Abstruct-A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person's face is the detailed texture of each eye's iris: An estimate of its statistical complexity in a sample of the human population reveals variation corresponding to several hundred independent degrees-of-freedom. Morphogenetic randomness in the texture expressed phenotypically in the iris trabecular meshwork ensures that a test of statistical independence on two coded patterns originating from different eyes is passed almost certainly, whereas the same test is failed almost certainly when the compared codes originate from the same eye. The visible texture of a person's iris in a real-time video image is encoded into a compact sequence of multi-scale quadrature 2-D Gabor wavelet coefficients, whose most-significant bits comprise a 256-byte "iris code." Statistical decision theory generates identification decisions from Exclusive-OR comparisons of complete iris codes at the rate of 4000 per second, including calculation of decision confidence levels. The distributions observed empirically in such comparisons imply a theoretical "cross-over" error rate of one in 131000 when a decision criterion is adopted that would equalize the false accept and false reject error rates. In the typical recognition case, given the mean observed degree of iris code agreement, the decision confidence levels correspond formally to a conditional false accept probability of one in about lo"'.

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Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor's famous theory of communication [J. Inst. Electr. Eng. 93, 429 (1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial-2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace.(ABSTRACT TRUNCATED AT 250 WORDS)

Abstract-A three-layered neural network is described for transforming two-dimensional discrete signals into generalized nonorthogonal 2-D "Gabor" representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide a complete image description in terms of locally windowed 2-D spectral coordinates embedded within global 2-D spatial coordinates. Because intrinsic redundancies within images are extracted, the resulting image codes can be very compact. However, these conjoint transforms are inherently difficult to compute because t e elementary expansion functions are not orthogonal. One o r t h o g o n k i n g approach developed for 1-D signals by Bastiaans [SI, based on biorthonormal expansions, is restricted by constraints on the conjoint sampling rates and invariance of the windowing function, as well as by the fact that the auxiliary orthogonalizing functions are nonlocal infinite series. In the present "neural network" approach, based upon interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights, the network finds coefficients for complete conjoint 2-D Gabor transforms without these restrictive conditions. For arbitrary noncomplete transforms, in which the coefficients might be interpreted simply as signifying the presence of certain features in the image, the network finds optimal coefficients in the sense of minimal mean-squared-error in representing the image. I n one algebraically complete scheme permitting exact reconstruction, the network finds expansion coefficients that reduce entropy from 7.57 in the pixel representation to 2.55 in the complete 2-D Gabor transform. In "wavelet" expansions based on a biologically inspired log-polar ensemble of dilations, rotations, and translations of a single underlying 2-D Gabor wavelet template, image compression is illustrated with ratios up to 20: 1. Also demonstrated is image segmentation based on the clustering of coefficients in the complete 2-D Gabor transform. This coefficient-finding network for implementing useful nonorthogonal image transforms may also have neuroscientific relevance, because the network layers with fixed weights use empirical 2-D receptive field profiles obtained from orientation-selective neurons in cat visual cortex as the weighting functions, and the resulting transform mimics the biological visual strategy of embedding angular and spectral analysis within global spatial coordinates.

Abstract-This paper presents the following four advances in iris recognition: 1) more disciplined methods for detecting and faithfully modeling the iris inner and outer boundaries with active contours, leading to more flexible embedded coordinate systems; 2) Fourier-based methods for solving problems in iris trigonometry and projective geometry, allowing off-axis gaze to be handled by detecting it and "rotating" the eye into orthographic perspective; 3) statistical inference methods for detecting and excluding eyelashes; and 4) exploration of score normalizations, depending on the amount of iris data that is available in images and the required scale of database search. Statistical results are presented based on 200 billion iris cross-comparisons that were generated from 632 500 irises in the United Arab Emirates database to analyze the normalization issues raised in different regions of receiver operating characteristic curves.