Transferring information using Bayesian priors on object categories Li Fei-Fei 1, Rob Fergus 2,...
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Transcript of Transferring information using Bayesian priors on object categories Li Fei-Fei 1, Rob Fergus 2,...
Constellation model of Constellation model of object categoriesobject categories
Fischler & Elschlager 1973 Yuille ‘91Brunelli & Poggio ’93 Lades, v.d. Malsburg et al. ‘93Cootes, Lanitis, Taylor et al. ’95 Amit & Geman ‘95, ’99Perona et al. ‘95, ‘96, ’98, ’00, ’03 Many more recent works…
X (location)
(x,y) coords. of region center
A (appearance)
Projection ontoPCA basis
c1
c2
c10
…..
normalize
11x11 patch
X (location)
(x,y) coords. of region center
A (appearance)
Projection ontoPCA basis
c1
c2
c10
…..
normalize
11x11 patchX A
h
XX
I
AA
The Generative Model
Hypothesis (h) node
X A
h
XX
I
AA
h is a mapping from interest regions to parts
3
5
91
2
46
7 10
8
e.g. hi = [3, 5, 9]
X A
h
XX
I
AA
h is a mapping from interest regions to parts
3
5
91
2
46
7 10
8
e.g. hj = [2, 4, 8]
The hypothesis (h) node
The appearance node
PCA coefficients on fixed basis
Pt 1. (c1, c2, c3,…)
Pt 2. (c1, c2, c3,…)
Pt 3. (c1, c2, c3,…)
X A
h
I
AAXX
X A
h
I
Appearance parameter node
Gaussian
Independence assumed between the P parts
P
Fixed PCA basis
XX AA
X A
h
I
P
Maximum Likelihood interpretation
observed variables
hidden variable
parametersXX AA
Also have background model – constant for given image
X A
h
I
PXX AA
a0X
B0X
m0X
β0X
a0A
B0A
m0A
β0A
MAP solutionChoose conjugate form:
Normal – Wishart distributions:
P(, ) = p(|)p() = N(|m, β ) W(|a,B)
observed variables
hidden variable
parameters
Introduce priors over parameters
priors
X A
h
I
PXX AA
a0X
B0X
m0X
β0X
a0A
B0A
m0A
β0A
Variational Bayesian model
observed variables
hidden variable
parameters
Estimate posterior distribution on parameters – approximate with Normal – Wishart-- has parameters: {mX, βX, aX, BX, m A, βA, aA, BA}
priors
ML/MAP LearningML/MAP Learning
n
1
2
where = {µX, X, µA, A}
ML/MAP
Weber et al. ’98 ’00, Fergus et al. ’03
X A
h
I
PAAXX
Performed by EM
Bayesian
Variational LearningVariational Learning
n
1
2
Parameters to estimate: {mX, βX, aX, BX, mA, βA, aA, BA}i.e. parameters of Normal-Wishart distributionFei-Fei et al. ’03, ‘04
X A
h
I
PXX AA
a0X
B0X
m0X
β0X
a0A
B0A
m0A
β0A
Performed by Variational Bayesian EM
E-Step
Random initializationVariational EMVariational EM
prior knowledge of p()
new estimate of p(|train)
M-Step
new ’s
(Attias, Hinton, Beal, etc.)
ExperimentsExperimentsTraining:
1- 6 images
(randomly drawn)
Detection test:
Datasets: foreground and background
The Caltech-101 Object Categories
www.vision.caltech.edu/feifeili/Datasets.htm
50 fg/ 50 bg images
object present/absent
The prior
• Captures commonality between different classes
• Crucial when training from few images
• Constructed by:– Learning lots of ML models from other classes– Each model is a point in θ space– Fit Norm-Wishart distribution to these points using moment
matching i.e. estimate {m0X, β0
X, a0X, B0
X, m0A, β0
A, a0A, B0
A}
What priors tell us? – 1. meansAppearanc
e
likely unlikely
Shape
What priors tell us? – 2. variability
Renoir
Picasso, 1951
Picasso, 1936
Miro, 1949
Warhol, 1967
Magritte, 1928
Arcimboldo, 1590
Da Vinci, 1507
likely
un
likely
Appearance Shape
Conclusions
• Hierarchical Bayesian parts and structure model
• Learning and recognition of new classes assisted by transferring information from unrelated object classes
• Variational Bayes superior to MAP