> From: Whitehouse Chantal <email@example.com>
> In the commentry by Latimer, C. R., could you please explain the
> > Whether or not the property of symmetry is captured or derivable
> > from a pixel-based decomposition depends entirely on how the
> > decomposition and its attributes are defined. For some
> > decompositions and their attributes (Gibson's 1969 graphemic
> > analysis which does not specify locations of parts within
> > characters) symmetry will not be derivable directly from the parts.
> > For other decompositions and their attributes, (Latimer, Joung &
> > Stevens, 1994; Sejnowski, Kinker & Hinton, 1986) symmetry will be
> > derivable.
> At the end of his commentary he writes,
> > the flexibility proposed by the authors may lie in the ability of
> > the brain to adopt efficient and context-sensitive decompositions
> > rather than attempting to create or derive features from a fixed
> > decomposition .
> What does he mean by "efficient and context-sensitive decompositions" ?
Think of pixels as just being light/dark points in a hugely magnified
newspaper photograph. You can think of this pixel projection as the
shadow cast by the object on your retina, or as a higher-level copy of
that shadow in your brain.
Even for a small pixel map, say, 10 x 10 pixels. That's only 100
pixels. But now think of all the 2-dimensional shapes you know --
letters, numbers, geometric shapes, animals, parts of animals, faces,
etc. Each of those things would cast a different "shadow" on this map,
and a different one also depending on how near or far, high or low or
tilted each would be. Now think of how many of all the possible
combinations of 100 pixel elements (= 100 x 99 x 98 ..... x 2 x 1)
you would need to have in your fixed feature "repertoire" in order to pick
out and correctly categorise all those possible shapes. Let's call that
total number M for monster.
Now forget about most of those shapes: Just think of the letters in
the alphabet, appearing in any size, position or orientation on the map
(never mind all the different possible type-faces!). A "decomposition"
is the repertoire of parts out of which you would build and recognise
all those letters DEFINED IN TERMS OF PIXELS IN THAT MATRIX.
You could start with an "X" of exactly the size and shape I just typed,
and list all the possible pixel combinations it could activate if it
cast its shadow on them. The number would be huge, but not as huge as
M. Let's call it little m. So your representation of that X could be
any of the combinations in little m, from the first, say, an X in the
leftmost uppermost corner of the pixel map, to the last, say in the
bottom right corner.
Not a very efficient representation of X. Maybe it would be simpler to
note that most of the letters are actually combinations of lines. So
instead of decomposing them into all the possible letter-specific pixel
combinations, we could decompose them into all the possible lines of a
fixed length (the rest would just be sums of them) in all possible
orientations and positions. This may sound bad too, but it seems to be
similar to what the brain does. Then the straight-line letters, anyway,
could be composed out of combinations of those line-features; they no
longer need a huge list of unique pixel combinations each: they are
combinations now of lines. This still is not efficient, however, and
there are better primitive features than lines that could be used.
So the answer to your first question -- what is pixel-based
decomposition -- is that it is a way of putting together (composing)
shapes out of features, where the features are pixel-based. Think of
the features as being composed of pixels and then the shapes as being
composed of the features. Whatever is composed, can be decomposed. If
the feature is a line, then you can decompose the shape into lines and
the lines into pixels, but you can't decompose a part of a line of a
figure into pixels. So if "two thirds of the way along a any line" turned
out to be an important feature for some reason, it could not be
recovered from this feature representation. ("Recover" means being able
to detect a shape on the basis of that particular feature.)
Latimer's example is symmetry: If "symmetry" is not a pixel-based
primitive feature, you may not be able to recover it, hence to
categorise on the basis of symmetry. Letters might be detectable in
terms of the number and shape of lines they contain, with no need to
specify the exact spatial relation between those parts. (An X might be
detectable as the only letter with two v's, so you may not need to
specify their exact position relative to one another; then the symmetry
between the 2 mirror-mage v's in the X would be unrecoverable.) So if
the exact position is not specified, you could not say which letters
were symmetrical and which not.
What Latimer means by "context-sensitive decompositions" is that it may
not be practical for the brain to see every shape as composed of the same
fixed set of features. The brain may know that in the context of letter
identification symmetry does not matter but in the context of face
identification it does. So although both letters and faces would be
"projected" on the same pixel map, one set of features would be used to
compose and decompose letters and a different set to compose and
Of course this is all quite vague, and it's not clear how the brain
would know which to use, and more important, what the actual and
possible features/compositions really are.
HARNAD Stevan firstname.lastname@example.org
Professor of Psychology email@example.com
Director, phone: +44 1703 592582
Cognitive Sciences Centre fax: +44 1703 594597
Department of Psychology http://www.cogsci.soton.ac.uk/~harnad/
University of Southampton http://www.princeton.edu/~harnad/
Highfield, Southampton ftp://ftp.princeton.edu/pub/harnad/
SO17 1BJ UNITED KINGDOM ftp://cogsci.soton.ac.uk/pub/harnad/
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