Introduction to biometrics - Iris Recognition

In this report an iris detection system will be designed, programmed and tested. It starts off by discussing the current state of biometric systems and how they are graded. It then goes on to introduce the various steps which are taken in iris detection and which variations are possible within these steps. Out of these variations a combined method is designed, consisting of preprocessing, feature extraction and matching of the iris. In preprocessing both the iris and pupil center are detected and used to normalise the iris. The iris is then normalised using a Doubly Pair Method. The feature extraction is then performed using a Gabor filter. In matching the iris a Hamming distance is used. In this paper three variations of this system will be tested, varying the detection method and the normalising method. A two point and a three point method of detecting the iris will be tested, and it will be tested whether or not the results improve when the outer 50% of the iris is excluded. Both for training as well as testing these systems the CASIA iris database 1.0 was used, consisting of 756 images of 108 eyes. In training, the first 70 images of ten eyes were used. The remaining images were used in the final test. The best results were achieved by combining the two-point method and excluding the outer 50% of the iris. On the personal computer used, the system takes 3 hours to analyse the CASIA iris database. It resulted in an Equal Error Rate of 7.63% and an failure to enroll of 6.1%. Finally, recommendations will be made to further improvement of the system

Koornwinder polynomials and the XXZ spin chain

Nonsymmetric Koornwinder polynomials are multivariable extensions of nonsymmetric Askey-Wilson polynomials. They naturally arise in the representation theory of (double) affine Hecke algebras. In this paper we discuss how nonsymmetric Koornwinder polynomials naturally arise in the theory of the Heisenberg XXZ spin-$\frac{1}{2}$ chain with general reflecting boundary conditions. A central role in this story is played by an explicit two-parameter family of spin representations of the two-boundary Temperley-Lieb algebra. These spin representations have three different appearances. Their original definition relates them directly to the XXZ spin chain, in the form of matchmaker representations they relate to Temperley-Lieb loop models in statistical physics, while their realization as principal series representations leads to the link with nonsymmetric Koornwinder polynomials. The nonsymmetric difference Cherednik-Matsuo correspondence allows to construct for special parameter values Laurent-polynomial solutions of the associated reflection quantum KZ equations in terms of nonsymmetric Koornwinder polynomials. We discuss these aspects in detail by revisiting and extending work of De Gier, Kasatani, Nichols, Cherednik, the first author and many others