Multi-object Tracking Using Particle Swarm Optimization on Target Interactions - Advances in Heuristic Signal Processing and Applications - page 66

Fig. 4.1 PSO based tracking using multi-patch object representation. Frames #431, 441, 453, 455,
460, 461, and the probability image of the target in frame #431

The distance between two symmetric positive definite matrices X and Y under the
Log-Euclidean Riemannian metric can be expressed as follows:

= log (X) log (Y) 2 .

dist (X,Y) − (4.5)

The Riemannian mean of several elements is an arithmetic mean of matrix elements.
Using the Log-Euclidean metric, the algorithm [ 25 ] for the incremental subspace
update can be employed directly.
In object tracking, we should seek in each frame a location for which the covari-
ance matrix within the object template is most similar to the covariance matrix of the
model template. Hence, we should find an object location x ∗ for which the distance
dist ( ) between the corresponding covariance matrix X and model covariance ma-

trix X assumes the minimal value, i.e., we have to minimize

· , ·

x ∗ = arg min

x

dist (X x ,X). (4.6)

This is a nonlinear optimization problem that is solved using the PSO algorithm,
which in each frame seeks for the best match.
Figure 4.1 depicts some tracking results that were obtained using the multi-patch
object representation and a PSO consisting of 10 particles and executing 10 itera-
tions. The tracking of a woman's face was done on color images of size 128 96. 1

We employed both horizontal and vertical patches. The horizontal patches were con-
structed through dividing vertically the object template into two adjoining patches.
Then such patches were divided into 10 horizontally oriented patches, in fives in
each of the two vertically oriented patches. The vertical patches were created anal-
ogously. The right most image depicts the probability image of the target in frame
#431. The detection of outliers is achieved through sorting the scores of the patches
and then omitting the poorest ones. The fitness function f g (x) is the average of K
such best matches between the patches of the template at the location x ∗ and the
corresponding patches of the model template.
A tracking algorithm built on the covariance score and with multi-patch object
representation can recover after substantial temporal occlusions or large movements.
Figure 4.2 illustrates some tracking results that were obtained on the image sequence
'S2L1_View_1' from PETS 2009 database [ 12 ], see also Fig. 4.3 . As we can ob-
serve, the walking woman is successfully tracked despite considerable and multiple
temporal occlusions with the static road sign and the pedestrians.

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1 Sequence obtained from http://robotics.stanford.edu/birch/headtracker .