Sampling for Part Based
Object Models
Daniel Huttenlocher
September, 2006
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
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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
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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
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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
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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
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Sampling Example for Tree [FH05]
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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
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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
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Detection Results
 Single class detection (equal ROC error)
– MAP of factored model vs. sampling from
factored model
– Significant at 95% confidence level except bikes
Airplanes
Cars (rear)
Faces
Motorbikes
MAP
94.3%
(hill climb)
94.4%
98.0%
98.6%
Sample
94.8%
95.0%
98.4%
98.8%
CFH05
FPZ05
93.0%
93.6%
90.3%
84.2%
96.4%
90.3%
93.3%
97.3%
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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
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