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CSSE463: Image Recognition Day 31

CSSE463: Image Recognition Day 31. This week Today: Intro to Kalman filtering for tracking Tomorrow: Project workday, status report due Questions?. Motion models for tracking.

dalton-morin
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CSSE463: Image Recognition Day 31

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  1. CSSE463: Image Recognition Day 31 • This week • Today: Intro to Kalman filtering for tracking • Tomorrow: Project workday, status report due • Questions?

  2. Motion models for tracking The Kalman filter is a probabilistic model that combines noisy measurements with the expected trajectory of the object. It works even with occlusion. Ideas presented here are from • http://www.cs.unc.edu/~welch/kalman/ • chapter 15.4 of Russell and Norvig, Artificial Intelligence: A Modern Approach, ed 2: Prentice Hall, 2003 • Chapter 16.6 of Sonka et al. • Kevin Murphy’s toolbox: http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html

  3. Scenarios Imagine: • Viewing a small bird flying through a forest • Tracking a missile given a blip every few seconds • Tracking planets, given intermittent observations

  4. Scenarios • Imagine: • Viewing a small bird flying through a forest • Tracking a missile given a blip every few seconds • Tracking planets, given intermittent observations • In each case: • The observations are noisy • But we can formulate an expectation about the trajectory

  5. Goal • We are trying to infer the state, X, of a dynamic system, given only noisy measurements, Z, over time Q1

  6. Example • Trajectory of a particle with acceleration due to gravity • State: • Position, velocity, and acceleration • Observations • Position only, corrupted by Gaussian noise Q2

  7. Formalism of model A linear system with Gaussian noise: and noisy measurements: Q3,4

  8. Algorithm • Give initial estimates of Iteratively: Predict Correct Q3-4

  9. Limitations • Must be a linear system • Noise must be Gaussian

  10. Applications and Extensions • Beyond just tracking and physical control…any system with continuous state variables and noisy measurements: • Economies! • Ecosystems! • To overcome linearity constraint: • Extended Kalman filters • Switching Kalman filters • Particle filters: Monte Carlo method

  11. Demos • Projectile motion (courtesy of Nathan Sickler) • Accelerometers:http://www.youtube.com/watch?v=AWAFFZ7rPDc • Tracking:http://www.youtube.com/user/rfengr (bright colors)http://www.youtube.com/watch?v=86UeUvI7pLQ (ES453: uniform ribbon)http://www.youtube.com/watch?v=U1L0X4cts8o (RC car) • Balancing robots:http://www.youtube.com/watch?v=46FswYw-m6o (inverted pendulum)http://www.youtube.com/watch?v=_TXfXoKyMzc&NR=1 (Boston Scientific’s Big Dog)

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