Sampling for Part Based Object Models

1. Sampling for Part BasedObject Models Daniel HuttenlocherSeptember, 2006

2. Part Based Object Recognition • Matching constellation models, pictorial structures, etc. • Dominated by energy minimization approaches • Local or global methods depending on problem definition • MAP estimation view • Computationally tractable global optimization depends on models that factor • Appearance of parts independent • Spatial model with low tree width

3. State of the Art? • Model introduced error • Model overly simplistic in order to be tractable • Computationally introduced error • Model “right thing” but don’t know how computational results related • Often not explicit about these sources of error • Precise description of what want to compute and what actually computing

4. Sampling • Statistical method for using tractable (factored) models as means of estimating intractable ones • Proposal distribution • Samples from distribution using factored model evaluated according to more general one • Want “enough” probability mass distributed around in proposal distribution • “Promiscuous” – likes multiple things • E.g., smoothing a distribution (temperature) • Does more than k-best

5. More Concrete • Part based graphical model, M=(V,E) • Parts V=(v1, …, vm) • Spatial relations (undirected edges) E={eij} • For detection, consider all configurations L PM(I) ≈ maxL PM(I|L) PM(L) • Efficient when factors PM(I|L) = viV PM(I|li) PM(L) = C M(LC) • For small cliques C, e.g, 2-cliques for tree

6. A Model that Doesn’t Factor • Patchwork-of-parts (POP) model proposed by Amit and Trouve • Star model with latent reference part • Account for part overlap by averaging probabilities for parts covering an image pixel • PM(I|L) no longer factors (sum over parts) • Use likelihood that factors for proposal distribution – overcounting (promiscuous) • Sample from posterior distribution and compute POP probability for these samples • Efficiently approximating MAP estimate

7. Sampling Example for Tree [FH05]

8. Comparison with Direct Minimization • Using posterior distribution for factored model – efficient to: • Compute marginals (box sum) • Generate samples • For tree, sample location for root from marginal, then sample children conditioned on root location • Evaluate general model on samples • As opposed to trying to optimize general model directly • Using difficult to characterize techniques

9. Simple Experiments • Pictorial structure model using oriented edge part templates • Star topology • Factored appearance model for proposal distribution vs. POP model • Six parts and Caltech-4 data, for comparison with some earlier results using similar models (without POP likelihood) • CFH05, same topology and part models • FPZ05, same topology

10. Detection Results • Single class detection (equal ROC error) • MAP of factored model vs. sampling from factored model • Significant at 95% confidence level except bikes

11. Not Limited to Appearance • Sampling is a general technique for approximating intractable distributions • Even easier when using to approximate MAP of those distributions • Tractable distributions can make explicit aspects of problem structure • Over-counting of scene evidence • Importance of kinematic tree spatial constraints for humans, vs. limb coordination