A method for rapid visual recognition of personal identity is described, based on the failure of 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 trabeclar meshwork ensures that a test of statistical independence on two coded patterns organizing 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 512 – byte “IRIS–CODE” statistical decision theory generates identification decisions from Exclusive-OR comparisons of complete iris code at the rate of 4,000 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 1,31,000 when a decision criterion is adopted that would equalize the False Accept and False Reject error rates.Reliable automatic recognition of persons has long been an attractive goal. As in all pattern recognition problems, the key issue is the relation between interclass and intra-class variability: objects can be reliably classified only if the variability among different instances of a given class is less than the variability between different classes. Iris patterns become interesting as an alternative approach to reliable visual recognition of persons when imaging can be done at distances of less than a meter, and especially when there is a need to search very large databases without incurring any false matches despite a huge number of possibilities. The iris has the great mathematical advantage that its pattern variability among different persons is enormous. In addition, as an internal (yet externally visible) organ of the eye, the iris is well protected from the environment and stable over time. As a planar object its image is relatively insensitive to angle of illumination, and changes in viewing angle cause only affine transformations; even the non-affine pattern distortion caused by pupillary dilation is readily reversible. Finally, the ease of localizing eyes in faces, and the distinctive annular shape of the iris, facilitates reliable and precise isolation of this feature and the creation of a size-invariant representation.
Algorithms developed by Dr. John Daugman at Cambridge are today the basis for all iris recognition systems worldwide
. IRIS SCAN AND BIOMETRICS
Biometrics, the use of a physiological or behavioral aspect of the human body for authentication or identification, is a rapidly growing industry. Biometric solutions are used successfully in fields as varied as e-commerce, network access, time and attendance, ATM’s, corrections, banking, and medical record access. Biometrics’ ease of use, accuracy, reliability, and flexibility are quickly establishing them as the premier authentication technology.
Efforts to devise reliable mechanical means for biometric personal identification have a long and colourful history. In the Victorian era for example, inspired by birth of criminology and a desire to identify prisoners and malefactors, Sir Francis Galton F.R.S proposed various biometric indices for facial profiles which he represented numerically. Seeking to improve on the system of French physician Alphonse Bertillon for classifying convicts into one of 81 categories, Galton devised a series of spring loaded “mechanical selectors” for facial measurements and established an Anthropometric Laboratory at south Kensington
The possibility that the iris of the eye might be used as a kind of optical fingerprint for personal identification was suggested originally by ophthalmologists who noted from clinical experience that every iris had a highly detailed and unique texture, which remained un changed in clinical photographs spanning decades ( contrary to the occult diagnostic claims of “iridology” ). Among the visible features in an iris, some of which may be seen in the close-up image of figure 1, are the trabecular meshwork of connective tissue (pectinate ligament), collagenous stromal fibers, ciliary processes, contraction furrows ,crypts, a serpentine vasculature, rings, corona, colouration, and freckles. The striated trabecular meshwork of chromatophore and fibroblast cells creates the predominant texture under visible light, but all of these sources of radial and angular variation taken together constitute a distinctive “fingerprint” that can be imaged at some distance from the person. Further properties of the iris that enhance its stability for use in automatic identification include.
• Its inherent isolation and protection from the external environment, being an
internal organ of the eye, behind the cornea and aqueous humour.
• The impossibility of surgically modifying it without unacceptable risk to vision
• Its physiological response to light, which provides a natural test against artifice.
3. TECHNOLOGY
3.1. Iris Recognition
Iris recognition leverages the unique features of the human iris to provide an unmatched identification technology. So accurate are the algorithms used in iris recognition that the entire planet could be enrolled in an iris database with only a small chance of false acceptance or false rejection. The technology also addresses the FTE (Failure To Enroll) problems, which lessen the effectiveness of other biometrics. The tremendous accuracy of iris recognition allows it, in many ways, to stand apart from other biometric technology is based on research and patents held by Dr. John Daugman.
