STEREO MATCHING USING POPULATION-BASED MCMC

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STEREO MATCHING USING POPULATION-BASED MCMC

• Joonyoung Park1
• Wonsik Kim2
• Kyoung Mu Lee2
• 1LG Electronics Inc.
• 2Computer Vision Lab.
• School of EECS
• Seoul National University, Korea

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Low-Level Vision as an Optimization Problem

• Stereo
• Photomontage
• Segmentation
• Denoising /Inpainting
• .
• .
• .

General pairwise MRF model
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Existing Methods for Optimization Problem

• fast
• easy to get stuck at local minimum

• Graph cuts
• aExpansion / Swap
• Message passing
• Belief Propagation (BP) / Tree-ReWeighted
  Message Passing (TRW)
• Sampling based method
• Gibbs sampler
• Swendsen-Wang Cuts

• slow
• global minimum

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Our Study
We develop a new efficient sampling based
optimization method. Population based MCMC
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What is sampling ?
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Sampling
To generate samples from a target distribution
Given probability distribution
Obtained samples
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Optimization previous sampling based methods

• Two important concepts
• Annealing Sample move

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Optimization previous sampling based methods
Annealing
...
...
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Optimization previous sampling based methods
Annealing
...
...
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Optimization previous sampling based methods
Annealing
...
Most Probable State!
...
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Optimization previous sampling based methods
Sample move

• Previous methods
• Gibbs sampler
• SwendsenWang Cuts

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Optimization previous sampling based methods
Sample move
Prev. Method? Gibbs Sampler
Flip the label of single node
Too slow (only local move)
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Optimization previous sampling based methods
Sample move
Prev. Method? Swendsen-Wang Cuts
Flip the label of a cluster
Still too slow (only local move)
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Optimization previous sampling based methods
Limitation of previous methods slow convergence
rate

• Fast cooling
• easy to get stuckat local minima

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Optimization Parallel tempering
Conventional annealing
...
time
Parallel tempering
time
time
time
...
time
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Optimization Parallel tempering
Conventional annealing
...
time
Parallel tempering
time
interaction!
time
interaction!
time
...
interaction!
time
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Population based MCMC

• It was originated from parallel tempering
• It uses multiple chains
• It allows more active interactions between
  chains.
• We designed 3 sample moves
• Mutation The move of single chain
• Exchange
• Crossover Ways of interaction between two
  chains

Our contribution!!
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Optimization Population based MCMC
PopMCMC Move? Mutation
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Optimization Population based MCMC
PopMCMC Move? Mutation
time
time
time
...
time
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Optimization Population based MCMC
PopMCMC Move? Mutation
time
time
time
...
time
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Optimization Population based MCMC
PopMCMC Move? Exchange
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Optimization Population based MCMC
PopMCMC Move? Exchange
time
time
time
...
time
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Optimization Population based MCMC
PopMCMC Move? Exchange
PopMCMC Move? Exchange
time
time
time
...
time
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Optimization Population based MCMC
PopMCMC Move? Crossover
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Optimization Population based MCMC
PopMCMC Move? Crossover
time
time
time
...
time
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Optimization Population based MCMC
PopMCMC Move? Crossover
time
time
time
time
...
time
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PopMCMC Overall
mutation
mutation
mutation
mutation
mutation
crossover/exchange
crossover/exchange
mutation
mutation
mutation
mutation
mutation
crossover/exchange
crossover/exchange
mutation
mutation
mutation
mutation
mutation
...
crossover/exchange
crossover/exchange
mutation
mutation
mutation
mutation
mutation
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Proposed Population-based MCMC
Advantages

• Global move
• Unlike Swendsen-Wang Cuts that performs only
  local move, our exchange and crossover moves
  allow global move.
• Fast Mixing
• Global move and parallel tempering enable fast
  mixing.

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Application to Stereo
Stereo Problem using Segment-based Energy
Model (A. Klaus et. al., ICPR 2006)
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Application to Stereo
Segment-based Energy Model
MRF DESIGN NODES
segmentsNEIGHBORS adjacent segments
LABELS planes of disparities
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Application to Stereo
Test Images
Tsukuba
Venus
Teddy
Cones
From Middlebury web-site
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Experimental Results
Disparity maps
Tsukuba Venus Teddy Cones
Bad pixels() 1.38 1.21 14.7 13.1
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Experimental Results
Convergence
Tsukuba
Cones
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Conclusion

• We develop a new efficient Population-based MCMC
  for optimization and applied it to stereo
  problem.
• It finds lower energy state compared with other
  methods.
• Other applications / More complex energy models

Future works
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Thank You
Computer Vision Lab. Seoul National
University http//cv.snu.ac.kr