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Let's side step to talk about deinterlacing. The marketing buzzword for deinterlacing has been "motion-adaptive" deinterlacing. This is as descriptive as "anti-aliasing" without knowing the number of taps, whether it's edge anti-aliasing, super-sampling, rotated grid, multi-sampled, etc.
Video deinterlacing is all about throwing away pixels that would otherwise cause feathering artifacts and coming up with ways to guess what the best restoration would be. Only poor quality video processors are non-motion-adaptive. This means 50% of the data is ignored. A motion-adaptive deinterlacer is one that selectively discards pixels. It can be as cool as a video processor that tries to map each pixel to a motion vector or as dumb as video processor that divides the screen in half and has the option of discarding the top half of one field, the bottom half of one field or both.
Once the pixels have been discarded, there is also a wide variety of algorithms that can be used for deinterlacing. Bob de-interlacing is the simplest intra-frame (a single frame) approach.
You always start with the destruction of a line of pixels. In bob reconstruction, those missing pixels are regenerated by averaging the pixel above and below. While this takes care of the feathering, you give up 50% of the resolution that's potentially recoverable.
So, suppose that you have these pixels at the odd rows 1 and 3:

The video processor has to figure out what 5 pixels should go in between

A simple bob would just average the pixel above and below for each.

Resulting in this:

A better intrafield method of deinterlacing is edge-adaptive diagonal interpolation in which you examine several pixels from the row above and below the discarded pixel instead of just the pixels above and below. If an edge is detected, then the missing pixel is interpolated by averaging the pixels along that edge. So, first the video processor looks for edges in several directions

When it detects the edge, it interpolates along that axis.

You can then use the nearest pixel outside of the edge resulting in

The difference doesn't looks like much until you take a step back and compare the two. With traditional bob, you get artifacts that result in jaggies but with edge-adaptive directional interpolation it looks exceptionally smooth. (Try squinting for the maximum effect).

Amazing isn't it? Diagonal filtering was a feature pioneered by Faroudja.
Done deal? Not quite. How do I know if the correct "edge" is the red part

or if the background happens to be red and the white line is what I'm supposed to interpolate?

Resulting in :

Was the picture supposed to represent a red slash on a white background or a bold white backslash on a red background?
It's impossible to say.
This again brings up the point that
diagnosis is just as important as the treatment when it comes to video processing. You could have two video processors with diagonal interpolation, but one might be more accurate at guessing the appropriate direction. Likewise, you could have an exceptionally exotic deinterlacing strategy that only worked in some conditions.
This is where trade secrets come in and this is where you find the challenge of diagnosis. A better video processor may choose to look at a larger area of surrounding pixels. The algorithms and thresholds used to identify edges can differ. ATI is likely using this general algorithm when it comes to their "vector adaptive deinterlacing" – the real question is how accurate their detection and diagnosis is.
Inter-field Strategies
Another approach to video deinterlacing would be an inter-field strategy where you incorporate data from historical fields to make decisions. In theory, additional data should give a video processor the ability to make a more informed decision, however it still boils down to how well the algorithms are – it's what you do what the information that counts. As you can imagine, the complexity for these algorithms are substantially higher.
NVIDIA uses temporal filtering in PureVideo, but the specifics aren't that clear. Since I talked about how ATI is likely doing their deinterlacing, it's seems unfair that I don't guess what I think NVIDIA is doing.
NVIDIA won't give the algorithm a name more detailed than "spatial-temporal deinterlacing" which suggests that a more descriptive name would reveal the trade secret. Since their regional based algorithm has fewer jaggies than regular linear line averaging, my guess is that they're possibly using some form of edge-line averaging which or multi-directional vertical-temporal filter. I'm not really sure yet.
Motion definitely is detected in a regional manner, but the regions don't seem to be traditional squares which is sort of interesting. The most significant strength of PureVideo seems to be its 3:2 detection strategy which works well both against bad-edits and unusual 3:2 based cadences. A good approach for this would be to strengthen the pulldown algorithm with something that compares the average pixel level between two fields against some threshold and using that more accurately detect bad-edits.
The really cool processors use an amalgam of algorithms in concert so that you're always picking the right interpolation strategy for the given content (which involves yet another algorithm to decide which algorithm to use).