3.2. The Iris
Iris recognition is based on visible qualities of the iris. A primary visible characteristic is the trabecular meshwork (permanently formed by the 8th month of gestation), a tissue that gives the appearance of dividing the iris in a radial fashion. Other visible characteristics include rings, furrows freckles, and the corona. Expressed simply, iris recognition technology converts these visible characteristics into a 512 byte IRIS CODE, a template stored for future verification attempts. 512 bytes is a fairly compact size for a biometric template, but the quantity of information derived from the iris is massive. From the iris 11mm diameter, Dr. Daugman’s algorithms provide 3.4 bits of data per square mm this density of information is such that each iris can be said to have 266 unique “spots”, as opposed to 13-60 for traditional biometric technologies. This 266 measurements is cited in all iris recognition literature: after allowing for the algorithm’s
correlative functions and for characteristics functions and for characteristics inherent to
most human eyes, Dr. Daugman concludes that 173 “independent binary degrees-of-freedom” can be extracted from his algorithm - an exceptionally large number for a biometric
3.3. The Algorithms
The first step is location of the iris by a dedicated camera no more than 3 feet from the eye. After the camera situates the eye, the algorithm narrows in from the right and left of the iris to locate its outer edge. This horizontal approach accounts for obstruction caused by the eyelids. It simultaneously locates the inner edge of the iris (at the pupil), excluding the lower 90 degree because of inherent moisture and lighting issues. The monochrome camera uses both visible and infrared light, the latter of which is located in the 700-900 nm range. Upon location of the iris, as seen above, an algorithm uses 2-D Gabor wavelets to filter and map segments of the iris into hundreds of vectors (known here as phasors). The wavelets of various sizes assign values drawn from the orientation and spatial frequency of select areas, bluntly referred to as the “what” of the sub-image, along with the position of these areas, bluntly referred to as the “where”. The “what” and “where” are used to form the Iris Code. Not the entire iris is used: a portion of the top, as well as 45 degree of the bottom, is unused to account for eyelids and camera-light reflections. For future identification, the database will not be comparing images of irises, but rather hexadecimal representations of data returned by wavelet filtering an d mapping.
4. FINDING AN IRIS IN AN IMAGE
To capture the rich details of iris patterns, an imaging system should resolve
a minimum of 70 pixels in iris radius. In the field trials to date, a resolved iris radius of 100 to 140 pixels has been more typical. Monochrome CCD cameras (480 x 640) have been used because NIR illumination in the 700nm - 900nm band was required for imaging to be invisible to humans. Some imaging platforms deployed a wide-angle camera for coarse localization of eyes in faces, to steer the optics of a narrow-angle pan/tilt camera that acquired higher resolution images of eyes. There exist many alternative methods for finding and tracking facial features such as the eyes, and this well researched topic will not be discussed further here. In these trials, most imaging was done without active pan/tilt camera optics, but instead exploited visual feedback via a mirror or video image to enable cooperating Subjects to position their own eyes within the field of view of a single narrow-angle camera.
Focus assessment was performed in real-time (faster than video frame rate)
by measuring the total high-frequency power in the 2D Fourier spectrum of each frame, and seeking to maximize this quantity either by moving an active lens or by providing audio feedback to Subjects to adjust their range appropriately. Images passing a minimum focus criterion were then analyzed to find the iris, with precise localization of its boundaries using a coarse - to - fine strategy terminating in single-pixel precision estimates of the center coordinates and radius of both the iris and the pupil. Although the results of the iris search greatly constrain the pupil search, concentricity of these boundaries cannot be assumed. Very often the pupil center is nasal, and inferior, to the iris center. Its radius can range from 0.1 to 0.8 of the iris radius. Thus, all three parameters defining the pupillary circle must be estimated separately from those of the iris.
Where I(x; y) is an image such as Fig 1 containing an eye. The operator
searches over the image domain (x; y) for the maximum in the blurred partial derivative with respect to increasing radius r, of the normalized contour integral of I(x; y) along a circular arc ds of radius r and center coordinates (x0; y0). The symbol * denotes convolution and G(r) is a smoothing function such as a Gaussian of scale σ. The complete operator behaves in effect as a circular edge detector, blurred at a scale set by σ, which searches iteratively for a maximum contour integral derivative with increasing radius at successively finer scales of analysis through the three parameter space of center coordinates and radius (x0, y0, r) defining a path of contour integration.
