Making the Right Moves: Guiding α-Expansion using Local Primal-Dual GapsDhruv Batra (TTI Chicago), Pushmeet Kohli (Microsoft Research Cambridge)

MAP Inference in MRFs

Expansion Algorithm

Primal-Dual Interpretation of Expansion

Local Primal-Dual Gap (LPDG)

Algorithm

Results

More Results

Graph Structure

MAP Inference

Variables Node / Edge Potentials

Energy / Cost Function

Current Soln 2-Label Problem + GC New Soln

Loop over α

α-Expansionα

Traditional Loop:

LPDG Loop:

Adaptive Re-ordering of Labels leads to Massive Speed-ups!

LP Relaxations [Schlesinger ‘76; Wainwright et al. ’05; Komodakis et al. ‘05]

Primal LP Dual LP

NormalizationNormalization

MarginalizationMarginalization

LagrangianLagrangian

MultipliersMultipliers

Local Primal-Dual Gap

Interpretation

Proposed Label Scores

LPDG-crisp

LPDG-deficit

LPDG-tradeoff

LPDG Full Sweep

LPDG Partial Sweep

Ordering of Expanded Labels

Move Number

Classical Expansions

Our Guided Expansions

1 Airplane Car

2 Bicycle Person

3 Bird Motorbike

4 Boat Train

5 Bottle Airplane

1 Airplane Sheep

2 Bicycle Dog

3 Bird Bird

4 Boat Cow

5 Bottle Cat

1 Airplane Airplane

2 Bicycle Bird

3 Bird Dog

4 Boat TV

5 Bottle Train

LPDG correlated with decrease in energy!

Cuts Runtime by ~50%

Partial Sweeps Effect of Initialization