# Uniqueness of Iris Pattern Based on the Auto-Regressive Model

## TL;DR

This paper explores a new method for iris recognition using Gaussian codewords and auto-regressive models to assess iris uniqueness.

## Contribution

The paper introduces a novel theoretical framework for iris recognition using nonlinear mapping and relative entropy-based uniqueness measures.

## Key findings

- The maximum iris population is characterized as a function of relative entropy between Gaussian codewords.
- The auto-regressive model provides a theoretical basis for nonlinear iris data mapping.
- Toy examples demonstrate the feasibility of the approach with small iris datasets.

## Abstract

In this paper, we evaluate the uniqueness of a hypothetical iris recognition system that relies upon a nonlinear mapping of iris data into a space of Gaussian codewords with independent components. Given the new data representation, we develop and apply a sphere packing bound for Gaussian codewords and a bound similar to Daugman’s to characterize the maximum iris population as a function of the relative entropy between Gaussian codewords of distinct iris classes. As a potential theoretical approach leading toward the realization of the hypothetical mapping, we work with the auto-regressive model fitted into iris data, after some data manipulation and preprocessing. The distance between a pair of codewords is measured in terms of the relative entropy (log-likelihood ratio statistic is an alternative) between distributions of codewords, which is also interpreted as a measure of iris quality. The new approach to iris uniqueness is illustrated using two toy examples involving two small datasets of iris images. For both datasets, the maximum sustainable population is presented as a function of image quality expressed in terms of relative entropy. Although the auto-regressive model may not be the best model for iris data, it lays the theoretical framework for the development of a high-performance iris recognition system utilizing a nonlinear mapping from the space of iris data to the space of Gaussian codewords with independent components.