The operator in (1) serves to find both the pupillary boundary and the outer
(limbus) boundary of the iris, although the initial search for the limbus also incorporates evidence of an interior pupil to improve its robustness since the limbic boundary itself usually has extremely soft contrast when long wavelength NIR illumination is used. Once the coarse-to-fine iterative searches for both these boundaries have reached single pixel precision, then a similar approach to detecting curvilinear edges is used to localize both the upper and lower eyelid boundaries. The path of contour integration in (1) is changed from circular to accurate, with spline parameters fitted by standard statistical estimation methods to describe optimally the available evidence for each eyelid boundary. The result of all these localization operations is the isolation of iris tissue from other image regions, as illustrated in Fig 1 by the graphical overlay on the eye.
5. IRIS FEATURE ENCODING
Each isolated iris pattern is then demodulated to extract its phase
information using quadrature 2D Gabor wavelets (Daugman 1985, 1988, 1994). This encoding process is illustrated in Fig 2. It amounts to a patch-wise phase quantization of the iris pattern, by identifying in which quadrant of the complex plane each resultant phasor lies when a given area of the iris is projected onto complex-valued 2D Gabor wavelets:
imaginary parts are either 1 or 0 (sgn) depending on the sign of the 2D integral; I(ρ ; φ) is the raw iris image in a dimensionless polar coordinate system that is size- and translation-invariant, and which also corrects for pupil dilation as explained in a later section; α and β are the multi-scale 2D wavelet size parameters, spanning an 8-fold range from 0.15mm to 1.2mm on the iris; ω is wavelet frequency, spanning 3 octaves in inverse proportion to β; and (r0; θ0) represent the polar coordinates of each region of iris for which the phasor coordinates h{Re ; Im} are computed. Such a phase quadrant coding sequence is illustrated for one iris by the bit stream shown graphically in Fig 1.
A desirable feature of the phase code portrayed in Fig 2 is that it is a cyclic,
or grey code: in rotating between any adjacent phase quadrants, only a single bit changes, unlike a binary code in which two bits may change, making some errors arbitrarily more costly than others. Altogether 2,048 such phase bits (256 bytes) are computed for each iris, but in a major improvement over the earlier (Daugman 1993) algorithms, now an equal number of masking bits are also computed to signify whether any iris region is obscured by eyelids, contains any eyelash occlusions, specular reflections, boundary artifacts of hard contact lenses, or poor signal-to-noise ratio and thus should be ignored in the demodulation code as artifact.
Only phase information is used for recognizing irises because amplitude information is not very discriminating, and it depends upon extraneous factors such as imaging contrast, illumination, and camera gain. The phase bit settings which code the sequence of projection quadrants as shown in Fig 2 capture the information of wavelet zero-crossings, as is clear from the sign operator in (2). The extraction of phase has the further advantage that phase angles are assigned regardless of how low the image contrast may be, as illustrated by the extremely out-of-focus image in Fig 3. Its phase bit stream has statistical properties such as run lengths similar to those of the code for the properly focused eye image in Fig 1. (Fig 3 also illustrates the robustness of the iris- and pupil - finding operators, and the eyelid detection operators, despite poor focus.) The benefit which arises from the fact that phase bits are set also for a poorly focused mage as shown here, even if based only on random CCD noise, is that different poorly focused irises never become confused with each other when their phase codes are compared. By contrast, images of different faces look increasingly alike when poorly resolved, and may be confused with each other by appearance-based face recognition algorithms.
6. THE TEST OF STATISTICAL
INDEPENDENCE
The key to iris recognition is the failure of a test of statistical independence,
which involves so many degrees-of-freedom that this test is virtually guaranteed to be passed whenever the phase codes for two different eyes are compared, but to be uniquely failed when any eye's phase code is compared with another version of itself.
