Tom Duff was educated at the universities of Waterloo and Toronto and has worked at the NYIT Computer Graphics Lab, the Lucasfilm computer

division, Bell Labs, and Pixar. His main research interest is in computer graphics and animation, but he has published broadly. (Other topics include operating systems, polymer physics, wireless networking, mathematics, and computer security.) Past work projects include writing (with Bill Reeves) the first version of Pixar's animation system, special effects in Star Trek II, Return of the Jedi and A Bugs Life,

a full-scale radio-controlled Walle and a light-field movie camera. He has half a dozen patents and two Academy Awards® for contributions to motion picture science and technology. When not at work, he is an opera singer, musical tinkerer, and grandparent. His Erdos number is 2.

## Compositing Digital Images, Revisited

Digital image compositing is a core technique of computer graphics, used for combining separately-produced elements into a composite image.

The technique, which underlies Photoshop's Layers and just about every other image manipulation system, augments the usual color components of image pixels with an extra value, invariably called alpha, that specifies how much of the background image should shine through the foreground when you layer two images.

This talk will go over a few theoretical things we have learned about compositing since 1984 when the first public description of digital compositing appeared. Alpha-augmented colors turn out to be mathematically interesting, and the mathematics has interesting applications.

In particular:

- Alpha-augmented colors, at least the non-opaque, have inverses. This has surprising applications, for example to rendering clouds in a REYES-style shading –before-hiding renderer.
- We can define a power function on alpha-augmented colors that gives us the mathematical leverage we need to properly do volume combining and deep compositing.
- Alpha-augmented colors form a Lie Group, which has a corresponding Lie Algebra with log and exponential maps joining the two. By mapping to the Lie Algebra we can properly define natural interpolants and splines on alpha-augmented colors.

Reception to follow in William G. Davis Computer Research Centre (DC) room 1301 (Fishbowl).

Space is limited. Register today!

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Waterloo, ON N2L 3G1

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