Daugman’s Framework

Daugman’s initial work described a video acquisition system requiring subjects to position their eye within the camera field of view [32,33]. Excessive eyelid occlusion was reduced by providing live feedback to cooperating subjects through an LCTV monitor or mirror.

Images were acquired at a spatial resolution of 480x640 in the visible spectrum of light. An update to this system suggested using a monochrome CCD video camera with near-infrared illumination in the 700-900nm band [26,30]. Near-infrared is invisible and unobtrusive to the human eye resulting in little impact on the size of the pupil (visible light can cause the pupil to dilate or constrict dependent upon light intensity). Furthermore, near-infrared illumination reveals rich detailed structure of irides that have strong pigmentation (such as dark brown eyes) which is not apparent under visible wavelengths since the melanin pigment in the iris absorbs most of the visible light while longer wavelengths are reflected [11,27].

The high frequency power in the 2D Fourier spectrum is quantified for each frame, acting as

a rough focus assessment, which ensures that subsequent processing stages perform success-fully.

After image acquisition, Daugman employs an efficient integro-differential operator for detecting the pupillary and iris boundaries [32]. It acts as a circular edge detector that iteratively searches through image space for a maximum contour integral derivative. Math-ematically it is described as:

where Gσ(r) is a Gaussian smoothing function at scale σ, convolution is denoted by ∗, and (r, x0, y0) correspond to the radius and center coordinates which define a path for contour integration. Daugman constrains the angular search path, ds, to the left and right quadrants of the iris (vertical edge tuning) since heterogeneous image structures such as eyelids or eyelashes may occlude the upper and lower border of the iris. Subsequent processing searches the interior of the localized iris for the pupil limbus using equation 2.1, while constraining the angular search path to the upper 270^◦ to avoid specular reflection induced by the light source. After both boundaries have been estimated, equation 2.1 is modified from circular to arcuate, for subsequent detection of the upper and lower eyelids which are modeled as splines [26].

After isolating the iris from adjacent periocular image structures, it is normalized to a doubly dimensionless polar coordinate system. Each cartesian point, (x, y), on the iris is assigned a pair of real dimensionless coordinates (r, θ), where r ∈ [0, 1] is the radius variable and θ ∈ [0, 2π] is the angular variable. Mathematically this representation from cartesian to

polar is expressed as:

I(x(r, θ), y(r, θ))−→ I(r, θ), (2.2)

x(r, θ) = (1− r)xp(θ) + rx_s(θ), (2.3) y(r, θ) = (1− r)yp(θ) + ry_s(θ), (2.4)

where x(r, θ) and y(r, θ) represent linear combinations of boundary points around the pupil and iris boundary. Fig. 2.2 provides a detailed illustration of this process. Normalization ensures that feature extraction is robust to geometric distortions and linear deformations associated with pupil dilation and constriction. (Proponents of alternative normalization models argue that this representation is only suitable as an approximation. Pupillary func-tions such as dilation and constriction cause elastic deformafunc-tions to surrounding iris tissue which may be represented better through nonlinear normalization models [54,109,116,118].) Daugman employs 2-dimensional (2D) Gabor filters for extracting features from isolated iris texture. The filters are convolved with the normalized iris data representation to extract image texture information. The coefficients associated with the phase response from each filter is quantized into a pair for bits depending on the sgn of the 2D integral in equation 2.5:

h_{Re,Im} = sgn

{Re,Im}

∫

ρ

∫

ϕ

I(ρ, ϕ)e^{−iw(θ0−ϕ)}· e^{−(r0−ρ)2α2} e^{−(θ0−ϕ)2β2} ρdρdϕ, (2.5) where I(ρ, ϕ) is the normalized raw iris representation; α, β, and ω represent the size and frequency parameters of the wavelet; (r₀, θ₀) define the polar coordinates. This process is re-peated across the entire iris region with different wavelet scales, frequencies, and orientations to extract a 2048 bit compact binary representation, called an iris code. The resulting binary

Pupil Boundary

Figure 2.2: Illustration of the mapping between cartesian coordinates and polar coordinates.

(x_p(θ), y_p(θ)) and (x_s(θ), y_s(θ)) represent a pair of points on the pupil and iris boundaries at angle θ and radius r respectively. This process effectively makes subsequent recognition steps robust to geometric distortions and linear deformations associated with pupil dilation and constriction.

code is supplemented with an equal number of masking bits, provided by the segmentation described in2.1, which demarcates artifacts in the iris region, such as eyelashes, eyelids, and specular reflections.

The difference between two iris codes is calculated by measuring the dissimilarity between them, known as a fractional hamming distance. Artifact regions, demarcated by masking bits, are excluded from the computation. This is illustrated as follows:

HD =

is the XOR operator and galleryM ask, probeM ask represent the masks signifying which bits should be excluded from the comparison between galleryCode, probeCode

respec-tively. This computation may be repeated several times while circular shifting either code along its angular coordinate (θ), keeping only the minimum hamming distance. This process aligns one code to the other which may be displaced due to roll rotation of the head. (Note that rotation of the eyeball along the yaw axis, resulting in an off-axis gaze or “off-angle”

iris, will not be corrected by this computation. Instead, transformations that project an off-angle iris image back into frontal view have been considered [29,34,94].)