1148
IEEE
TRANSACTIONS ON
PA’ITERN ANALYSIS
AND
MACHINE INTELLIGENCE,
VOL.
15,
NO.
11,
NOVEMBER
1993
High Confidence Visual Recognition
of
Persons
by
a Test
of
Statistical Independence
John
G.
Daugman
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”’.
Index
Terms-
Image analysis, statistical pattern recognition,
biometric identification, statistical decision theory, 2-D Gabor
filters, wavelets, texture analysis, morphogenesis.
I.
INTRODUCTION
FFORTS
to
devise reliable mechanical means for bio-
E
metric personal identification have a long and colorful
history. In the Victorian era for example, inspired by the
birth of criminology and a desire
to
identify prisoners and
malefactors, Sir Francis Galton F.R.S.
[
131
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 Kensing-
ton [13]. Other biometric identifiers that have been adopted
historically, ranging from cranial dimensions
to
digit length, as
Manuscript received August
31,
1992; revised December
16,
1992. This
work was supported
in
part by
US.
National Science Foundation Presidential
Young
Investigator Award
No.
1RI-8858819 and by research grants
from
the
Kodak Corporation. Recommended
for
acceptance by Editor-in-Chief
A.
K.
Jain.
The author is with Faculty
of
Biology, Cambridge University, Downing
St.,
Cambridge CB2
3EJ,
England.
IEEE
Log
Number 9212305.
well as some of the numerous geometric facial measurements
currently being tried, are described in
[17],
[25].
Today there is renewed interest in reliable, rapid, and
unintrusive means for automatically recognizing the identity
of persons. Security breaches in access
to
restricted areas at
airports are known
to
have contributed to terrorism; and credit
card fraud now costs six billion dollars annually
[3].
Other
applications for high confidence personal identification include
passport control, bank automatic teller machines, protected
access
to
premises or assets, law enforcement, government in-
telligence, entitlement verification, birth certificates, licenses,
and any existing use of keys or cards. Some of the identifying
biometric features now under investigation for potential
use
include hand geometry, blood vessel patterns in the retina
or hand, fingerprints, voice-prints, and handwritten signature
dynamics. The critical attributes for any such measure are: the
number of degrees-of-freedom of variation in the chosen index
across the human population, since this determines uniqueness;
its immutability over time and its immunity
to
intervention;
and the computational prospects for efficiently encoding and
reliably recognizing the identifying pattern.
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 [l], [12], [24],
who noted from clinical experience that every iris had a
highly detailed and unique texture, which remained unchanged
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 Fig.
1,
are the trabecular meshwork of
connective tissue (pectinate ligament), collagenous stromal
fibres, ciliary processes, contraction furrows, crypts, a ser-
pentine vasculature, rings, corona, coloration, and freckles
[l], [ll], [12], [24]. The striated trabecular meshwork of
chromatophore and fibroblast cells creates the predominant
texture under visible light [24], 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 suitability
for use in automatic identification include
1)
its inherent
isolation and protection from the external environment, being
an internal organ of the eye, behind the cornea and the aqueous
humor;
2)
the impossibility of surgically modifying it without
unacceptable risk
to
vision; and
3)
its physiological response
to light, which provides a natural test against artifice.
A
property the iris shares with fingerprints is the random
morphogenesis of its minutiae. Because there is no genetic
0162-8828/93$03.00
0
1993 IEEE
DAUGMAN:
HIGH
CONFIDENCE
VISUAL
RECOGNITION
OF
PERSONS
BY
A
TEST
OF
STATISTICAL
INDEPENDENCE
1149
Fig.
1.
Close-up image illustrating the trabecular meshwork and other fea-
tures
of
a human iris.
penetrance in the expression of this organ beyond its anatom-
ical form, physiology, color and general appearance, the iris
texture itself is stochastic or possibly chaotic. Since its detailed
morphogenesis depends on initial conditions in the embryonic
mesoderm from which it develops
[11],
the phenotypic ex-
pression even of two irises with the same genetic genotype
(as in identical twins, or the pair possessed by one individual)
have uncorrelated minutiae. In these respects the uniqueness
of every iris parallels the uniqueness of every fingerprint,
common genotype or not. But the iris enjoys further practical
advantages over fingerprints and other biometrics for purposes
of automatic recognition, including
4)
the ease of registering
its image at some distance from the Subject without physical
contact, unintrusively and perhaps inconspicuously; and
5)
its
intrinsic polar geometry, which imparts a natural coordinate
system and an origin of coordinates.
Unknown until the present work was whether mathemat-
ically there were sufficient degrees-of-freedom, or forms of
variation in the iris among individuals, to impart
to
it the
same singularity as a conventional fingerprint. Also uncertain
was whether efficient algorithms could be developed to extract
a detailed iris description reliably from a live video image,
generate a compact code for the iris (of minuscule length
compared with image data size), and render a decision about
individual identity with high statistical confidence, all within
less than one
second of computation time on a general-
purpose microprocessor. The present report resolves all of
these questions affirmatively and describes a working system.
