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Michael Isard and Andrew Blake, IJCV 1998 Presented by Wen Li Department of Computer Science & Engineering Texas A&M University
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Problem Description Previous Methods CONDENSATION Experiment Conclusion
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What’s the task Track outlines and features of foreground objects Video frame-rate Visual clutter
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Challenges Elements in background clutter may mimic parts of foreground features Efficiency
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Directed matching Geometric model of object + motion model Kalman Filter
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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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Assumption Gaussian prior Markov assumption
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Essential Technique Bayes filter Limitation Gaussian distribution Does not work well in “clutter” background
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Stochastic framework + Random sampling Difference with Kalman Filter Kalman Filter – Gaussian densities Condensation – General situation
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Symbols + goal Assumptions Modelling Dynamic model Observation model Factored sampling CONDENSATION algorithm
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Symbols x t – the state of object at time t X t – the history of x t, {x 1,…, x t } z t – the set of image features at time t Z t – the history of z t, {z 1,…, z t } Goal Calculate the model of x at time t, given the history of the measurements. -- P(x t | Z t )
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Assumptions Markov assumption ▪ The new state is conditioned directly only on the immediately preceding state ▪ P(x t | X t-1 )=p(x t |x t-1 ) z t -- Independence (mutually and with respect to the dynamical process) ▪ P( Z t | X t )=∏ p(z i |x i ) ▪ P(z i |x i ) = p(z|x)
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Dynamic model P(x t |x t-1 ) Observation model
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Propagation – applying Bayes rules Cannot be evaluated in closed form
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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 π i 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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Factored Sampling -- illustration
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The CONDENSATION algorithm – finally! Initialize p(x 0 ) For any time t ▪ Predict: select a sample set {s’ t (1),…, s’ t (N) } from old sample set {s t- 1 (1),…, s t-1 (N) } according to π t-1 (n) predict a new sample-set {s t (1),…, s t (N) } from {s’ t (1),…, s’ t (N) }, using the dynamic model we mentioned previously ▪ Measure: calculate weights π i according to observed features, then calculate mean position of x t as in the single image
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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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On Rapid Motions Through Clutter
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On Articulated Object
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On Camouflaged Object
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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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Problems might be Initialization “hand-drawn” shape-space
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