A color image is a 5 dimensional graph -- nothing more -- nothing less.

If you understand this concept, and can work with it, image processing
becomes almost trivial.  The three dimensions are x, y, red, green and
blue.  The first two are spatial dimensions and the last three are
spectral dimensions.

The image can be rotated spatially by using a dot product of a unit
vector in x and y.  The result is to simply turn the image so that the
top of the image is no longer up.  The same thing is possible with the
spectral dimensions.  One way to rotate the spectral dimensions is to
use eigen vectors. 

An image is a more general thing than a picture.  A picture is an
image, but an image may not be a picture.  Pictures are representations
of what we see and are, therefore, limited to the three color receptors
in the eye, namely red, green and blue (RGB).  Images can be made of
other spectral channels, many of which we cannot see with the eye.  By
combining other channels of information and assigning red, green and
blue to them we can make a color image.  These are sometimes called
false color images because the colors are arbitrary and not what would
be seen by the eye.  These images are no more false color than the
graph of a sound wave is a false graph.  Sound does not make air move
up and down as it moves through the air but the pressure changes can be
plotted as y along an x axis of time to help visualize the process. 
The same is done with color to help visualize spectral data. 

     Without getting into a long discussion on color perception the
point needs to be made that we do not see red, green and blue as color
axis.  We see intensity, hue, and saturation (IHS) axis which are
perceptually orthogonal (changing one does not effect the other axes). 
Since we use red, green and blue to make images this is the color
coordinate system we will use to plot images.  Plotting images in IHS
is considerably more complicated than using RGB and does not neces-
sarily produce a better product.  An experienced observer can perceive
both systems on an RGB graph. 

     The system presented here allows you to (1) look at full color
images, (2) make color images by combining different spectral planes,
(3) spectrally rotate the images using an eigen vector program and
finally (4) to view any RGB image in all 5-dimensions at once. 
Moreover, all of this can be done on an inexpensive computer with VGA
color.  The first two options are done with a program called imvis, the
3rd by program eigen and the last by program make5d.
  
     In order to make a 5-D image you must have an 8-bit color image,
preferrably one made by imvis from a set of red, green and blue images.
The label file must look like example 3 above with the file names of
the input files.  Program 'make5d' will read these images and the 8-bit
color composit and make a 4 pannel display file which can be quickly
recalled in the future.  A sampled version of the original 8-bit image
will be in the upper right corner of the screen.  The lower half of the
screen will show the three sides of the color cube and the pixels will
be plotted on them.  This is a representation of a 3-D histogram giving
the (1) front, (2) side and (3) top of the color cube.  After the
'.X5D' (or '.S5D' if you are using standard VGA) file is created you
may use the view option of the program. 


Option 1:  "cursor on image"

     A cursor will appear ont the sampled image and, using the arrow
keys and '+' and '-', it can be moved around on the sampled image.  As
it moves it will plot in the upper right quadrant of the screen (1)
pixel location on the screen, (2) the 8-bit number ploted on the screen
(DN value), (3) the RGB colors used by the color look up table to plot
the image pixel, and (4) the actual data file values of the red, green
and blue channels.  At the same time 3 other cursors will appear on the
color cube histogram plots and move to show where this pixel is
spectrally.

Option 2:  "rectangle image"

     Option 2 allows a rectangle of any size and shape to be placed on
the image and all of the pixels within its bourders marked in white on
the color cube plots below.  Hitting the lower case 'f' on the keyboard
will flash these points black and white.  Hitting 'c' will change the
colors through all of the 16 VGA colors available to the system.  The
'Enter' key marks the pixels and the 'Esc' key exits the mode.

Option 3:  "slice RGB scatter"

     This option allows you to cut a box out of the color cube and see
where these pixels are on the spatial display -- the image.  Hitting a
number from 1 to 3 will change the active color cube display you are
working with.  The active box has a white number rather than light
grey.  The arrow keys move the sides of the box in or out.  Use 'i' for
in or 'o' for out to change direction.  Use 'Enter' to plot, 'f' to
flash and 'Esc' to exit as before.