CONDENSATION – Conditional Density Propagation for Visual Tracking
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CONDENSATION – Conditional Density
Propagation for Visual Tracking
Michael Isard and Andrew Blake, IJCV 1998
Presented by Wen LiDepartment of Computer Science & Engineering
Texas A&M University
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Outline
Problem Description Previous Methods CONDENSATION Experiment Conclusion
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Problem Description
What’s the task Track outlines and features of foreground
objects Video frame-rate Visual clutter
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Problem Description
Challenges Elements in background clutter may
mimic parts of foreground features Efficiency
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Previous Methods
Directed matching Geometric model of object + motion model
Kalman Filter
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Kalman Filter
Main Idea Model the object Prediction – predict where the object
would be Measurement – observe features that
imply where the object is Update – Combine measurement and
prediction to update the object model
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Kalman Filter
Assumption Gaussian prior
Markov assumption
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Kalman Filter
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Kalman Filter
Essential Technique Bayes filter
Limitation Gaussian distribution Does not work well in “clutter”
background
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CONDENSATION
Stochastic framework + Random sampling
Difference with Kalman Filter Kalman Filter – Gaussian densities Condensation – General situation
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CONDENSATION
Symbols + goal Assumptions Modelling
Dynamic model Observation model
Factored sampling CONDENSATION algorithm
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CONDENSATION
Symbols xt – the state of object at time t Xt – the history of xt, {x1,…, xt} zt – the set of image features at time t Zt – the history of zt, {z1,…, zt}
Goal Calculate the model of x at time t, given
the history of the measurements. -- P(xt |Zt)
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CONDENSATION
Assumptions Markov assumption▪ The new state is conditioned directly only on
the immediately preceding state▪ P(xt|Xt-1)=p(xt|xt-1)
zt -- Independence (mutually and with respect to the dynamical process)▪ P(Zt |Xt)=∏ p(zi|xi)▪ P(zi|xi) = p(z|x)
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CONDENSATION
Dynamic model P(xt|xt-1)
Observation model
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CONDENSATION
Propagation – applying Bayes rules
Cannot be evaluated in closed form
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CONDENSATION
Factored Sampling Approximate the probability density p(x|
z) In single image Step 1: generate a sample set {s(1),…,
s(N)} Step 2: calculate the weight πi
corresponding to each s(i), using p(z | s(i)) and normalization
Step 3: calculate the mean position of x, that
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CONDENSATION
Factored Sampling -- illustration
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CONDENSATION The CONDENSATION algorithm – finally!
Initialize p(x0) For any time t▪ Predict:
select a sample set {s’t(1),…, s’t
(N)} from old sample set {st-1
(1),…, st-1(N)} according to π t-1
(n)
predict a new sample-set {st(1),…, st
(N)} from {s’t(1),…,
s’t(N)}, using the dynamic model we mentioned previously
▪ Measure:calculate weights πi according to observed features, then calculate mean position of xt as in the single image
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CONDENSATION
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Experiment
On Multi-Model Distribution
The shape-space for tracking is built from a hand-drawn template of head and shoulder
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N=1000, frame rate=40 ms
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Experiment
On Rapid Motions Through Clutter
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Experiment
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Experiment
On Articulated Object
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Experiment
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Experiment
On Camouflaged Object
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Conclusion
Good news: Works on general distributions Deals with Multi-model Robust to background clutter Computational efficient Controllable of performance by sample
size N Not too difficult
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Conclusion
Problems might be Initialization “hand-drawn” shape-space