Fast Memory-Efficient Generalized Belief PropagationFast Memory-Efficient Generalized Belief PropagationM.Pawan Kumar P.H.S. Torr M.Pawan Kumar P.H.S. Torr

Oxford Brookes University, UK Oxford Brookes University, UK

Robust Truncated Model (RTM)

ResultsAim: To reduce time and memory requirements of Generalized Belief Propagation.

Belief Propagation

Reduction in Time and Memory Requirements

Model Time Memory

RTM O(nL/nC)

Truncation = 0 O(nL/nC) O((nL/nC) S-1)

Bipartite Graphs Half

Pairwise Potentials (xi,xj)

Loopy Belief Propagation (LBP)• Regions of size 2

• Inaccurate Bethe approximation

• Computationally inexpensive

Generalized Belief Propagation (GBP)

• Regions of arbitrary size S

• Accurate Kikuchi approximation

• Computationally expensive

nL

nC

• 100 random MRFs for varying nC/nL

Time Memory

• 1000 synthetic pairs of graphs• 7% noise added

Subgraph Matching

Method Time Memory Accuracy

LBP 2 sec 4 MB 78.61%

GBP - > 350 MB -

Efficient LBP 0.2 sec 0.4 MB 78.61%

Efficient GBP 4.3 sec 3.5 MB 95.79%

Outline

Texture

Object Recognition

MRF Regions+ Messages

MRF Regions+ Messages

ROC Curves - 450 +ve and 2400 -ve images

Part likelihood Spatial Prior

• Time = 16 sec. Memory = 0.5 MB

• Sites of MRF are clustered into regions.

• Regions pass messages to subregions until convergence.

G1 = (V1,E1) G2 = (V2,E2) MRF

Bipartite Graphs

• Message within A depends only on messages from B (and vice versa).

MRF Regions

Memory-Efficient GBP Truncation Factor = 0

P Q

nC

Do not contributeto message

P Q

nC

• Divide MRF into smaller MRFs which can be solved one at a time.

Fast LBP

• The same label xi of site i is used to computed the terms T2 and T3.Proof in paper.

• Term T1 takes O(nL/nC) less time than message M.

A

A

B

B

ij

• Number of stored messages reduced by O((nL/nC)S-1).

• Number of stored messages can be halved.

nC

Highest LB Label

j ij j

nC

ij jOR

Message M = max xi (xi,xj) * Local Belief (xi)

Fast GBP Message M = max xi (xi,xj)* (xi,xj) * LB(xi,xj) * LB(xi,xk)

ijk

nC

jk

ijk

nC

jk

OR

ij j ik k*

T1

T2 T3

Highest LB(xi,xj) Label

Highest LB(xi,xk) Label