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Belief Propagation in Large, Highly Connected Graphs for 3D Part-Based Object Recognition

Belief Propagation in Large, Highly Connected Graphs for 3D Part-Based Object Recognition. Frank DiMaio and Jude Shavlik Computer Sciences Department University of Wisconsin – Madison USA. Part-Based Object Recognition.

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Belief Propagation in Large, Highly Connected Graphs for 3D Part-Based Object Recognition

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  1. Belief Propagation in Large, Highly Connected Graphs for 3D Part-Based Object Recognition Frank DiMaio and Jude Shavlik Computer Sciences Department University of Wisconsin – Madison USA

  2. Part-Based Object Recognition • A part-based modeldescribes an object using a pairwise Markov Field(Felzenszwalb et al 2000, Sudderth et al 2004, Isard 2003) • Object described using • Undirected part graph G=(V,E) • Vertex potential functions • Edge potential functions

  3. Part-Based Object Recognition • Probability of a configuration U={ui} – given an image I– isthe product of potential functions • For part-based object recognition • Skeletal graphfor tightly coupled parts • Occupancy graph ensures no other parts collide in 3D space

  4. Inferring Part Locations with Belief Propagation (BP) • Want to find part configuration maximizing product of potential functions • Use belief propagation (BP) to approximatemarginal distributions • Iterative, message-passing method (Pearl 1988) • A message, mi→j, from part i to part j indicates where i currently expects to find j

  5. b( left arm | image) b( right arm | image) b( left leg | image) b( right leg | image) Belief Propagation Example b( head | image) b( torso | image)

  6. mhead→torso(torso) mL.arm→torso mR.arm→torso mL.leg→torso mR.leg→torso Belief Propagation Example b( head | image) b( torso | image)

  7. Belief Propagation Example b( head | image) b( left arm | image) b( right arm | image) b( torso | image) b( left leg | image) b( right leg | image)

  8. What if the Graph has Thousands of Parts? • In a graph with N parts and E edges • BP running time and memory requirements O(E) • Skeleton graph typically sparse – O(N) edges • Occupancy graph fully connected – O(N2) edges • In very large graphs, O(N2) runtime intractable • AggBP (our system) approximates O(N2) occupancy messages using O(N) messages

  9. Message Approximation Illustrated 1 5 5 7 8 3 3 4 2 6 6

  10. Message Approximation Illustrated 1 5 7 8 3 4 2 6 Accumulator

  11. GLY9 ARG8 GLU11 ARG10 ILE7 ARG12 GLU14 PHE13 GLN6 MET15 PHE16 LEU5 ARG17 GLU18 THR4 LEU19 ASN20 PHE3 ALA22 GLU21 LEU23 TYR2 GLU24 LEU25 GLU1 LYS26 ASP27 GLN29 ALA28 GLY31 ALA30 Experiment I: Density Map Interpretation GLU TYR PHE THR LEU GLN ILE ARG GLY ARG GLU ARG PHE …

  12. LoopyBP vs. AggBP:Runtime 30 25 20 LoopyBP Normalized Runtime 15 10 AggBP 5 0 15 25 35 45 55 65 75 85 95 Number of Parts

  13. 10 8 6 RMS Error 4 LoopyBP 2 AggBP 0 0 5 10 15 20 BP iteration LoopyBP vs. AggBP: Accuracy

  14. allow spatial overlap increase branching factor vary radii Experiment II: Synthetic Graph Generator [skeleton graph]

  15. LoopyBP vs. AggBP:Accuracy 6 AggBP 4 RMS Error LoopyBP 2 0 0 2 4 stdev(part size) 0 1 2 5

  16. Conclusions • AggBP makes belief propagation tractable in large, highly connected graphs • For part-based modeling, runtime and storage is reduced from O(N2) to O(N) • AggBP’s solutions on two datasets are as good as standard BP’s in less time

  17. Acknowledgements • Dr. George Phillips • NLM Grant 1R01 LM008796 • NLM Grant 1T15 LM007359

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