Image Processing Reference

In-Depth Information

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-

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

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

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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