Multiresolution Gauss Markov Random Field Models

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Date
1998-10-15Author
Krishnamachari, Santhana
Chellappa, Rama
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This paper presents multiresolution models for Gauss Markov random
fields (GMRF) with applications to texture segmentation. Coarser
resolution sample fields are obtained by either subsampling or local
averaging the sample field at the fine resolution. Al though Markovianity
is lost under such resolution transformation, coarse resolution non-Markov
random fields can be effectively approximated by Markov fields. We present
two techniques to estimate the GMRF parameters at coarser resolutions from
the fine resolution parameters, one by minimizing the Kullback-Leibler
distance and another based on local conditional distribution invariance.
We show the validity of the estimators by comparing the power spectral
densities of the Markov approximation and the exac t non-Markov measures.
We also allude to the fact that different measures (different GMRF
parameters) on the fine resolution can result in the same probability
measure after subsampling and show the results for the first and second
order cases.
We apply this multiresolution model to texture segmentation.
Different texture regions in an image are modeled by GMRFs and the
associated parameters are assumed to be known. Parameters at lower
resolutions are estimated from the fine resolution paramete rs. The
coarsest resolution data is first segmented and the segmentation results
are propagated upwards to the finer resolution. We use iterated
conditional mode (ICM) minimization at all resolutions. A confidence
measure is attached to the segmentation r esult at each pixel and passed
on to the higher resolution. At each resolution, ICM is restricted only to
pixels with low confidence measure. Our experiments with synthetic,
Brodatz texture and real satellite images show that the multiresolution
technique results in a better segmentation and requires lesser
computation than the single resolution algorithm.
(Also cross-referenced as UMIACS-TR-94-136)