Unformatted text preview: paper presents a new approach to the realtime
tracking of nonrigid objects based on visual features
such as color and/or texture, whose statistical distributions characterize the object of interest. The proposed
tracking is appropriate for a large variety of objects with
di erent color/texture patterns, being robust to partial
occlusions, clutter, rotation in depth, and changes in
camera position. It is a natural application to motion
analysis of the mean shift procedure introduced earlier
6, 7]. The mean shift iterations are employed to nd
the target candidate that is the most similar to a given
target model, with the similarity being expressed by a
metric based on the Bhattacharyya coe cient. Various test sequences showed the superior tracking performance, obtained with low computational complexity.
The paper is organized as follows. Section 2 presents
and extends the mean shift property. Section 3 introduces the metric derived from the Bhattacharyya coefcient. The tracking algorithm is developed and analyzed in Section 4. Experiments and comparisons are
given in Section 5, and the discussions are in Section 6. h The minimization of the average global error between
the estimate and the true density yields the multivariate
Epanechnikov kernel 25, p.139]
1 ;1
2
2
KE (x) = 0 cd (d + 2)(1 ; kxk ) if kxk < 1
otherwise
(2)
where cd is the volume of the unit ddimensional sphere.
Another commonly used kernel is the multivariate normal
KN (x) = (2 );d=2 exp ; 1 kxk2 :
(3)
2
Let us introduce the pro le of a kernel K as a function k : 0 1) ! R such that K (x) = k(kxk2 ). For
example, according to (2) the Epanechnikov pro le is
1 ;1
2
kE (x) = 0 cd (d + 2)(1 ; x) if x < 1
otherwise (4)
and from (3) the normal pro le is given by
1
kN (x) = (2 );d=2 exp ; 2 x :
(5)
Employing the pro le notation we can write the density
estimate (1) as
n
2!
^K (x) = 1 d X k x ; xi
f
:
(6)
nh
h
i=1 We denote
g(x) = ;k0 (x)
(7)
assuming that the derivative of k exists for all x 2
0 1), except for a nite set of points. A...
View
Full Document
 Fall '10
 Staff
 Math, The Land, Nonparametric statistics, kernel, Kernel density estimation, Density estimation, Bhattacharyya coe cient

Click to edit the document details