# The termination threshold used in step 5 is derived

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Unformatted text preview: constraining the vectors representing y0 and y1 to be within the same pixel in image coordinates. The tracking consists in running for each frame the optimization algorithm described above. Thus, given the target model, the new location of the target in the current frame minimizes the distance (18) in the neighborhood of the previous location estimate. e cient (17) is approximated as (after some manipulations) s m m qu ^ 1 X pp (^ )^ + 1 X p (y) ^^ ^u y0 qu 2 ^u p(y) q] 2 pu (^ 0 ) ^y u=1 u=1 (23) where it is assumed that the target candidate fpu (y)gu=1:::m does not change drastically from the ^ initial fpu (^ 0 )gu=1:::m , and that pu (^ 0 ) > 0 for all ^y ^y u = 1 : : : m. Introducing now (21) in (23) we obtain! nh m 2 Xp X ^^1 pu (^ 0 )^u + Ch wi k y ; xi ^yq 2 p(y) q] 2 h u=1 i=1 (24) s m where X qu : ^ wi = b(xi ) ; u] p (^ ) (25) ^y u0 u=1 Thus, to minimize the distance (18), the second term in equation (24) has to be maximized, the rst term being independent of y. The second term represents the density estimate computed with kernel pro le k at y in the current frame, with the data being weighted by wi (25). The maximization can be e ciently achieved based on the mean shift iterations, using the following algorithm. ^^ Bhattacharyya Coe cient p(y) q] Maximization Given the distribution fqu gu=1:::m of the target model ^ ^ and the estimated location y0 of the target in the previous frame: 1. Initialize the location of the target in the cur^ rent frame with y0 , compute the distribution fpu (^ 0 )gu=1:::m , and evaluate ^y p ^y ^ ^yq p(^ 0) q] = Pm=1 pu(^ 0 )^u : u 4.3 Scale Adaptation The scale adaptation scheme exploits the property of the distance (18) to be invariant to changes in the object scale. We simply modify the radius h of the kernel pro le with a certain fraction (we used 10%), let the tracking algorithm to converge again, and choose the radius yielding the largest decrease in the distance (18). An IIR lter is used to derive the new radius based on the cu...
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## This note was uploaded on 11/27/2011 for the course MATH 3484 taught by Professor Staff during the Fall '10 term at University of Central Florida.

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