The test of statistical independence is implemented by the simple Boolean
Exclusive-OR operator (XOR) applied to the 2,048 bit phase vectors that encode any two iris patterns, masked (AND'ed) by both of their corresponding mask bit vectors to prevent non-iris artifacts from influencing iris comparisons. The XOR operator Ä detects disagreement between any corresponding pair of bits, while the AND operator Ç ensures that the compared bits are both deemed to have been uncorrupted by eyelashes, eyelids, specular re-flections, or other noise. The norms (|| ||) of the resultant bit vector and of the AND'ed mask vectors are then measured in order to compute a fractional Hamming distance (HD) as the measure of the dissimilarity between any two irises, whose two phase code bit vectors are denoted {codeA, codeB} and whose mask bit vectors are denoted {maskA, maskB}:
The denominator tallies the total number of phase bits that mattered in iris
comparisons after artifacts such as eyelashes and specular reflections were discounted, so
the resulting HD is a fractional measure of dissimilarity; 0 would represent a perfect
match. The Boolean operators Ä and Ç are applied in vector form to binary strings of
length up to the word length of the CPU, as a single machine instruction. Thus for example
on an ordinary 32-bit machine, any two integers between 0 and 4 billion can be XOR'ed in a single machine instruction to generate a third such integer, each of whose bits in a binary expansion is the XOR of the corresponding pair of bits of the original two integers. This implementation of (3) in parallel 32-bit chunks enables extremely rapid comparisons of
iris codes when searching through a large database to find a match. On a 300 MHz CPU, such exhaustive searches are performed at a rate of about 100,000irises per second. Because any given bit in the phase code for an iris is equally likely to be 1 or 0, and different irises are uncorrelated, the expected proportion of agreeing bits between the codes for two different irises is HD = 0.500.
The histogram in Fig 4 shows the distribution of HDs obtained from 9.1
million comparisons between different pairings of iris images acquired by licensees of these algorithms in the UK, the USA, Japan, and Korea. There were 4,258 different iris images, including 10 each of one subset of 70 eyes. Excluding those duplicates of (700 x
9) same-eye comparisons, and not double-counting pairs, and not comparing any image
with itself, the total number of unique pairings between different eye images whose HDs could be computed was ((4,258 x 4,257 – 700 x 9) / 2) = 9,060,003. Their observed mean
HD was p = 0:499 with standard deviation σ = 0:0317; their full distribution in Fig 4 corresponds to a binomial having N = p(1-p)/σ2 = 249 degrees-of-freedom, as shown by the solid curve. The extremely close fit of the theoretical binomial to the observed distribution is a consequence of the fact that each comparison between two phase code bits from two different irises is essentially a Bernoulli trial, albeit with correlations between successive “coin tosses”.
In the phase code for any given iris, only small subsets of bits are mutually
independent due to the internal correlations, especially radial, within an iris. (If all N = 2; 048 phase bits were independent, then the distribution in Fig 4 would be very much sharper, with an expected standard deviation of only (p(1- p)/N ) 1/2 = 0:011 and so the HD interval between 0.49 and 0.51 would contain most of the distribution.) Bernoulli trials that are correlated (Viveros et al. 1984) remain binomially distributed but with a reduction in N, the effective number of tosses, and hence an increase in the _ of the normalized HD distribution. The form and width of the HD distribution in Fig 4 tell us that the amount of difference between the phase codes for different irises is distributed equivalently to runs of 249 tosses of a fair coin (Bernoulli trials with p = 0:5;N = 249). Expressing this variation as a discrimination entropy (Cover and Thomas 1991) and using typical iris and pupil diameters of 11mm and 5mm respectively, the observed amount of statistical variability among different iris patterns corresponds to an information density of about 3.2 bits/mm2 on the iris.
The theoretical binomial distribution plotted as the solid curve in Fig 4 has
the fractional functional form
. To
validate such a statistical model we must also study the behaviour of the tails, by examining quantile-quantile plots of the observed cumulatives versus the theoretically predicted cumulatives from 0 up to sequential points in the tail. Such a “Q-Q” plot is given in Fig 5.
The straight line relationship reveals very precise agreement between model
and data, over a range of more than three orders of magnitude. It is clear from both Figures 4 and 5 that it is extremely improbable that two different irises might disagree by chance in fewer than at least a third of their bits. (Of the 9.1 million iris comparisons plotted in the histogram of Figure 4, the smallest Hamming Distance observed was 0.334.) Computing the cumulative of f(x) from 0 to 0.333 indicates that the probability of such an event is about 1 in 16 million. The cumulative from 0 to just 0.300 is 1 in 10 billion. Thus, even the
observation of a relatively poor degree of match between the phase codes for two different
iris images (say, 70% agreement or HD = 0.300) would still provide extraordinarily compelling evidence of identity, because the test of statistical independence is still failed so convincingly.
