الفهرس 
Chapter 1: IntroductionOnly 14 pages are availabe for public view
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Abstract
With the development of mathematics along decades, the
branch of quaternion mathematics has evolved as a solution to
several complex problems. Quaternion mathematics are based on
complex numbers that comprise a real part and three complex
parts. Quaternion mathematics were introduced to solve the
rotation problems of dynamic systems. This trend has come soon
to all branches of science. It found applications in signal and
image processing such as adaptive filtering, image encryption,
and 3D graphics. In this thesis, the quaternions are used to
represent color images acquired as biometrics. The three
complex parts of the quaternion used in our work represent the
color image components, while the real part is kept to zero.
Quaternion mathematical operations are developed in this thesis
to generate intentionally distorted versions of the biometrics to
be used for identification instead of the original biometrics. The
intended distortion effect is similar to the encryption effect as it
masks the details of the original biometric images. This trend of
using alternatives to original biometrics is known as cancellable
biometrics. Its major objective is to save the original biometrics
from being hacked if they are used in biometric databases. Three algorithms based on quaternion mathematics are
presented in this thesis to generate cancellable biometric
templates. The first one depends on certain quaternion
multiplication processes between the original color biometric
and an auxiliary image to induce the required degree of distortion
in biometric templates. The second one depends on the
utilization of FRFT with quaternion mathematics. The third one
depends on the utilization of rotation of quaternions to get the
required distortion level. Both algorithms are tested in the
cancellable biometrics recognition framework using Equal Error
Rate (EER) and Area under Receiver Operating characteristic
(AROC) curve to validate the proposed cancellable biometrics
scenarios. Simulation results have proved EER values close to
zero and AROC values close to one. Hence, the proposed
algorithms can be considered as good candidates for cancellable
biometric security systems.