Analysis of caotic structures in eye iris images

Throughout history, analyzing and understanding the time and space related events has been main theme of scientific studies. Dynamic, nonlinear, and deterministic structures of these events are concepts tightly related to the chaotic theory. Chaotic theory is used in the analysis of problems in many diverse field of disciplines such as mathematics, physics, and philosophy. In this work, the chaotic structure of iris is examined and the supporting experimental results are interpreted and their use in the biomedical field is evaluated. The eye images used in the thesis has been taken from the UBIRIS dataset. The raw iris data is segmented by detecting the pupil and iris boundaries using the Daugman's integro-differential operator. Iris images are transformed into time series by two different methods in order to form the phase space, in which the presence of chaotic structure is subsequently analysed. After this stage, the features to be used as information are the pixel values that make up the iris pattern. Such an application that converts iris region into time series and performs chaotic analysis does not exist in the literature. Three dimensional Lyapunov exponents are calculated from the time series obtained by first using the circular method, which are found to be positive. In the second method, the rectangular structure obtained by transforming the polar coordinates of the iris images is transformed into time series. This method has been preferred in order to reduce the distortions caused by the structure of the iris and the pupil. The phase space is formed by examining various delay and embedding dimension values so as to obtain the largest exponent values, of whom the maximum ones are inspected among the others. Finally, classification has been performed in the data set of 100 persons using the largest exponent values obtained.