[Blindmath] Life After Images

[Richard Baldwin]

A couple of years ago, I watched a very interesting series on TV named
"Life After People." The thesis was that suddenly for unknown reasons, all
humans disappeared from the earth. The series went on to explore what would
happen to everything that people left behind: buildings, pets, livestock,
plants, etc.

The purpose of this post is to promote thought, discussion, and perhaps
innovation.

Assume that all of sudden, for some unknown reason, every device on earth
capable of displaying images as we know them (regular arrays of colored
pixels) were to become non-functional. Assume also that every picture on
earth was suddenly erased, but the data behind those pictures were left
intact.

Also assume that devices capable of producing more image data, such as
digital cameras, would continue to exist in a fully functional form.

At that point, there would exist giga-giga-bytes of digital image data
throughout the world, with more on the way, but there would be no way to
display that data in the conventional sense of a visible picture.

Would mankind simply allow all of the information stored in that data to
become lost, or would mankind find alternative ways to retrieve and use the
information in that data. I believe that the latter would be true. While
many might throw up their hands in despair, a few really bright
entrepreneurs might find ways to extract and use that information, some for
the benefit of mankind and perhaps some to the detriment of mankind.

Well, we know that isn't going to happen. However, we also know that there
is a large community of very bright people who are deprived of the ability
to extract and use the information contained in that data in the
conventional way -- pictures. Might there be some bright entrepreneurial
mathematicians, physicists, engineers, and digital signal processors within
that community who are willing to think about and innovate new and
different ways to extract and use that information.

Let me sow a few seeds for thought to see if any of them will take root,
grow, and blossom.

To begin with, forget about image data as being associated with pictures.
Instead, think of the data in an image file as a very large set of
numerical values, which, when arranged in a particular way and presented in
a particular format will cause a sighted person like myself to see
recognize patterns in the data. However, there may be other arrangements
and other formats that are as useful or possibly more useful but which
don't ordinarily evoke human recognition of such patterns.

Using Fourier transform theory, we can transform that data into the
wave-number domain and for certain sets of data, that format might be more
useful than the typical space-domain format.  For example, one can perform
a forward Fourier transform on a set of image data, add a watermark in the
wave-number domain, and then perform an inverse Fourier transform back to
the space domain. At that point, the watermark will still be there, but it
will be hidden. If the image is later used in violation of a copyright, as
long as the space-domain version has not been modified modified (a very big
IF), it can be transformed back into the wave-number domain to expose the
hidden watermark.

Along these same lines, transforms that are very similar to Fourier
transforms are commonly used in the compression of image data and humans
aren't expected to view those data as pictures in the transformed state.

One interesting way to think about image data is as a set of 3D vectors in
a 3D world where the axes are red, green, and blue instead of the typical
x, y, and z. When thinking along those lines, each pixel is a vector having
magnitude and direction. Lots of interesting things can be done with
vectors, such as addition, subtraction, dot products, cross products, etc.
Could these techniques be used to extract information from image data and
present that information in a format that doesn't require sight? I don't
know. I'm asking the question just to get you thinking.

This group is advertised as being "Blind Math list for those interested in
mathematics." Think about image data as fertile ground for the application
of innovative mathematical concepts -- not just data for use to create
pictures for sighted people.

You can also think about the data in an image file as describing three
different 3D surfaces which may, or may not be correlated with one another.
If the data is represented in an RGB format, it can be thought of as
representing a red surface, a green surface, and a blue surface. If the
data is represented in an HSB or HSV format, it can be thought of as
representing a hue surface, a saturation surface, and a brightness surface.

What would you get if you were to convolve a red surface with a hue
surface. I don't have the slightest idea. Probably garbage! But then again,
maybe not garbage. Despite the low odds, such an operation might produce
something useful.

What would you get if you were to subtract the vector representing each
pixel from each of the eight neighboring pixel vectors and keep the vector
difference with the greatest magnitude. I do know the answer to that
question and the result is somewhat useful, but I will "leave it as an
exercise for the student" to think about it.

What would you get if you were to perform a two-dimensional Fourier
transform on the 3D hue surface, set the transform results near the origin
to zero, and then perform an inverse transform back to the hue-space
domain? Would the result be useful? I don't know. I have never done it.

These questions represent only a few of the many mathematical operations
that can be performed on existing image data in an attempt to extract
useful information that may not require sight to be useful.

Food for thought.

Dick Baldwin

-- 
Richard G. Baldwin (Dick Baldwin)
Home of Baldwin's on-line Java Tutorials
http://www.DickBaldwin.com

Professor of Computer Information Technology
Austin Community College
(512) 223-4758
mailto:Baldwin at DickBaldwin.com
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