A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION
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This is a friendly approach to particle filters. Some hints, examples, and good practices to be able to successfully apply particle filters to solve your computer vision pro
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A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION
- 1. A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION Concepts, hints and examples 1 2/2/2011 Dr.-Ing. Marcos Nieto Doncel Investigador/Researcher mnieto@vicomtech.org
- 2. Outline Motivation Bayesianframework Samplingsolution Examples 2 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 3. Motivation Forwhat? Obtainestimates of a recursive/dynamicsystem Let’sstay in computervisionapplications W H (x0,y0) 3 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 4. Motivation Why? Deterministicapproach Probabilisticapproach vs 4 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 5. Motivation How? Define yourtarget Define yourfunctions Select a type of filteradaptedto 1) and 2) Implement and run Optionally: Writeyourpaper and share : ) 5 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 6. Bayesianfiltering Target: xk Itevolvesthrough time accordingtosomedynamics, properties, interaction, etc. W W H H (x0,y0) x0 y0 Prior / Dynamics / Transition… p(xk|xk-1) 6 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 7. Bayesianfiltering Observations: z1:k Noisy, distorted, indirect Typically, differentdimensionaliy Likelihood / Observationmodel / Measurements… p(zk|xk) 7 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 8. Bayesianfiltering Posterior distribution: p(xk|z1:k) Probability density function This is all you can expect to know Typicallywewant a point-estimate of thisdistribution At each time instant: x*k At theend 8 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 9. Bayesianfiltering Time K-1 K K+1 p(zk|xk): Observation model zk-1 zk zk+1 Measurements (visible) xk-1 xk xk+1 States (hidden) p(xk|xk-1): Dynamic model 9 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 10. Bayesianfiltering How? Prediction Use thedynamics, guessfutureaccordingto Correction Obtain a new observation, and applyBayes’ rule Likelihood Prediction Posterior p(xk|xk-1) 10 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 11. Particlefilters Solvethroughsampling! Letusapproximate posterior as a set of samples Samples / Particles / Hypotheses Weighted UnWeighted 11 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 12. Particlefilters Understandingparticles Eachparticlerepresents a hypothesis Remember! wewilltypicallywantjustonepoint-estimate Bestparticle, mean particle, mode, median… W W H H (x0,y0) x0 y0 12 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 13. Particlefilters Howtosample? Importancesampling MarkovChain Monte Carlo Gibbssampling Slicesampling … Howmanysamples? As much as requiredtotrackthe posterior! 13 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 14. Particlefilters Sequentialimportancesampling (SIR) 14 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 15. Particlefilters Sequentialimportancesampling (SIR) 15 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 16. SIR – example (I) Single object tracking 16 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 17. SIR – example (I) Linear-Gaussiandynamics Generate N samplesstartingfrompreviousstateaddingestimatedvelocity And someGaussiannoise Thenoisemakesthatsamples are different! 17 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 18. SIR - example (I) Likelihoodbasedonsegmentationorcolor histogram Evaluateeachpredictedsampleaccordingtothisvalue Likelihoodfunctionshouldreturnhighvaluesfor “good” hypotheses, and lowfor “bad” hypotheses 18 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 19. SIR – example (II) Eye-tracking Linear predictionwon’twork Theprojection of theeyemovementonthescreenisdifficulttopredict Define a combination of linear-Gaussian + uniform 19 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 20. 20 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 21. 21 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 23. SIR Problems Requirednumber of samplesincreaseexponentiallywithproblemdimension Severalobjects/elements? Define a multimodal posterior and generatemultiplepoint-estimates Clusterparticles Increasestate vector dimension Variable number of objects? Addexternalhandler Includethenumber of objects as another variable toestimate 23 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 24. Particlefilters MCMC More flexible Theproblem of dimensionissoftened Directlysamplefromthe posterior Researchers are focusing in MCMC Manyexcellentworksthatproposesolutionstomultipleobject, interaction, entering-exiting, number of samplesreduction, etc. 24 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 25. Particlefilters MCMC Generate a Markovchain of samplesdirectlyfromthe posterior 25 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 26. MCMC Metropolis-Hastings Startsomehow Propose a movement Acceptwithprobabilityequaltothe ratio betweenproposedvalue and previousone Prob. = 1 ifproposedisbetterthanprevious Prob. = ratio ifnot Metropolis-Hastings allowsobtainingsamplesforanarbitrarydistributionbymaking a chainwhichacceptsorrejectsmovements 26 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 27. MCMC Each sample is a hypothesis of the state of all objects Multipleobjects State vector includingallthedimensions of allobjects Metropolis-Hastings: Generate a chain of N samples Foreachsample, use theinformation of allthesamples at theprevioustime instant After the chain is completed, we have the sample-basedapproximation of the posterior 27 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 28. MCMC Marginalizedproposalmoves Proposemovement of a single dimension at each new sample E.g.don’tpropose a move in alldimensionsforallobjects Choose a dimension randomly and update it Burn-in period Stop when stationary function is reached. Or when maximum number of samples is reached. x W y … … x W H x x W L 28 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 29. MCMC Interactionbetweenobjects MarkovRandomField (MRF) factor 29 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 30. MCMC Variable number of objects Add an external detector, and modify state size Reversible-Jump MCMC Define an Enter move (creates an object) Define an Exit move (removes an object) Define an Update move (updates existing objects) 30 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 31. Discussion Whatshould I use? SIR MCMC Kalman? 31 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 32. Discussion Ifdynamics and observation are linear, and withGaussiannoise Use Kalman, thisistheoptimumsolution Ifnot, considerusing a particlefilter 32 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 33. Discussion SIR Use itif target dimensionislow (3-5) Use itifyou plan toparallelizeprocessing Rememberparticles are independentonefromanother Wouldrequireimportantdesignissuesfor Managingmultipleobjects Managing variable number of objects 33 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 34. Discussion MCMC Use itifdimensionsincrease It can notbeparallelized Rememberthatparticlesform a chain, and eachonedependsonthepreviousone Adaptedtomultipleobjects MRF interactioniseasytoinsert Metropolis-Hastings can beefficientlyadaptedtomultipleobject 34 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 35. Summary Define your target Determine itsdynamics Define thelikelihood Select a filterthatadaptstotheproblem Implementit Runitcarefullyselectingtheappropriateparameters of yourfunctions, number of particles, etc. 35 Marcos Nieto, PhD - mnieto@vicomtech.org 2/2/2011
- 36. 2/2/2011 36 Dr.-Ing. Marcos Nieto Doncel Investigador/Researcher mnieto@vicomtech.org http://marcosnieto.net/