1. Biointelligence Laboratory, Seoul National University
Ch 6. Markov Random Fields 6.10 Coupled Markov Random Fields 6.11 Compound Gauss-Markov Random Fields Adaptive Cooperative Systems, Martin Beckerman, 1997.
Summarized by
J.-W. Ha
Biointelligence Laboratory, Seoul National University

2. (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Contents
6.10 Coupled Markov Random Fields
The Line Process
Coupled Markov Random Fields and Integration
6.11 Compound Gauss-Markov Random Fields
(C) 2009, SNU Biointelligence Lab, 

3. (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Line Process
Coupled
Pixel Process + Line Process
Line process : discontinuity-preserving, boundary-strengthening
The Line Process
Second Markov random fields
Employ the Gibbs-Markov equivalence to produce a simple in terms of clique potentials.
Is defined over a dual lattice and encodes discontinuity information
Be visualized as a 2-D array of 2N2 line elements, one horizontal and one vertical line for each pixel in the primary pixel lattice.
(C) 2009, SNU Biointelligence Lab, 

4. (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Line Process
the first order relations
The Suspension of smoothing at surface boundary
Line element is ON → second term = 0
Prevents the unwanted phase transitions by suspending
Small islands of pixels
(6.120)
(6.121)
(6.122)
(C) 2009, SNU Biointelligence Lab, 

5. (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Line Process
Off-on system of line elements
Six elements : empty, isolated singleton, corner, straight line, tee, crossing
Clique potentials
Generalized Ising Hamilton
A simple way of strengthening boundaries
The lowest energies : All ON or All Off
(6.123)
(C) 2009, SNU Biointelligence Lab, 

6. Coupled Markov Random Fields and Integration
The goal
Image reconstruction : remove noise, blur, distortions and artifacts while preserving boundaries
Segmenting : reconstruct and identify the individual surfaces
Removing noise and artifacts while preserving and strengthening boundaries.
Integration
Added task : combine 2D image from many perceptual domains
It can be done by coupled MRF
(C) 2009, SNU Biointelligence Lab, 

7. Coupled Markov Random Fields and Integration
Underlying Assumptions
3D physical scenes are composed of surfaces
Input : 2D projection of 3D scene
Output : image description in terms of surfaces, attendant discontinuities, stable physical properties
J.J. Gibson : invariant properties of surfaces were perceived directly from the spatiotemporal patterns of light reaching the observer as contained in the ambient optic array.
Barrow et al. replace the concept of direct perception with a computational theory for the reconstruction of surfaces
(C) 2009, SNU Biointelligence Lab, 

8. Coupled Markov Random Fields and Integration
Computational theory of perception
Intrinsic images
Arrays of elements that are in precise registrations with respect to the original images
Each array describes an invariant physical characteristic of the underlying physical surfaces and also contains information regarding the discontinuities associated with that property.
Ex : distance(depth), albedo, local surface orientation, illumination
Constrains to reconstruct
Problems of recovering the properties of 3D surfaces from 2D images
Needed to restrict the many possible surface reconstructions to physically meaningful one
(C) 2009, SNU Biointelligence Lab, 

9. Coupled Markov Random Fields and Integration
Coupling Model
Simultaneously extract surface and boundary information
Consider the integration of information contained in the various intrinsic images
One for the pixel process and one for the line process
(C) 2009, SNU Biointelligence Lab, 

10. Coupled Markov Random Fields and Integration
An Example of the integration of data from multiple moduels
(C) 2009, SNU Biointelligence Lab, 

11. Coupled Markov Random Fields and Integration
ICM algorithms for Coupled MRF
Initialize the pixel lattice by choosing the value at each site that maximizes the likehood.
Initialize all dual lattices using the initial pixel values according to Eq.(6.120)
Select a primary dual lattice pair
Select a lattice site in the manner of a raster scan
Replace the pixel grey values with the mode for the neighborhood.
Go back to step 4 and continue the raster scan
Initialize the dual lattice using the updated pixel values
Select a dual lattice site in the manner of a raster scan
If flipping the spin lowers the energy, then flip the spin; otherwise do not flip.
Go back to step 8 and continue the raster scan
Repeat steps 3 to 10 for the next pair of coupled lattices
Iterate five or six times, repeating steps 3 to 10 for the three lattice pairs
(C) 2009, SNU Biointelligence Lab, 

12. Coupled Markov Random Fields and Integration
Compound Gauss-MRF
These models extend the method of Geman and Geman to non-compact, continuous-valued range spaces
Reconstruction
Given the degraded observed image g, reconstruct f
Appending a line or structure process
(C) 2009, SNU Biointelligence Lab, 

13. Coupled Markov Random Fields and Integration
A model consisting of a continuous valued pixel process plus a discrete valued line process
(C) 2009, SNU Biointelligence Lab,