Fast Memory-Efficient Generalized Belief Propagation

1. Fast Memory-Efficient Generalized Belief Propagation Aim:To reduce time and memory requirements of Generalized Belief Propagation. Results Fast LBP Message M = max xi (xi,xj) * Local Belief (xi) • 100 random MRFs for varying nC/nL Highest LB Label Belief Propagation nC nC OR • Sites of MRF are clustered into regions. • Regions pass messagesto subregions until convergence. ij j ij j ij j Time Memory Fast GBP Message M = max xi (xi,xj)* (xi,xj) * LB(xi,xj) * LB(xi,xk) Loopy Belief Propagation (LBP) Subgraph Matching • Regions of size 2 • Inaccurate Bethe approximation • Computationally inexpensive nC ijk jk nC T1 ijk jk OR G2 = (V2,E2) G1 = (V1,E1) MRF MRF Regions+ Messages Highest LB(xi,xj) Label • 1000 synthetic pairs of graphs • 7% noise added Generalized Belief Propagation (GBP) * ij j ik k Highest LB(xi,xk) Label T3 T2 • Regions of arbitrary size S • Accurate Kikuchi approximation • Computationally expensive • 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. Memory-Efficient GBP Truncation Factor = 0 MRF Regions+ Messages Robust Truncated Model (RTM) Do not contribute to message Object Recognition nL Outline nC nC nC Texture P Q P Q • Divide MRF into smaller MRFs which can be solved one at a time. Part likelihood Spatial Prior • Number of stored messages reduced by O((nL/nC)S-1). A B Bipartite Graphs Pairwise Potentials (xi,xj) • Time = 16 sec. Memory = 0.5 MB ROC Curves - 450 +ve and 2400 -ve images A B Regions MRF • Message within A depends only on messages from B (and vice versa). Reduction in Time and Memory Requirements • Number of stored messages can be halved.