CS223B-L11-Tracking

CS223B-L11-Tracking - Stanford CS223B Computer Vision,...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Stanford CS223B Computer Vision, Winter 2008/09 Lecture 11 Tracking Motion Professor Sebastian Thrun CAs: Ethan Dreyfuss, Young Min Kim, Alex Teichman
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Overview The Tracking Problem Bayes Filters Particle Filters Kalman Filters Using Kalman Filters
Background image of page 2
Sebastian Thrun CS223B Computer Vision, Winter 2009 The Tracking Problem Can we estimate the position of the object? Can we estimate its velocity? Can we predict future positions? Image 4 Image 1 Image 2 Image 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 The Tracking Problem Given Sequence of Images Find center of moving object Camera might be moving or stationary We assume: We can find object in individual images. The Problem: Track across multiple images. Is a fundamental problem in computer vision
Background image of page 4
Sebastian Thrun CS223B Computer Vision, Winter 2009 Rao-Blackwellized Particle Filter Methods Bayes Filter Particle Filter Uncented Kalman Filter Kalman Filter Extended Kalman Filter
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Further Reading…
Background image of page 6
Sebastian Thrun CS223B Computer Vision, Winter 2009 Example: Moving Object
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Kalman Filter Tracking
Background image of page 8
Sebastian Thrun CS223B Computer Vision, Winter 2009 Particle Filter Tracking
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Mixture of KF / PF (Unscented PF)
Background image of page 10
Sebastian Thrun CS223B Computer Vision, Winter 2009 Overview The Tracking Problem Bayes Filters Particle Filters Kalman Filters Using Kalman Filters
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Example of Bayesian Inference ? Environment prior p(staircase) = 0.1 Bayesian inference p(staircase | image) p(image | staircase) p(staircase) p(im | stair) p(stair) + p(im | no stair) p(no stair) = 0.7 0.1 / (0.7 0.1 + 0.2 0.9) = 0.28 Sensor model p(image | staircase) = 0.7 p(image | no staircase) = 0.2 p(staircase) = 0.28 Cost model cost(fast walk | staircase) = $1,000 cost(fast walk | no staircase) = $0 cost(slow+sense) = $1 Decision Theory E[cost(fast walk)] = $1,000 0.28 = $280 E[cost(slow+sense)] = $1 =
Background image of page 12
Sebastian Thrun CS223B Computer Vision, Winter 2009 Bayes Filter Definition Environment state x t Measurement z t Can we calculate p ( x t | z 1 , z 2 , …, z t ) ?
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 Bayes Filters Illustrated
Background image of page 14
Sebastian Thrun CS223B Computer Vision, Winter 2009 Bayes Filters: Essential Steps Belief: Bel( x t ) Measurement update: Bel( x t ) Bel( x t ) p( z t | x t ) Time update: Bel( x t +1 ) Bel( x t ) p(x t +1 |u t ,x t )
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sebastian Thrun CS223B Computer Vision, Winter 2009 x = state t = time z = observation u = action η = constant Bayes Filters ) , | ( ) ( 0 0 t t t t u z x p x Bel = ) , , , | ( ) , , , , | ( 0 1 1 0 1 1 z z u x p z z u x z p t t t t t t t - - - - = ) , , , | ( ) | ( 0 1 1 z z u x p x z p t t t t t - - = 1 0 1 1 0 1 1 ) , , | ( ) , , , | ( ) | ( - - - - - = t t t t t t t t dx z u x p z u x x p x z p 1 1 1 1 ) ( ) , | ( ) | ( - - - - = t t t t t t t dx x Bel u x x p x z p ) , , , , | ( 0 1 1 u z u z x p t t t t - - = Markov Bayes Markov 1 0 2 1 1 1 1 ) , , | ( ) , | ( ) | ( - - - - - - = t t t t t t t t t dx u u z x p u x x p x z p
Background image of page 16
Sebastian Thrun CS223B Computer Vision, Winter 2009 Bayes Filters x = state t
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 74

CS223B-L11-Tracking - Stanford CS223B Computer Vision,...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online