1. Visual Tracking: Case Study CMPUT 615 Nilanjan Ray

2. KF: Quick Review System equations: State update equations: Measurement equations: Kalman gain matrix:

3. Alpha-Beta KF The system equations become: Here, actually we have two such system equations. One for the x-direction and the other for the y-direction. Note that this is a constant velocity motion model; the acceleration is a zero mean Gaussian noise here

4. Alpha-Beta KF: State Update Equations Two state update equations become:

5. Alpha-Beta KF: Measurement Equations Measurement equations: Kalman gain matrix: alpha beta

6. Measurements? Centroid measurement x-direction y-direction

7. Measurements… Template matching by normalized cross-correlation where, mean intensity: where, mean template intensity:

8. How Do We Obtain Noise Parameters? For estimating q one needs to observe a few object locations, track them manually and fit a Gaussian model by MLE to find out q For estimating r, training sequence is usually of little use. If one assumes sub-pixel accuracy for the measurement, then r = 1/sqrt(3) can be taken.

9. How Do We Initiate KF? Do we remember the first model assumption of SDE? –The distribution of p(x 0 ) is known This means we know x 0|0 and P 0|0 Typically P 0|0 is assumed a diagonal matrix

10. Visual Results Tracking leukocytes with alpha-beta KF along with centroid measurement