### Space Dimensions

For the purposes of our discussion, a Space is defined by the image bands.
Each band defines one dimension of the space. Thus if we have two spectral bands
they define a two dimensional space. This space can be visualized by plotting
the two spectral intensities for each pixel in a 2 dimensional x-y plot such
as the figure below which is a plot of bands 1 and 2 from the Morro Bay scene.

If we add another band, then we will have a 3 dimensional space.
We can still visualize this and even make a 3D model (as shown
below with blue data points on the tips of red pins to show location
on the Band 1 - Band 2 plane) but when we add the fourth band,
we must resort to arguments by analogy to the lower dimensional
2D and 3D spaces.

With the 7 spectral bands available from Thematic Mapper, a 7 dimensional
space is defined by the observations.

Nicholas M. Short, Sr.
email: nmshort@ptd.net

Dr. Jon W. Robinson (robinson@ltpmail.gsfc.nasa.gov)