Well, I figured the point of the question would be pretty clear seeing as
you were claiming a logical/mathematical description of images would be
inadequate, but I don't think that could be further from the truth...

You could recreate a large amount of detail in an image using mathematics
and it would be a great deal more compact of a description than a bitmap
representation. AND, you could store the mathematical properties of the
image in a DB of some sort to find similar shapes within a large body of
images.

When you remember scenes from years ago, it is unlikely that you remember
which way the grain of the wood was facing, or how many scratches were on
the left side of a corner table's handle... so why not represent them in a
similar manner as vector images?

Using a mathematical description would allow for a more compact, searchable,
and inference-available representation.

To me, keeping a little box of mathematical expressions to describe an image
is a far better choice of both memory and potential processing power than to
lug around a bitmap or any sort, unless you want to store the image in case
you find another way to interpret it.

Though humans don't remember everyday scenes through mathematical
description, we do prune out the irrelevant stuff by only remembering
general shapes, common textures, and orientations (unless we make it a
priority to remember specific features).

Mathematical equations and logical statements might not tell YOU a lot about
an image, but if someone were to sit down and carefully describe an image
using logical statements, equalities, and mathematical expressions, and if
someone were to sit down and carefully read these... with time the image
would emerge, though we humans aren't suited for this task, a machine will
be more than capable, and it would be a much wiser use of resources.

- Joe

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agi
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