Tracking H akan Ard o March 4, 2013 H akan Ard o Tracking - PowerPoint PPT Presentation

Introduction Tracking with static camera Tracking with moving camera Tracking H˚ akan Ard¨ o March 4, 2013 H˚ akan Ard¨ o Tracking March 4, 2013 1 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection Outline Introduction 1 State space Sliding Window Detection Tracking with static camera 2 Greedy Kalman filter Particle filter Tracking with moving camera 3 Self-motion H˚ akan Ard¨ o Tracking March 4, 2013 2 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection State space State: position X = ( X , Y , Z , 1), velocity, v = ( v x , v y , v z , 0), ... Observation: detection in image x = ( x , y , 1) Observation model: λ x = PX Dynamic model: X t +1 = X t + v t and v t +1 = v t Sthocastic dynamic model: Introduce noise, random numbers q and w X t +1 = X t + v t + q v t +1 = v t + w Sthocastic observation model: Introduce noise, a random number r λ x = P X + r H˚ akan Ard¨ o Tracking March 4, 2013 3 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection Sliding window detectors H˚ akan Ard¨ o Tracking March 4, 2013 4 / 57

Introduction Tracking with static camera Tracking with moving camera State space Sliding Window Detection Detection probability H˚ akan Ard¨ o Tracking March 4, 2013 5 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Greedy tracker H˚ akan Ard¨ o Tracking March 4, 2013 6 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter STC Lecture Series An Introduction to the Kalman Filter Greg Welch and Gary Bishop University of North Carolina at Chapel Hill Department of Computer Science http://www.cs.unc.edu/~welch/kalmanLinks.html UNC Chapel Hill Computer Science Slide 1 H˚ akan Ard¨ o Tracking March 4, 2013 7 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter HUMAN AND SYSTEMS ENGINEERING: Gentle Introduction to Particle Filtering Sanjay Patil 1 and Ryan Irwin 2 Graduate research assistant 1 , REU undergrad 2 Human and Systems Engineering URL: www.isip.msstate.edu/publications/seminars/msstate/2005/particle/ H˚ akan Ard¨ o Tracking March 4, 2013 8 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Some Intuition UNC Chapel Hill Computer Science Slide 5 H˚ akan Ard¨ o Tracking March 4, 2013 9 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter First Estimate Conditional Density Function z 1 σ 2 , z 1 1 = z 1 x ˆ N( z 1 , σ z 1 2 ) σ 1 = σ 2 2 ˆ z 1 -2 0 2 4 6 8 10 12 14 UNC Chapel Hill Computer Science Slide 6 H˚ akan Ard¨ o Tracking March 4, 2013 10 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Second Estimate Conditional Density Function z 2 σ 2 , z 2 2 ) N( z 2 , σ z 2 2 = ...? x ˆ σ 2 = ...? 2 ˆ -2 0 2 4 6 8 10 12 14 UNC Chapel Hill Computer Science Slide 7 H˚ akan Ard¨ o Tracking March 4, 2013 11 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Combine Estimates [ ] z 1 + σ z 1 [ ] z 2 ( 2 + σ z 2 ) ( 2 + σ z 2 ) = σ z 2 σ z 1 σ z 1 x ˆ 2 2 2 2 2 [ ] = ˆ 1 + K 2 z 2 − ˆ x x 1 where ( 2 + σ z 2 ) K 2 = σ z 1 σ z 1 2 2 UNC Chapel Hill Computer Science Slide 8 H˚ akan Ard¨ o Tracking March 4, 2013 12 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Combine Variances 1 σ 2 = 1 σ z 1 ( ) + 1 σ z 2 ( ) 2 2 2 UNC Chapel Hill Computer Science Slide 9 H˚ akan Ard¨ o Tracking March 4, 2013 13 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Combined Estimate Density Conditional Density Function ˆ σ 2 ) x, ˆ N( x = ˆ x ˆ 2 2 = σ 2 σ ˆ 2 -2 0 2 4 6 8 10 12 14 UNC Chapel Hill Computer Science Slide 10 H˚ akan Ard¨ o Tracking March 4, 2013 14 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Add Dynamics dx / dt = v + w where v is the nominal velocity w is a noise term (uncertainty) UNC Chapel Hill Computer Science Slide 11 H˚ akan Ard¨ o Tracking March 4, 2013 15 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering algorithm step-by-step (1) Particle Filtering – Gentle Introduction and Implementation Demo Page 7 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 16 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering step-by-step (2) Particle Filtering – Gentle Introduction and Implementation Demo Page 8 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 17 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering step-by-step (3) Particle Filtering – Gentle Introduction and Implementation Demo Page 9 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 18 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering step-by-step (4) Particle Filtering – Gentle Introduction and Implementation Demo Page 10 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 19 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering step-by-step (5) Particle Filtering – Gentle Introduction and Implementation Demo Page 11 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 20 / 57

Introduction Tracking with static camera Tracking with moving camera Greedy Kalman filter Particle filter Particle filtering step-by-step (6) Particle Filtering – Gentle Introduction and Implementation Demo Page 12 of 20 H˚ akan Ard¨ o Tracking March 4, 2013 21 / 57