On Tuesday 28 November 2006 17:50, Philip Goetz wrote: > I see that a raster is a vector. I see that you can have rasters at > different resolutions. I don't see what you mean by "map the regions > that represent the same face between higher and lower-dimensional > spaces", or what you are taking the limit of as resolution goes to > infinity, or why you don't just stick with one particular resolution.
Take rasters representing the faces of Tom and Dick. Just for concreteness let's assume they're 16K numbers long. Each one represents a point in a 16K-dimensional space. If we think of all the points in the space that are pictures of Tom, they form a (probably connected) region in the space. All the pictures that represent Dick form a similar shape, offset from the Tom region. There's a larger region that contains both of them that is the union of all men's faces, and a larger one yet that's all human faces, and so forth. Now imagine the picture of Tom being shrunk until it's only 1/4 of the original raster. It's still Tom's face so it's still part of the Tom region of the 16K-D space, but 12K of those dimensions can change however they like and not affect the Tom-ness of the picture. A 4K-D slice across this subspace would look like the original space would if it only had 4K dimensions in the first place -- and it will also resemble a diagonal slice across the big part of the Tom region. 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. So, of course, is the Dick's face region, but note that at they lower limits of resolution they begin to overlap; after a while you're just able to recognize a human face but not say whose. So even if you started out saying "only 16K-D space, fixed resolution," you wind up having to work with the other dimensionalities anyway. Cheers, --Josh ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