A convenient source of genetically identical irises is the right and left pair
from any given person; such pairs have the same genetic relationship as the four irises of monozygotic twins, or indeed the prospective 2N irises of N clones. Although eye colour is of course strongly determined genetically, as is overall iris appearance, the detailed patterns of genetically identical irises appear to be as uncorrelated as they are among unrelated eyes. Using the same methods as described above, 648 right/left iris pairs from 324 persons were compared pairwise. Their mean HD was 0.497 with standard deviation 0.031, and their distribution was statistically indistinguishable from the distribution for unrelated eyes. A set of 6 pairwise comparisons among the eyes of actual monozygotic twins also yielded a result (mean HD = 0.507) expected for unrelated eyes. It appears that the phenotypic random patterns visible in the human iris are almost entirely epigenetic.
7. RECOGNIZING IRISES REGARDLESS OF SIZE, POSITION, AND ORIENTATION
Robust representations for pattern recognition must be invariant to changes
in the size, position, and orientation of the patterns. In the case of iris recognition, this means we must create a representation that is invariant to the optical size of the iris in the image (which depends upon the distance to the eye, and the camera optical magni_cation factor); the size of the pupil within the iris (which introduces a non-af_ne pattern deformation); the location of the iris within the image; and the iris orientation, which
depends upon head tilt, torsional eye rotation within its socket (cyclovergence), and camera angles, compounded with imaging through pan/tilt eye-finding mirrors that introduce additional image rotation factors as a function of eye position, camera position, and mirror angles. Fortunately, invariance to all of these factors can readily be achieved.
For on-axis but possibly rotated iris images, it is natural to use a projected
pseudo polar coordinate system. The polar coordinate grid is not necessarily concentric, since in most eyes the pupil is not central in the iris; it is not unusual for its nasal displacement to be as much as 15%. This coordinate system can be described as doubly-dimensionless: the polar variable, angle, is inherently dimensionless, but in this case the radial variable is also dimensionless, because it ranges from the pupillary boundary to the limbus always as a unit interval [0, 1]. The dilation and constriction of the elastic meshwork of the iris when the pupil changes size is intrinsically modelled by this coordinate system as the stretching of a homogeneous rubber sheet, having the topology of an annulus anchored along its outer perimeter, with tension controlled by an (off-centered) interior ring of variable radius.
The homogeneous rubber sheet model assigns to each point on the iris,
regardless of its size and pupillary dilation, a pair of real coordinates (r; θ) where r is on the unit interval [0, 1] and θ is angle [0, 2_]. The remapping of the iris image I(x; y) from raw Cartesian coordinates (x; y) to the dimensionless nonconcentric polar coordinate system (r; θ) can be represented as
I(x(r; θ); y(r; θ ) ! I(r; θ) (5)
where x(r; θ ) and y(r; θ) are de_ned as linear combinations of both the set
of pupillary boundary points (xp(θ ); yp(θ )) and the set of limbus boundary points along the outer perimeter of the iris (xs(θ ); ys(θ )) bordering the sclera, both of which are detected by _nding the maximum of the operator (1).
x(r; θ) = (1 - r) xp(θ ) + r xs(θ ) (6)
y(r; θ) = (1- r) yp(θ ) + r ys(θ ) (7)
Since the radial coordinate ranges from the iris inner boundary to its outer
boundary as a unit interval, it inherently corrects for the elastic pattern deformation in the iris when the pupil changes in size.
