🚀 go-pugleaf

Ken Turkowski suggests that arbitrary kernels could be used on an image pyramid,
and asks if one is constrained to box filters for summed area tables.

I've been thinking along similar lines myself.  Viewed abstractly, we can
regard the image pyramid, summed area table, or other texture representation
as a data structure, and regard filtering requests ("please give me a filtered
sample of this region") as accesses or queries of that database.
People typically use a trilinear interpolation access function on pyramids
and a rectangle corner access function on summed area tables,
but we're free too choose others.

Since the original image can be recovered from either of these data structures,
they have the same information content, so any conceivable weighted average of
pixels in the texture image is computable with either.  They are at their
best, however, when filtering square and rectangular areas, respectively.
The trick is to find combinations of data structure and access function which
give the quality and speed that you want.

Ken Perlin discovered a generalization of summed area tables which admits
triangular and higher order filter convolutions.  I described it in:
    Paul Heckbert, "Filtering by Repeated Integration", SIGGRAPH 86, pp. 317-321
Also watch for a paper on this topic by Leonard Ferrari et al. in the journal
"Computer Vision, Graphics, and Image Processing".

And I discuss the arbitrary-filters-on-a-pyramid idea in the upcoming:
    "Survey of Texture Mapping", IEEE Computer Graphics and Appl., Nov. 1986

Inventing new data structures and access functions for texturing
is fun and easy - ya'll should try it!
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By the way, I'm collecting a list of Unsolved Problems in Computer Graphics.
Please mail me (DON'T POST!) your suggestions.

Paul Heckbert
Pixar				415-499-3600
P.O. Box 13719			UUCP: {sun,ucbvax}!pixar!ph
San Rafael, CA 94913		ARPA: ph%pixar.uucp@ucbvax.berkeley.edu