure 1) consists of the following 
devices: 
• a turntable (Figure la) with a diameter of 50 cm, whose 
desired position can be specified with an accuracy of 
0.05°. The turntable is used to obtain multiple views of the 
object observed. 
• two monochrome CCD-cameras (Figure lb and lc) with a 
focal length of 16 mm and a resolution of 768x576 pixels. 
One camera (Camera-1 in Figure 1) is used for acquiring 
the images of the object's silhouettes and the other 
(Camera-2 in Figure 1) for the acquisition of the images of 
the laser light projected onto the object. 
• a laser (Figure Id) used to project a light plane onto the 
object. The laser is equipped with a prism in order to span 
a plane out of the laser beam. The color of the projected 
light is red. 
• a lamp (Figure le) used to illuminate the scene for the 
acquisition of the silhouette of the object. The object 
should be clearly distinguishable from the background 
independent from the object's shape or the type of its 
surface. For that reason back-lighting [5] is used. A large 
(approx. 50x40 cm) rectangular lamp is put behind the 
turntable (as seen from the camera). In addition, a white 
piece of paper, larger than the lamp, is put right in front of 
the lamp, in order to make the light more diffuse. 
The whole system is protected against the ambient light by a 
thick black curtain. 
(c) Camera-2 (d) Laser (e) Lamp 
(b) Camera-1 (a) Turntable 
Figure 1. Acquisition System 
tional axis of the turntable. Camera-2 in Figure 2 views the 
light plane also from an angle of about 45° (a in Figure 2). The 
relative position of the two cameras to one another is not impor 
tant, since the acquisition of the silhouettes and the acquisition 
of the laser light projection are independent from one another. 
Figure 2. Geometrical setup of acquisition system 
Prior to any acquisition, the system is calibrated in order to 
determine the inner and outer orientation of the camera and the 
rotational axis of the turntable. The calibration method used 
was exclusively developed for the Shape from Silhouette 
algorithm presented and it is described in detail in [20] and 
[7,21]. 
3. MODEL REPRESENTATION 
There are many different model representations in computer 
vision and computer graphics used. Here we will mention only 
the most important ones. Surface-based representations describe 
the surface of an object as a set of simple approximating 
patches, like planar or quadric patches [12]. Generalized 
cylinder representation [17] defines a volume by a curved axis 
and a cross-section function at each point of the axis. Over 
lapping sphere representation [14] describes a volume as a set 
of arbitrarily located and sized spheres. Approaches such as 
these are efficient in representing a specific set of shapes but 
they are not flexible enough to describe arbitrary solid objects. 
Two of the most commonly used representations for solid 
volumes are boundary representation (B-Rep) and constructive 
solid geometry (CSG) [17]. The B-Rep method describes an 
object as a volume enclosed by a set of surface elements, 
typically sections of planes and quadratic surfaces such as 
spheres, cylinders and cones. The CSG method uses volume 
elements rather than surface elements to describe an object. 
Typical volume elements are blocks, spheres, cylinders, cones 
and prisms. These elements are combined by set operations into 
the modeled object. The B-Rep and CSG method suffer from 
quadratic growth of elemental operations as the complexity of 
the modeled object increases. 
The geometrical setup of the acquisition devices is shown in 
Figure 2. Both cameras are placed about 50 cm away from the 
rotational axis of the turntable. Ideally the optical axis of the 
camera for acquiring object's silhouettes (Camera-1 in Figure 2) 
lies nearly in the rotational plane of the turntable, orthogonal to 
the rotational axis. The camera for acquiring the projection of 
the laser plane (Camera-2 in Figure 2) onto the object views the 
turntable from an angle of about 45°(/? in Figure 2). The laser is 
directed such that the light plane it projects contains the rota 
An octree [3] is a tree-formed data structure used to represent 3- 
dimensional objects. Each node of an octree represents a 
cube subset of a 3-dimensional volume. A node of an octree 
which represents a 3D object is said to be: 
• black, if the corresponding cube lies completely within the 
object 
• white, if the corresponding cube lies completely within the 
background, i.e., has no intersection with the object