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Pyramidal Implementation of Lucas Kanade Feature Tracker

Pyramidal Implementation of Lucas Kanade Feature Tracker. Jia Huang Xiaoyan Liu Han Xin Yizhen Tan. Abstract. Introduction Tracking algorithm Lucas-Kanade algorithm Iterative implementation Tracking features analysis Feature lost Feature selection. Objective.

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Pyramidal Implementation of Lucas Kanade Feature Tracker

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  1. Pyramidal Implementation of Lucas Kanade Feature Tracker Jia Huang Xiaoyan Liu Han Xin Yizhen Tan

  2. Abstract • Introduction • Tracking algorithm • Lucas-Kanade algorithm • Iterative implementation • Tracking features analysis • Feature lost • Feature selection

  3. Objective • For a given point u in image A, find its corresponding location v = u + d in image B. d Image B Image A

  4. Residual function and Window size To find the location  Minimize residual function: : Integration window size Nature tradeoff: Small integration window Higher accuracy Larger integration window Higher robustness

  5. Pyramid Implementation of LK algorithm • Calculate a set of pyramid representations of original image • Apply traditional tracking algorithm for each level • Results of current iteration is propagated to next iteration • Key point: the same window size is used for each level Top View Side View

  6. Lucas-Kanade algorithm(1) • At the level L, we define images A and B:

  7. Lucas-Kanade algorithm(2) • At the optimum, the first derivative of • After first order Taylor expansion • Components in the equation above

  8. Lucas-Kanade algorithm(3) Two derivative images are expressed: With these notation, we can get: The optimum optical flow vector is

  9. Pyramidal diagram Inner loop: K-level K initialized to 1, assume that the previous computations from iterations 1,2,...,k-1 provide an initial guess The new translated image according to Iterative scheme of LK algorithm(1)

  10. Iterative scheme of LK algorithm(2) • The goal: to compute the residual pixel motion vector , that minimizes the error function • Image mismatch vector , where the image difference delta I k defined as: • New pixel displacement guess is computed for the next iteration step k+1:

  11. Iterative scheme of LK algorithm(3) • On average, 5 iterations are enough • At the 1st iteration (k=1), the initial guess is set to zero • The final solution for the optical flow vector is • Outer loop: L-level • The vector d is propagated to the next level L-1 and overall procedure is repeated L-1, L-2, …, 0

  12. Declaring a Feature Lost • Several cases of lost feature • the point falls outside of the image • image patch around the tracked point varies too much between image A and image B • too large displacement • How to solve it • combine a traditional tracking approach with an affine image matching

  13. Feature Lost Example(1) Image A Image B

  14. Feature Lost Example(2) Image A Image B

  15. Feature Selection • Intuitive To select the point u on image A good to track. • Process steps: • Compute the G matrix and λm • Call λmax the maximum value of λm • Retain the pixels that have a λm value larger than a percentage of λmax • Retain the local max. pixels • Keep the subset of those pixels so that the minimum distance between pixels is larger than a threshold

  16. Example of LK Feature Tracking Image A Image B

  17. More Examples Image A Image B

  18. Summary • Lucas-Kanade Feature Tracker is one of the most popular versions of two-frame differential methods for motion estimation • Iterative implementation of the Lucas-Kanade optical flow computation provides sufficient local tracking accuracy.

  19. Thanks for your attention Any question?

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