Object Tracking over Multiple Uncalibrated Cameras Using Visual, Spatial and Temporal Similarities - Advanced Concepts for Intelligent Vision Systems - page 170

σ x 1 σ y 1
σ y 1 cos 2 θ + σ x 1 sin 2 θ

σ x 2 σ y 2
σ y 2 cos 2 θ + σ x 2 sin 2 θ

σ 1 = 2 = , . (2)

where σ x 1 and σ y 1 , are the standard deviations of the potential new kernel in
the x and y directions respectively, and σ x 2 and σ y 2 are the standard deviations
similarly of the existing kernel. Finally, these values are used to compute a
similarity score s ,givenby,

d 2
1 . 5min( σ 1 ,σ 2 ) ) .

s =max(0 , 1 − (3)

When determining the similarity score, we wish to consider not only the separa-
tion of the centres of the kernels, but also their respective spreads. The sizes and
shapes of the distributions affect the similarity score, as well as the locations
of their centres. The existing kernel with the largest similarity score is used as
the kernel of the tracked object in the local camera if the squared distance, d 2 ,
is less than an empirically determined threshold, e.g. min( σ 1 ,σ 2 )
6

.Otherwise,the

new kernel is constructed and used.

Linking kernels using the signature-based kernel matching method.
After constructing and disseminating the local track snapshot and receiving for-
eign track snapshots to and from other cameras respectively, links between the
local kernel and kernels in foreign cameras are determined using a signature-
based kernel matching method. This is performed as follows.
For each stored foreign track snapshot, the visual distance is found between
the signature in the local track snapshot and the signature in the foreign track
snapshot. In order to calculate this, first the signature in the local track snapshot
is rescaled using a lighting compensation method. The histogram bin boundaries
of the signature are linearly scaled by the ratio of the average luminance of the
foreign signature to the average luminance of the local signature. Following this,
using the distance metric defined on the signature, the visual distance between
the brightness rescaled signature in the local track snapshot and the signature in
the foreign track snapshot, d s , is calculated. If the visual distance is greater than
the maximum signature distance, d s max , then no further processing is performed
for that foreign track snapshot. Otherwise, the signature weight w s is calculated:
w s = d s max −

d s if d s d s max .

≤ (4)

The signature weight is then used to initialise or strengthen a linked pair of
kernels between the local kernel and the kernel in the foreign track snapshot. If
a link between these two kernels does not exist yet, one is created with a kernel
link weight , w k , equal to the signature weight, i.e.,
w init = w s .

(5)

Otherwise, if a linked pair of kernels already exists between these two kernels,
its kernel link weight is incremented as follows,
w new = w old + w s . (6)