Demodulation by complex-valued wavelets for stochastic pattern recognition: How iris recognition works

Samples from stochastic signals having sufficient complexity need reveal only a little unexpected shared structure, in order to reject the hypothesis that they are independent. The mere failure of a test of statistical independence can thereby serve as a basis for recognizing stochastic patterns, provided they possess enough degrees-of-freedom, because all unrelated ones would pass such a test. This paper discusses exploitation of this statistical principle, combined with wavelet image coding methods to extract phase descriptions of incoherent patterns. Demodulation and coarse quantization of the phase information creates decision environments characterized by well separated clusters, and this lends itself to rapid and reliable pattern recognition. An example of this approach is the author's algorithms for iris recognition, now deployed in several countries. The principle underlying iris recognition is the failure of a test of statistical independence on iris phase structure encoded by multi-scale quadrature wavelets. Combinatorial complexity of this phase information across different persons spans about 249 degrees-of-freedom and generates a discrimination entropy of about 3.2 bits/mm(2) over the iris, enabling real-time identification decisions with enough accuracy to support exhaustive searches through very large databases. This paper presents the results of 9.1 million comparisons among eye images acquired in trials of these algorithms in Britain, Europe, Japan, Korea, and the USA.