The localization of the iris and the coordinate system described above
achieve invariance to the 2D position and size of the iris, and to the dilation of the pupil within the iris. However, it would not be invariant to the orientation of the iris within the image plane. The most ef_cient way to achieve iris recognition with orientation invariance is not to rotate the image itself using the Euler matrix, but rather to compute the iris phase code in a single canonical orientation and then to compare this very compact representation at many discrete orientations by cyclic scrolling of its angular variable. The statistical consequences of seeking the best match after numerous relative rotations of two iris codes
are straightforward. Let f0(x) be the raw density distribution obtained for the HDs between
different irises after comparing them only in a single relative orientation; for example, f0(x) might be the binomial de_ned in (4). Then F0(x), the cumulative of f0(x) from 0 to x, becomes the probability of getting a false match in such a test when using HD acceptance criterion x:
x
F0(x) = ò f0(x) dx (8)
0
or, equivalently,
f0(x) = d/dx F0(x) (9)
Clearly, then, the probability of not making a false match when using
criterion x is 1-F0(x) after a single test, and it is [1 - F0(x)] n after carrying out n such tests independently at n different relative orientations. It follows that the probability of a false match after a “best of n” tests of agreement, when using HD criterion x, regardless of the actual form of the raw unrotated distribution f0(x), is:
Fn(x) = 1- [ 1- F0(x) ] (10)
and the expected density fn(x) associated with this cumulative is
fn(x) = d/dx Fn(x) = n f0(x) [ 1- F0(x) ]n-1 (11)
Each of the 9.1 million pairings of different iris images whose HD
distribution was shown in Fig 4, was submitted to further comparisons in each of 7 relative orientations. This generated 63 million HD outcomes, but in each group of 7 associated
with any one pair of irises, only the best match (smallest HD) was retained. The histogram of these new 9.1 million best HDs is shown in Fig 7. Since only the smallest value in each group of 7 samples was retained, the new distribution is skewed and biased to a lower
mean value (HD = 0.458), as expected from the theory of extreme value sampling. The solid curve in Fig 7 is a plot of (11), incorporating (4) and (8) as its terms, and it shows an excellent fit between theory (binomial extreme value sampling) and data. The fact that the
minimum HD observed in all of these millions of rotated comparisons was about 0.33 illustrates the extreme improbability that the phase sequences for two different irises might disagree in fewer than a third of their bits. This suggests that in order to identify people by their iris patterns with high confidence, we need to demand only a very forgiving degree of match (say, HD ≤ 0.32).
8. UNIQUENESS OF FAILING THE TEST OF
STATISTICAL INDEPENDENCE
The statistical data and theory presented above show that we can perform iris recognition successfully just by a test of statistical independence. Any two different irises are statistically .guaranteed. to pass this test of independence, and any two images that fail this test (i.e. produce a HD ≤ 0.32) must be images of the same iris. Thus, it is the unique failure of the test of independence, that is the basis for iris recognition.
It is informative to calculate the significance of any observed HD matching score, in terms of the likelihood that it could have arisen by chance from two different irises. These probabilities give a confidence level associated with any recognition decision. Fig 8 shows the false match probabilities marked off in cumulatives along the tail of the distribution presented in Fig 7 (same theoretical curve (11) as plotted in Fig 7 and with the justification presented in Fig 4 and Fig 5.) Table 1 enumerates the cumulatives of (11) (false match probabilities) as a more fine-grained function of HD decision criterion in the range between 0.26 and 0.35. Calculation of the large factorial terms in (4) was done with Stirling's approximation which errors by less than 1% for n ≥9:
n! » exp(n ln (n) – n + ½ ln(2pn)) (12)
The practical importance of the astronomical odds against a false match when the match quality is better than about HD ≤ 0.32, as shown in Fig 8 and in Table 1, is that such high confidence levels allow very large databases to be searched exhaustively without succumbing to any of the many opportunities for suffering a false match. The requirements of operating in one-to-many “identification” Mode are vastly more demanding than operating merely in one-to-one “verification” Mode (in which an identity must first be explicitly asserted, which is then verified in a yes/no decision by comparison against just the single nominated template). If P1 is the false match probability for single one-to-one verification trials, then clearly PN, the probability of making at least one false match when searching a database of N unrelated patterns, is:
PN = 1 – (1-P1)N (13)
Because (1 - P1) is the probability of not making a false match in single comparisons; this must happen N independent times; and so (1 - P1)N is the probability that such a false match never occurs. It is interesting to consider how a seemingly impressive
biometric one-to-one ‘verifier’ would perform in exhaustive search mode once databases
become larger than about 100, in view of (13). For example, a face recognition algorithm that truly achieved 99.9% correct rejection when tested on non-identical faces, hence making only 0.1% false matches, would seem to be performing at a very impressive level because it must confuse no more than 10% of all identical twin pairs (since about 1% of all persons in the general population have an identical twin). But even with its P1 = 0.001, how good would it be for searching large databases? Using (13) we see that when the search database size has reached merely N = 200 unrelated faces, the probability of at least one false match among them is already 18%. When the search database is just N = 2000 unrelated faces, the probability of at least one false match has reached 86%. Clearly, identification is vastly more demanding than one-to-one verification, and even for moderate database sizes, merely “good” Verifiers are of no use as identifiers. Observing the approximation that PN » NP1 for small P1 << 1/N << 1, when searching a database of size N an identifier needs to be roughly N times better than a verifier to achieve comparable odds against making false matches.
