CI PA 2003 XIX"' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
to distinguish the object from the environment. The pixels 
position in the IHS-colorspace is examined in order to decide if 
it represents background or object. Since the blue background is 
sufficiently homogeneous, we can easily define a hue domain 
which is considered background. We performed the image 
segmentation using the academic software HsbVis (HSB- 
Visualization) that allows interactive segmentation and color 
channel splitting and merging on a graphical user interface. 
Shape from silhouette algorithms start with an opaque volume 
that encloses the entire scene. This volume is discretized into 
voxels. If we know the calibration information and image 
orientation data, we can construct a bounding pyramid for each 
silhouette image. Each point in silhouette defines a line in 
object space that intersects the object at some depth. The 
combination of all these rays for all foreground silhouette 
points defines a cone in which the objects should lie. In order to 
compute the silhouette cone, we projected all voxels in the cube 
into every image, if the image coordinate defines a background 
pixel, the voxel is marked to be deleted (voting). 
Shape from silhouette algorithms intersect all silhouette cones 
from multiple images to achieve the estimate geometry of the 
object that is called the visual hull. In Figure 3, for simplicity, 
the volume constructed is shown in 2D with its input images in 
ID. The black polygon shows the visual hull of the object. 
Figure 3: Method of volume intersection. 
Shape from silhouette method is a conservative method and it 
does not carve away the voxels it should not. Thus, visual hull 
contains the true shape. When the greater number of views is 
used, this technique progressively refines the object model. 
However, if only a few views are used the recovered shape can 
be very coarse since it cannot detect the object concavities. 
Therefore silhouette contours alone cannot recover the object 
model geometry precisely and should be supported by another 
technique to get into the critical, concave areas. See (Kuzu and 
Rodehorst, 2000) or (Kuzu and Sinram, 2002) for more details. 
3.2 Voxel Neighborhood 
Before we introduce some tools regarding voxels, we want to 
clarify the understanding of neighborhood in 3D. When we 
investigate digital raster images, a pixel has neighbors of two 
degrees: those connected by an edge and those connected only 
by a node. They are also called 4- and 8-connected 
neighborhoods. 
Figure 4: A voxel and its neighbors 
In the three dimensional case, a voxel has six neighbors 
connected by a face, twelve connected by an edge and another 
eight connected by a node, which results in a total of 26 
neighbors. Following 2D images, we call them 6-, 18- and 26- 
connected neighborhoods. Figure 4 illustrates the different 
degrees of neighborhood. 
3.3 Line Traversal 
Line traversal becomes an important tool for various tasks. For 
example projections of voxels to pixels and vice versa require a 
line traversal. The basic challenge is to do an operation on each 
voxel along a line, which is defined by a start- and endpoint. 
The first task would be to define a sensible start- and endpoint. 
The line itself is defined by the image projection center (X 0 , Y 0 , 
Z„) and either a voxel (V x , V Y , V 7 ) or a pixel (/, k, -c). Running 
any kind of operator on a voxel only makes sense within the 
defined voxel cube, since there is no information outside. Thus, 
for the sake of performance, we have to define the line so that it 
completely encloses the cube, but not much longer. 
The simplest limitation might be to look for those two ^.-values, 
so that: 
f x' 
(*oi 
Y 
= R-'A 
y* -To 
+ 
r„ 
voxel 
pixel 
j 
will completely enclose the voxel cube for every image point. 
In order to do so, the eight corners of the cube have to be 
processed for each image only once. Figure 5a illustrates this 
method. 
Figure 5: Geometric restriction of the line traversal. 
A second approach might be to enclose the cube with a sphere 
and calculate its two intersection points (if any) with the line of 
sight. Here, the A.-factor is individual for each pixel, so that we 
can expect a tremendous loss in performance, outweighing the 
advantage that the line might be a better approximation. This 
approach is shown in Figure 5b. 
The second line tracing problem is the connectivity of the line. 
In three dimensions we can either define 6-, 18-, or 24- 
connected lines. In consequence more or fewer voxels will be 
traversed. 
Although the algorithm for the 18-connected line is easier to 
implement, the 6-connected line includes some more voxels.