Energy functions

1
Energy functions

• f(p) ?0,1 Ising model
• Can solve fast with graph cuts
• V(?,?) T??? Potts model
• NP-hard
• Closely related to Multiway Cut Problem
• Local minimum via expansion move algorithm

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Stereo
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Potts model for stereo
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Multiway cut problem
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Multiway cuts correspond to labelings for Potts
model
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t-link
n-link
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Ideal results
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Expansion moves
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Expansion moves in action
For each move we choose expansion that gives the
largest decrease in the energy binary
energy minimization subproblem
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Binary sub-problem
Input labeling
Expansion move
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Expansion move energy
Goal find the binary image with lowest energy
Binary image energy depends on f,?
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Original energy function
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Binary image notation
Also depends on f,?!
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Binary data energy (given f,?)
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Binary smoothness energy
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Binary energy minimization

• Finding the cheapest expansion move requires
  minimizing
• Can be done efficiently by graph cuts!

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Graph cuts solution

• This can be done as long as V has a specific form
  (works for arbitrary D)
• Regularity constraint for f,? we need

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Regular choices of V

• Suppose that V is a metric
• Then what?

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Metric choices of V
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Robust
Not robust
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Robustness matters!
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Potts regularity (the hard way)
Case f(p)f(q)?
v
Case f(p)?, f(q)??
v
Case f(p)??, f(q)??
v