ronse@prlb2.UUCP (Ronse) (08/20/85)
I would like to find references on general properties and applications of
causal Markov fields defined not only on 1-D chains, but also on various
ordered structures, such as 2-D raster images, trees, etc.. I am planning
to write something on the subject, but I want to be sure that my results
are new.
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maldoror@prlb2.UUCP
{enea,hirst1,inria,mcvax,munnari,philabs,seismo,unido}!prlb2!maldoror
Christian Ronse
Philips Research Laboratory Brussels
Av. E. Van Becelaere, 2 b. 8
B-1170 Brussels, Belgiumshankar@brand.UUCP (Shankar Chatterjee) (08/27/85)
A lot of work is currently being done on the application of Markov Random Fields
(MRF) in 2-D signal/image processing. There are several research groups in
U.S. who are doing some useful study in this area, notably from Univ. of Mass.,
Brown University, and also here at Univ. of So. Calif., and elsewhere.
There is an excellent book on MRF by R. Kindermann and J.L. Snell, "Markov
Random Fields and Their Applications",published in 1980 by Amer. Math. Soc..
I think MIT press has also published another book in 1984 (I wish I could
remember any more details about it !). Also there is another book called
"The Statistical Analysis of Spatial Pattern" by M.S. Bartlett (published by
Chapman and Hall, 1976), which deals with it to some extent. There are some
more books on it. There is a classic paper by J.E. Besag, "Spatial interaction
and the statistical analysis of lattice systems", in J. Royal Stat. Soc.,
series B, vol. 36, 1974, which is referred to almost by anyone working in this
area.
MRF's are also related to Gibbs' random field (GRF). In fact MRF can be
considered as a subset of GRF. A recent paper by Geman & Geman in IEEE Trans.
on Patt. Anal. & Mach. Intel. in Nov. 1984 discusses this issue. However, the
problem of computing parameters has not been explored fully.
One of the earliest works in causal MRF as applied to 2-D images was by
L. Kanal ("Markov Mesh Models", in Image Modelling, Academic Press, 1980). Also
D.K. Pickard came up with another idea in "A curious binary lattice process",
J. Appl. Prob., vol 14, 1977. Even though, causal MRF guarantees (in most
cases) faster computation, fewer people are looking into it as images and many
other 2-D signals are "inherently non-causal" in nature.