On 11/29/06, J. Storrs Hall, PhD. <[EMAIL PROTECTED]> wrote:
On Wednesday 29 November 2006 16:04, Philip Goetz wrote:
> On 11/29/06, J. Storrs Hall, PhD. <[EMAIL PROTECTED]> wrote:
> > There will be many occurances of the smaller subregions, corresponding to
> > all different sizes and positions of Tom's face in the raster. In other
> > words, the Tom's face region is fractal.
>
> Are you saying that a hierarchy of categories is just a linear chain
> of resolutions?
A *linear* chain of resolutions would be just one root-to-leaf path in an
abstraction tree (root=lo-res, leaves = all the hi-res pix that would map
into that lo-res one). The whole tree would be a hierarchy of categories.
I meant that a linear chain of resolutions would create a tree,
because at finer resolutions, you would have more categories.
At the raster level, you can brighten or dim any one pixel without
substantially changing whose face it is. At higher levels of abstraction you
can move the vector along dimensions of lighting, orientation, and size
without changing whose face it is. These invariants can be captured by
transformations or projections in the space -- they're the kind of regularity
that I'm trying to capture implicitly by using n-spaces, rather than having
to represent explicitly in pointer-and-tag record structures.
What is a pointer-and-tag record structure, and what's it got to do
with n-dim vectors?
I still don't know why you talk about using different numbers of
dimensions simultaneously. Seems to me that you can capture these
invariants in whatever dimensionality you choose, so no need to talk
about fractal representations.
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