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kSquared

Reading material for filtering theory, specifically anisotropic

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I'm interested in reading about the theory behind anisotropic filtering -- who came up with it, why the need for it arose, et cetera. I've tried going back to the research, but I couldn't come up with any kind of seminal paper. It may have been one of those evolutionary concepts that was refined over several years/publications. That's where I need the help of people more knowledgeable than myself. I'm not interested in a particular implementation, although code I can use is fine; I'm more interested in the mathematics behind it and the proof that it's correct. If someone could point me in the right direction, I'd be much obliged. I have access to most scholarly journals, so it's not a problem if the papers aren't publicly available. Thanks!

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Whenever the original paper was published, and by who, it's bound to be somewhere in SIGGRAPH proceedings. I'd estimate late 70s or early 80s, but I could be way off. It wouldn't surprise me if someone at Pixar came up with it during the development of RenderMan. You might want to look into heavily cited papers on texture mapping in general: you never know, maybe the term 'anisotropic filtering' only came about long after it was invented.

~phil

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Paul Heckbert's thesis, "Fundamentals of Texture Mapping and Image Warping" might be a good start, it's available at http://www.cs.cmu.edu/~ph/. It goes through the mathematics of aliasing, and covers the Elliptical Weighted Average filter. It also has a lot of references to earlier literature on texture mapping.

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Perona and Malik were the first guys to do this (AFAIK). I just copied this bib ref:

P. Perona, J. Malik, "Scale-space and edge detection using anisotropic diffusion", PAMI 12(7), pp. 629-639, 1990.

The guys are electrical engineers, so the maths could look somewhat strange for a PDE guy (what I suppose you are if you're interested in the maths). The proof is quite difficult. Unfortunately, I don't know a paper about a correct mathematical proof.

You might also be interested in this.

Lutz

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Anisotropic diffusion is not the same thing as anisotropic texture filtering. The former takes an image and uses local properties to adaptively blur it. The latter takes a mapping from texture space into screen space, computes a pixel footprint and attempts to approximate the integral over that footprint.

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Ouch, I read "anisotropic diffusion" instead of "anisotropic filtering"!
My fault - I should have read the post more thoroughly.

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