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In such systems, there is a bigger need for data management, 
compared to the offline systems. Therefore, it would be useful 
to test the foveation as a compression method for online VEs, 
for now, without assuming any eye tracking. 
It is possible to track the head or eyes of the viewer also in front 
of an average computer monitor, if there is the necessary 
equipment, e.g. a camera following the user's head. This kind 
of systems based on a desktop computer, are known and called 
as “fishtank VR” in part of the VR literature. The needed 
accessories are not built in to the computers though, not just 
yet. When the purpose is to pass the notion and the experience 
of a VE to the public, obviously, minimum resources should be 
assumed. 
When resources are at a minimum and we know that the eyes 
cannot be tracked, it is possible to work around the problem by 
tracking the pointing device. Cursor's position on the screen is 
known at all times, and one can often assume that the user is 
looking at where the pointer is. Particularly if the user is in an 
interactive environment, it is highly likely that she is interacting 
with an object by pointing at it, therefore she must be looking 
there. This knowledge is utilized in all 3D environments when a 
method such as visibility culling or Distance LOD is 
implemented. 
For the Foveated LOD, or the Eccentricity LOD, instead of 
tracking the eye, interaction with the user by asking her to click 
at the point of interest, or chose an area of interest is used as the 
intermediate solution, like in the 2D image coding systems that 
will be mentioned later in this paper. 
2D Foveation 
Foveation has successfully been implemented as a space-variant 
image coding system by several groups or researchers. At this 
point, a brief look into a few examples and a review of some of 
the approaches in 2D applications will be given. There are a 
large number of publications that reports the geometry, the 
techniques and algorithms used for foveated image coding. 
The common approach involves decoding the image with low- 
pass filtering methods into a foveation pyramid, and then 
decoding it back by up-sampling, interpolation and blending to 
make it into a smooth, displayable result image. (UTEXAS 
2002, Chang 1998, Chang & Yap 1997, Kortum and Geisler 
1996, Reddy 1997) 
Use of Gaussian filters and wavelet compression techniques 
dominate the foveated space-variant image coding applications 
along with log-polar mapping. A C source code for a Gaussian 
implementation is published under General Public Licence 
(GPL) by Reddy (Reddy 1997) and a small application called 
“Foveator” solely for the image-foveation purpose can be found 
in (UTEXAS 2002). *Foveator" is compiled for Windows only 
and the source code is not published. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
Figure 3: Some visual results using the “Foveator” program 
from UTEXAS. First image is original. The other two images 
are foveated, centered in where the arrows are pointing. 
The notion of foveation is popular particularly for network 
applications when the images are large - as an alternative to 
typical progressive image coding algorithms. Naturally, 2D 
foveation algorithms are never concerned with depth, which is 
relevant for photogrammetry and VR. 
3D Foveation: Eccentricity LOD 
In most 3D applications, online or offline, it is acknowledged 
that a LOD management is useful and necessary. (Hoppe 1996, 
Reddv 1997, Luebke et.al. 2003) In general, there are three 
types of LOD; diserete, continuous and view-dependent 
(Luebke etal.) and LOD algorithms consist of three major 
parts: generation, selection and switching. (Móller & Haines, 
2003) 
The applications that include foveation-like ideas are not too 
many in 3D, perhaps its obvious complexity makes it more 
computationally expensive than advantageous. But the concept 
is exhaustively studied in the literature. For instance, as 
mentioned earlier, Reddy introduces the “Perceptually- 
modulated LOD” for VR, thercfore for 3D. A chapter in this 
work is aforementioned equal of foveation, the Eccentricity 
LOD. (Reddy 1997) 
In another work, it is reported that “the system works with both 
2D and 3D image datasets" — but in this case mentioned 3D