The use of Spatial Frequency in quantifying scene complexity
The use of spatial frequency (SF) to quantify scene complexity is common among studies concerning motion sickness induced by vection drums (e.g., Hu et al., 1997). So, Ho and Lo (2001) extended the idea to quantify the scene complexity of a virtual environment (VE).

Step 1 -

the calculation of Spatial Frequency along EACH row and column of ONE snap shot of a VE

During a VR simulation, a snap shot is captured and stored in the 'Portable Grey-Map' format so that the gray scales of all the pixel elements could be extracted as a matrix (255 is white and 0 is black). The gray scale value of each pixel element represents its luminance level. According to So, Ho, and Lo (2001), effects of color is ignored at this stage. [In fact, the effects of color is currently being studied by one of our MPhil students - YSL].

The changes of gray scale values along each row and column are then extracted. Figure1 illustrates the extraction of the gray scale values along one row of a snap shot. As shown in the figure, the plot of gray scales across the horizontal pixel space clearly illustrates the changes of scales due to objects in the VE. Fast Fourier Transforms (FFTs) are then applied to this extracted gray scale history and the result is the power spectral density (PSD) function of this gray scale series. Using a method reported in So, Ho and Lo (2001) (called 'Combined method'), the Spatial Frequency (SF) of this row is calculated. This process is then repeated for all the rows and the average SF is the SF_horizontal of this snap shot. When the whole process is repeated for the columns of this snap shot, the average SF_vertical is calculated. Finally, the SF_radial is calculated as the geometric mean of the SF_horizontal and SF_vertical.

A program to perform this routine automatically has been developed under the signal processing software MATLABR. A Web-enabled demonstration has been set up. Using this demo, users can upload a .bmp or .jpg picture and our server will calculate and email the SF_horizontal, SF_vertical, and SF_radial to you. [NB: The FTP facilitate has to be turned off to avoid frequent hacking problem. Please send your .jpg file with a description of the field-of-view in degree to rhyso@ust.hk and we send you the calculated spatial frequency information.

Figure 1 - an illustration of how the Spatial Frequency (SF) of along a row of a snap shot of a virtual environment is extracted and calculated (adopted from So, Ho, and Lo, 2001).

Step 2 -

Repeat step 1 for many snap shots of the same VE

Step 1 is repeated for many snap shots of the same VE. So far, we have been sampling two snap shots per second through out the entire duration of a VR simulation. This, of course, is over-sampling and our MPhil student (YSL) is studying the optimal number of samples needed.

Significant relationships between SFs and levels of cybersickness
Initial evidence has been reported in So, Ho and Lo (2001) and further evidence has been found and will be published soon.