Men are silhouetted against a video screen with an Samsung logo as they pose with an Apple iPhone 4 smartphone in this photo illustration taken in the central Bosnian town of Zenica, May 17, 2013. (DADO RUVIC/REUTERS)

Legal representatives from Apple and Samsung were back in federal court in California on Tuesday, this time to decide how much the Korean firm owes the tech giant for patent infringement.

In August 2012, a federal jury handled Apple a big victory in its suit against Samsung when it found that the Korean firm had infringed on a several Apple patents for its smartphone and tablet features. The jury fined Samsung more $1 billion in damages.

But that amount was reduced to around $639 million in March by Judge Lucy Koh of the U.S. District Court in California’s Northern District, who ruled that the jury had miscalculated its estimate of damages. The retrial is to determine out how much Samsung should pay Apple in addition to the $639 million.

Apple is likely to try and recoup the roughly $411 million in damages that were vacated from the original finding that 28 Samsung phones infringed on Apple patents. Bloomberg reported that some analysts expect Apple to ask for more than the original $1 billion.

The damages case is the latest phase in a bitter patent dispute between Apple and Samsung, who have each accused the other of infringing on technical and design patents. The firms have filed numerous legal complaints around the world, asking courts to assess damages, block imports and order changes to products already on the market.

So far in the United States, Apple has seen more legal success than Samsung. The Korean company won a ruling in June that would have blocked the sales of older iPhones on AT&T’s network. But that ban was ultimately overturned by the Obama administration. The administration then declined to overturn a similar ban against Samsung products in October, after the International Trade Commission ruled Samsung had infringed on Apple patents.

Apple and Samsung are also scheduled to begin a second, separate patent trial before Koh next spring.

Reporting from the San Jose courthouse Tuesday, Howard Mintz of the San Jose Mercury News said that Koh made another appeal to Apple and Samsung to settle that case — with no luck. She then moved on to the jury selection process.

Mintz reported that Koh expects this trial to last through Tuesday, with jury deliberations beginning on Wednesday.

Apple and Samsung declined to comment on the court proceedings.

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