The final case study involves an application of the dimensional stacking technique to a ``real world'' problem. During the summer of 1989, a data base with over 21000 records was created based on simulations which modeled how a pavement crack would appear given certain conditions of sunlight, crack configuration, and pavement material. The goal of the research was to determine robust viewing parameters for automated pavement crack detection. Each record contained seven parameters and the resulting value of the modeling process (corresponding to the contrast level between the pavement and the crack); see LeBlanc et. al. (4) and Wittels et. al. (22) for more details on the data set.
For viewing in N-Land, this becomes an eight-dimensional data set. The structure that was desired was a clustering of ``high'' data values, indicating large intensity contrast between pavement distress (cracks) and the surrounding pavement in an image. The data is first displayed on channel 0 as shown in Figure 5a. Note that due to holes in the parameter space (not all combinations were tested), there is some extra white space in the images. To avoid confusion with the high intensities which indicate good contrast levels, we would normally color the background with some color not represented in the data. By switching through the channels, the mapping shown in Figure 5b seemed to exhibit some of the desired structure (a subspace of ``high'' values). By using clipping, these values were isolated from the rest of the data as shown in Figure 5c.
These examples provide a good idea of the abilities of dimensional stacking in general and the N-Land environment in particular. It works equally well with simple N-dimensional hyperobjects as with actual high-dimensional data generated as a result of a complex simulation. In addition, certain preprocessing operations have been developed to aid in the pursuit of N-dimensional structure, as described below.
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