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