The algorithms for iris recognition exploit the extremely rapid attenuation
of the HD distribution tail created by binomial combinatorics, to accommodate very large database searches without suffering false matches. The HD threshold is adaptive, to maintain PN < 10-6 regardless of how large the search database size N is. As Table 1 illustrates, this means that if the search database contains 1 million different iris patterns, it is only necessary for the HD match criterion to adjust downwards from 0.33 to 0.27 in order to maintain still a net false match probability of 10-6 for the entire database.
9. DECISION ENVIRONMENTS FOR IRIS
RECOGNITION
The overall “decidability” of the task of recognizing persons by their iris patterns is revealed by comparing the Hamming Distance distributions for same versus for different irises. The left distribution in Fig 9 shows the HDs computed between 7,070 different pairs of same-eye images at different times, under different conditions, and usually with different cameras; and the right distribution gives the same 9.1 million comparisons among different eyes shown earlier. To the degree that one can confidently decide whether an observed sample belongs to the left or the right distribution in Fig 9, iris recognition can be successfully performed. Such a dual distribution representation of the decision problem may be called the .decision environment, . Because it reveals the extent to which the two cases (same versus different) are separable and thus how reliably decisions can be made, since the overlap between the two distributions determines the error rates.
Whereas Fig 9 shows the decision environment under less favorable conditions (images acquired by different camera platforms), Fig 10 shows the decision environment under ideal (almost artificial) conditions. Subjects' eyes were imaged in a laboratory setting using always the same camera with fixed zoom factor and at fixed distance, and with fixed illumination. Not surprisingly, more than half of such image comparisons achieved an HD of 0.00, and the average HD was a mere 0.019. It is clear from comparing Fig 9 and Fig 10 that the “authentics” distribution for iris
recognition (the similarity between different images of the same eye, as shown in the left-side distributions), depends very strongly upon the image acquisition conditions. However, the measured similarity for .imposters. (The right-side distribution) is
apparently almost completely independent of imaging factors. Instead, it mainly reflects just the combinatorics of Bernoulli trials, as bits from independent binary sources (the phase codes for different irises) are compared.
For two-choice decision tasks (e.g. same versus different), such as biometric decision making, the “decidability” index d’ measures how well separated the two distributions are, since recognition errors would be caused by their overlap. If their two means are μ1 and μ2, and their two standard deviations are σ1 and σ2, then d’ is defined as
| m 1 - m 2 |
d¢ = —————— (14)
[ (σ12 + σ22)/2]1/2
This measure of decidability is independent of how liberal or conservative is the acceptance threshold used. Rather, by measuring separation, it reflects the degree to which any improvement in (say) the false match error rate must be paid for by a worsening
of the failure-to-match error rate. The performance of every biometric technology can be
calibrated by its d’ score. The measured decidability for iris recognition is d’= 7:3 for the non-ideal (crossed platform) conditions presented in Fig 9, and it is d’ = 14:1 for the ideal imaging conditions presented in Fig 10.
Based on the left-side distributions in Figs 9 and 10, one could calculate a
table of probabilities of failure to match, as a function of HD match criterion, just as we did earlier in Table 1 for false match probabilities based on the right-side distribution. However, such estimates may not be stable because the “authentics” distributions depend strongly on the quality of imaging (e.g. motion blur, focus, noise, etc.) and would be different for different optical platforms Imaging quality determines how much the same iris distribution evolves and migrates leftward, away from the asymptotic different-iris distribution on the right. In any case, we note that for the 7,070 same-iris comparisons shown in Fig 9, their highest HD was 0.327 which is below the smallest HD of 0.329 for the 9.1 million comparisons between different irises. Thus a decision criterion slightly below 0.33 for the empirical data sets shown can perfectly separate the dual distributions At this criterion, using the cumulative of (11) as tabulated in Table 1, the theoretical false match probability is 1 in 4 million.
