Apple's case against Samsung spans utility patents, design patents, trade dress, and trademarks. Among the utility patents asserted by Apple against Samsung is US 7,812,828, Ellipse Fitting for Multi-Touch Surfaces.
The inventors are Wayne Westerman and John G. Elias, formerly of Fingerworks.
Though it issued on October 12, 2010, the patent actually dates back to a January 26, 1998 provisional application, and is a continuation of US 7,339,580, which is in turn a continuation of US 6,323,846. (I suspect attorneys for Samsung are already verifying support in the original specification for the '828 claims being asserted by Apple.)
The patent is notable for listing over four pages of "References Cited." This could become even more important depending on the outcome of Microsoft v. i4i at the Supreme Court, where Microsoft is arguing for a lowered bar for proving the defense of invalidity when art has not been considered by the USPTO. In this case, a lot of art has been considered by the USPTO.
Claim 1 of the '828 patent is quite broad:
1. A method of processing input from a touch-sensitive surface, the method comprising:
receiving at least one proximity image representing a scan of a plurality of electrodes of the touch-sensitive surface;
segmenting each proximity image into one or more pixel groups that indicate significant proximity, each pixel group representing proximity of a distinguishable hand part or other touch object on or near the touch-sensitive surface; and
mathematically fitting an ellipse to at least one of the pixel groups.
While the images from the design patent claims will dominate the news stories, this is certainly the utility patent to watch.

Other coverage:
- Apple v. Samsung: The Multi-touch Patent
- Flashback: Macworld 2007: "...and boy, have we patented it."
- Apple v. Samsung: Design Patents & Egyptian Goddess
- WSJ: Apple Files Patent Suit Against Samsung Over Galaxy Line of Phones and Tablets


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