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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
Outline
Problem Description Previous Methods CONDENSATION Experiment Conclusion
Problem Description
What’s the task Track outlines and features of foreground
objects Video frame-rate Visual clutter
Problem Description
Challenges Elements in background clutter may
mimic parts of foreground features Efficiency
Previous Methods
Directed matching Geometric model of object + motion model
Kalman Filter
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
Kalman Filter
Assumption Gaussian prior
Markov assumption
Kalman Filter
Kalman Filter
Essential Technique Bayes filter
Limitation Gaussian distribution Does not work well in “clutter”
background
CONDENSATION
Stochastic framework + Random sampling
Difference with Kalman Filter Kalman Filter – Gaussian densities Condensation – General situation
CONDENSATION
Symbols + goal Assumptions Modelling
Dynamic model Observation model
Factored sampling CONDENSATION algorithm
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)
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)
CONDENSATION
Dynamic model P(xt|xt-1)
Observation model
CONDENSATION
Propagation – applying Bayes rules
Cannot be evaluated in closed form
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
CONDENSATION
Factored Sampling -- illustration
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
CONDENSATION
Experiment
On Multi-Model Distribution
The shape-space for tracking is built from a hand-drawn template of head and shoulder
N=1000, frame rate=40 ms
Experiment
On Rapid Motions Through Clutter
Experiment
Experiment
On Articulated Object
Experiment
Experiment
On Camouflaged Object
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
Conclusion
Problems might be Initialization “hand-drawn” shape-space