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From: Thomas Richter on 12 Apr 2010 10:58
MBALOVER wrote:
> Hi all,
>
> I am wondering if you guys know any paper or book chapter discussing
> optimal linear prediction for 2D or more specifically for image
> processing?

I'm not sure that there is a single source that discusses all available
linear predictors, but there are a couple of classical results. -
depending on your definition of optimality.

For example, if "optimality" is defined in terms of optimal
decorrelation, then the answer is the KLT (the operator that
diagonalizes the correlation matrix). Then again, you have more
classical results that the KLT is, for stationary (position-independent)
processes just the Fourier transformation.

A couple of predictors are discussed in the classical
"Digital pictures: representation, compression, and standards" by
Netravali et al. Probably a bit outdated, but still a good introduction.

Greetings,
Thomas
From: James Dow Allen on 12 Apr 2010 14:14
On Apr 12, 6:26 am, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote:
> MBALOVER wrote:
> > I am wondering if you guys know any paper or book chapter discussing
> > optimal linear prediction for 2D or more specifically for image
> > processing?
>
> Plane prediction is very common in video processing:
>
>   A | B
> -------
>   C | X
>
> X predicted = B + C - A

Very simple non-linear predictors can be better than even
the best linear predictors. For example, B + C - median(A,B,C)
may be better than the B + C - A just mentioned, and has
the advantage that the prediction is always "in-range"
(violation of which could be inconvenient).

There are alternate formulations that may look quite
different from " B + C - median(A, B, C) " but are in fact
equivalent. This particular predictor has been rediscovered
at least 3 times.

James
From: HardySpicer on 13 Apr 2010 15:22
On Apr 12, 8:32 am, MBALOVER <mbalov...(a)gmail.com> wrote:
> Hi all,
>
> I am wondering if you guys know any paper or book chapter discussing
> optimal linear prediction for 2D or more specifically for image
> processing?
>
> I tried to look for it in the library in my university but could not
> find it.
>
> Thank you.

The 1D theory should carry through for filtering,smoothing and
prediction.
Should be a huge literature.


Hardy
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