Notwithstanding this diversity among iris patterns and their apparent singularity because of so many dimensions of random variation, their utility as a basis for automatic personal identification would depend upon their relative stability over time. There is a popular belief that the iris changes systematically with one's health or personality, and even that its detailed features reveal the states of individual organs (“iridology “); but such claims have been discredited (e.g. Berggren 1985; Simon et al. 1979) as medical fraud. In any case, the recognition principle described here is intrinsically tolerant of a large proportion of the iris information being corrupted, say up to about a third, without significantly impairing the inference of personal identity by the simple test of statistical independence.
10. SPEED PERFORMANCE SUMMARY
On a 300 MHz Sun workstation, the execution times for the critical steps in
iris recognition are as follows, using optimized integer code:
The search engine can perform about 100,000 full comparisons between different irises per second, because of the efficient implementation of the matching process in terms of elementary Boolean operators Ä and ∩ acting in parallel on the computed phase bit sequences. If database size was measured in millions of enrolled persons, then the inherent parallelism of the search process should be exploited for the sake of speed by dividing up the entire search database into units of about 100,000 persons each. The mathematics of the iris recognition algorithms make it clear that databases the size of entire nations could be searched in parallel to make a confident identification decision, in about 1 second using parallel banks of inexpensive CPUs, if such large national iris databases ever came to exist.
11. IRIS FOR IDENTIFICATION
11.1. Advantages:
Ø Highly protected, internal organ of the eye
Ø Externally visible; patterns imaged from a distance
Ø Iris patterns possess a high degree of randomness
Ø Variability; 244 degrees-of-freedom
Ø Entropy; 3.2 bits per square-millimeter
Ø Uniqueness: set by combinatorial complexity
Ø Changing pupil size confirms natural physiology
Ø Pre-natal morphogenesis (7th month of gestation)
Ø Limited genetic penetrance of iris pattern
Ø Pattern apparently stable throughout life
§ Encoding and decision-making are tractable
§ Image analysis and encoding time: 1second
§ Decidability index (d-prime): d’=7.3 to 11.4
§ Search speed: 100000 Iris Codes per second
11.2. Disadvantages:
Ø Small target (1 cm) to acquire from a distance 1 meter
Ø Moving target ….with in another ….on yet another
Ø Located behind a curved, wet, reflecting surface
Ø Deforms non-elastically as pupil changes size
Ø Partially occluded by eyelids, often drooping
12. IRIS RECOGNITION IN ACTION
Iris-based identification and verification technology has gained acceptance in a no: of different areas. Where as the technology in its early days was fairly cumbersome and expensive, recent technological breakthroughs have reduced both the size and prize of iris recognition (also know informally as iris scan) devices. This, in turn, has allowed for much grater flexibility of implementation. Iris-based biometric technology has always been an exceptionally accurate one, and it may soon grow much more prominent.
12.1. Applications:
Ø Computer login: the iris as a living password
Ø National border controls: the iris as a living passport
Ø Telephone call charging without cash, cards, or PIN numbers
Ø Secure access to bank cash machine accounts
Ø Ticket less air travel
Ø driving licenses, and other personal certificate
Ø Forensics: birth certificates
Ø Tracing missing or wanted persons
Ø Anti-terrorism
Ø “Biometric-key cryptography” for encrypting/decrypting messages
Ø Automobile ignition and unlocking
Ø Credit card authentication
Ø Internet security; control of access to privileged information
13 CONCLUSION
Aristotelian philosophy held that the o(ãdos, distinguishing essence) of something resided in that quality which made it different from everything else. When we need to know with certainty who an individual is, or whether he is who he claims to be, we normally rely either upon something that he uniquely possesses (such as a key or a card), something that he uniquely knows (such as a password or PIN), or a biological characteristic (such as his appearance). Technologically the first two of these criteria have been the easiest to confirm automatically, but they are also the least reliable, since (in Aristotelian terms) they do not necessarily make this individual different from all others. Today we hold that the uniqueness of a person arises from the trio of his genetic genotype, its expression as phenotype, and the sum his experiences. For purposes of rapid and reliable personal identification, the first and third of these cannot readily be exploited: DNA testing is neither real-time nor unintrusive; and experiences are only as secure as testimony. The remaining unique identifiers are phenotypic characteristics. It is hard to imagine one better suited than a protected, immutable, internal organ of the eye, that is readily visible externally and that reveals random morphogenesis of high statistical complexity.
No comments:
Post a Comment
leave your opinion