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4 Cumulative Brightness Transfer Function
The main aim of this procedure is to relate all color distributions to a refer one,
previously selected. So, after this step, players of the same class should have the
same appearance, independently from the acquisition camera settings, and from
the color content of the image. We evaluated the histograms in the RGB channels
for all the segmented images of each of the N cameras. The histograms were gen-
erated by using 64 bins for each channel. We wanted to estimate BTFs between
the reference camera and the others N
1. We propose the generic algorithm
relative to two different cameras and FOVs and we use it between each cameras
and the reference one. For each couple of images from different FOVs( i 1 ,j 2 )we
want to estimate a BTF f 1 , 2 such that, for each couple of images ( i 1 ,j 2 ), given
the brightness values B i 1 ( k )and B j 2 ( k )wehave B j 2 ( k )= f 1 , 2 ( B i 1 ( k )) where
k =0 , .., 63 represents the number of bins, i 1 =1 , .., M represents the number of
images in the camera, j 2 =1 , .., N the number of images in the reference cam-
era. For each possible couple of histograms ( i 1 ,j 2 ) we evaluated the brightness
transfer function
f i 1 j 2 ( B i 1 ( k )) = B j 2 ( k )
(1)
using the inverted cumulative histogram, that is
f i 1 j 2 ( B i 1 ( k )) = H 1
( H i 1 ( B i 1 ( k )))
(2)
j 2
Using this concept we evaluate the cumulative BTF (CBTF) proposed in [7].
The generation of the CBTF involves an amalgamation of the training set before
computing any BTFs. An accumulation of the brightness values is computed on
all the training images of the generic camera obtaining a cumulative histogram
H 1 . The same is done for all the corresponding training images of the reference
camera obtaining
H 2 . The CBTF
f 1 , 2 is
H 2 1 ( H 1 ( B 1 ( k )))
f 1 , 2 ( B 1 ( k )) =
(3)
also in this case evaluated by using the inverted cumulative histogram. Notice
that the same algorithm could be implemented starting from different part of
the same FOV in order to smooth different color appearance due to different
illuminations (play field with shadow and non uniform brightness).
5 Classification Algorithms
In our experiments we have implemented and tested three methodologies, belong-
ing to different categories, to perform an unsupervised classification of players in
five different classes (two teams, two goalkeepers, and ocials): MBSAS (sequen-
tial algorithm), BCLS (competitive algorithm) and K-means (hard-clustering al-
gorithm). We remain the reader to [9] for a detailed explanation of them. The
algorithms need the definition of a proximity measure d ( x, C ), a threshold of
similarity th and the maximum number of clusters q . Euclidean distance has
been used for similarity evaluations, while the maximum number of cluster has
 
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