Multi Scale Markov Random Field
Image Segmentation
Taha hamedani
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Renormalization Group Approach(RGA)
• Based on renormalization group ideas from statistical
physics
• The RGA consists of two major steps: a renormalization
step and a processing step. In the former step, we
iteratively build a sequence of coarser and coarser grids :
• and a corresponding sequence of energy functions
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• The Hamiltonians are obtained from the original energy U
iteratively as follows:
• for each m; 1 < m < M , we choose a conditional probability :
• The energy function of coarser grids are computed by the
next formula:
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• coarse-to-fine processing starting at the bottom
level: First we solve the problem at the coarsest
level then we move upwards transmitting the
obtained information at level m to the level m-1
above.
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• At level m-1, the processing is done under a
constraint introduced by the level m below
• First, we find the global minimum of
, then
we are looking for the global minimum of
but searching only in a smaller subspace of
configurations constrained by the minimum via
the equation:
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MRF Multi scale
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To generate the multiscale version of the monogrid
model:
• divide the initial grid into blocks of size n x n (2 x 2
here)
• associate the same label to the pixels of a block
• coarser scales are defined similarly with blocks
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Neighborhood system
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Equavalent model
• These sites form a coarse grid isomorphic to the corresponding scale
• To each block, we associate a unique site having the common label of
the corresponding block.
• The isomorphism is just a projection of the coarse label field to the
fine grid.
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Energy function of course grid
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Multiscale relaxation scheme
• Using a top-down strategy in the pyramid:
1. The problem is solved at a higher level
2. 2. The lower level is initialized by the projection of the resulting
labeling.
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Advantages vs Drawbacks
Advs.
• At coarser grids, the state space has only a few elements => fast
convergence properties on a sequential machine.
• For deterministic relaxation methods (ICM. . . ), the final result is
improved
Drawbacks.
• The multiscale scheme demands usually more iterations than the
monogrid version.
• On a SIMD machine (CM200 for ex.), the multiscale scheme may be
slower than the monogrid one (the rapidity depends only on the
Virtual Processor Ratio)
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Supervised multiscale segmentation
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New neighboring system
• Keeping the interactions at each level, we
introduce a new interaction between two
neighbor grids:
• Each site interacts with its ancestor and its
descendants.
• We consider only the first and second order
cliques.
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Energy function
• For the cliques which are located on the
same level, the potential is not changed.
• For the cliques which site astride two
neighbor levels, we will favor similar classes:
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