A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION
•Descargar como PPTX, PDF•
2 recomendaciones•1,361 vistas
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
Recomendados
Recomendados
Más contenido relacionado
Similar a A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION
Similar a A FRIENDLY APPROACH TO PARTICLE FILTERS IN COMPUTER VISION (20)
Último
Último (20)
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/