Image Processing Reference
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image at hand and thus independently from what previously seen. The extracted features at
diferent scales by rough fuzzy sets are clustered from an unsupervised NN by minimizing
the fuzziness of the output layer. The new method, named multiscale rough neural network
(MS-RNN), was designed to detect frontal faces in color images and to be not sensitive to vari-
ations of scene conditions, such as the presence of a complex background and uncontrolled
illumination. The proposed face-detection method has been applied to real-time face tracking
using Kalman filtering algorithm [ 22 ] , this filter is used to predict the next face-detection win-
dow and smooth the tracking trajectory. The article is structured as follows. In Section 2 , we
explain the basic theories behind the proposed method, i.e., rough sets, fuzzy sets, and their
synergy. Section 3 describes the face-detection method and illustrates how these theories are
applied to the process of digital images relative to the proposed method, which is speciically
described in Sections 4 and 5 . Section 6 introduces the proposed face-tracking method. Section
7 reports the results obtained using the proposed method, through an extensive set of exper-
iments on CMU-PIE [ 23 ] , color FERET [ 24 , 25 ] , IMM [ 26 ] , and CalTech [ 27 ] face databases; in
addition, the effectiveness of the proposed model is shown when applied to the face-tracking
problem on a database of YouTube video and the standard IIT-NRC [ 28 ] facial video database,
comparing them with the recent results on the same topic. Lastly, some concluding remarks
are presented in Section 8 .
2 Theoretical background
Let X = { x 1 , …, x n } be a set and
an equivalence relation on X , i.e.,
is reflexive, symmet-
ric, and transitive. As usual, X / denotes the quotient set of equivalence classes, which form
a partition in X , i.e., x y means the x and y cannot be took apart. The notion of rough set [ 19 ]
borns to answer the question of how a subset T of X can be represented by means of X /
. It
consists of two sets:
where [ x ]
denotes the class of elements x , y X such that x
y and RS ( T ) and RS ( T ) are,
respectively, the upper and lower approximation of T by
, i.e.,
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