11.
IMAGE
ANALYSIS
A.
Operators for Locating
an
Iris
Iris analysis begins with reliable means for establishing
whether an iris is visible in the video image, and then precisely
locating its inner and outer boundaries (pupil and limbus).
Because of the felicitous circular geometry of the iris, these
tasks can be accomplished for a raw input image
1(x,y)
by
integrodifferential operators that search over the image domain
(fr.
y)
for the maximum in the blurred partial derivative, with
respect
to
increasing radius
T,
of the normalized conto
integral of
I(.rl
y)
along a circular arc
ds
of radius
T
ai
center coordinates
(TO.
yo):
where
*
denotes convolution and
G,(r)
is a smoothii
function such as a Gaussian of scale
o.
The complete operator
behaves in effect as a circular edge detector, blurred at a scale
set by
o,
that 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
(TO,
yo,
T)
defining the path of contour
integration.
At first the blurring factor
o
is set for a coarse scale of
analysis
so
that only the very pronounced circular transition
from iris to (white) sclera is detected. Then after this strong
circular boundary
is
more precisely estimated, a second search
begins within the confined central interior of the located iris for
the fainter pupillary boundary, using a finer convolution scale
o
and a smaller search range defining the paths
(z~,y~.r)
of
contour integration. In the initial search for the outer bounds of
the iris, the angular arc of contour integration
ds
is restricted
in range
to
two opposing
90"
cones centered on the horizontal
meridian, since eyelids generally obscure the upper and lower
limbus of the iris. Then in the subsequent interior search for
the pupillary boundary, the arc of contour integration
ds
in
operator
(1)
is restricted
to
the upper
270"
in order
to
avoid
the corneal specular reflection that is usually superimposed in
the lower
90"
cone of the iris from the illuminator located
below the video camera. Taking the absolute value in
(1)
is
not required when the operator
is
used first to locate the outer
boundary
of
the iris, since the sclera is always lighter than
the iris and
so
the smoothed partial derivative with increasing
radius near the limbus
is
always positive. However, the pupil
is
not always darker than the iris, as in persons with normal
early cataract or significant back-scattered light from the lens
and vitreous humor; applying the absolute value in
(1)
makes
the operator a good circular edge-finder regardless of such
polarity-reversing conditions. With
o
automatically tailored
to
the stage of search for both the pupil and limbus, and by
making it correspondingly finer in successive iterations, the
operator defined in
(1)
has proven to be virtually infallible
in locating the visible inner and outer annular boundaries of
irises.
For rapid discrete implementation of the integrodifferential
operator in
(l),
it is more efficient
to
interchange the order
of convolution and differentiation and
to
concatenate them,
before computing the discrete convolution of the resulting
operator with the discrete series of undersampled sums of
pixels along circular contours of increasing radius. Using the
finite difference approximation to the derivative for a discrete
1150
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NOVEMBER
1993
series in
n,
1
1
-- -
G:)(n)
=
-GG,(nAr)
-
-GG,((n
-
l)Ar),
dr
Ar
Ar
(2)
_I
where
Ar
is a small increment in radius, and replacing the
convolution and contour integrals with sums, we can derive
through these manipulations an efficient discrete operator (see
(3)
at the bottom of the page) for finding the inner and outer
boundaries of an iris where
A0
is the angular sampling interval
along the circular arcs, over which the summed
I(z,
y)
pixel
intensities represent the contour integrals expressed in
(1).
A
nonlinear enhancement of this operator makes it more
robust for detecting the inner boundary of the iris. Because
the circular edge that defines the pupillary boundary is often
very faint, especially in dark-eyed persons, it is advantageous
to
divide each term in the convolution summation over
k
in
(3)
by a further contour integral around a smaller radius
(k
-
2)Ar.
This divisor becomes very small and stable as the
parameters
(nAr,
20,
yo)
of contour integration become well-
matched to the true location and size of the pupil, and this
helps the resulting sum
of
ratio terms (see
(4)
at the bottom
of the page)
to
achieve a distinctive maximum that reliably
locates the pupillary boundary. In essence, dividing by the
second contour integral exploits the fact that the interior of the
pupil is generally both homogeneous and dark. This creates a
suddenly very small divisor when the parameters
(nAr,
50,
yo)
are optimal for the true pupil, thus producing a sharp maximum
in the overall search operator
(4).
Using multigrid search with gradient ascent over the image
domain
(z,g)
for the center coordinates and initial radius
of each series of contour integrals, and decimating both the
incremental radius interval
Ar
and the angular sampling
interval
A8
in successively finer scales
of
search spanning four
octaves, these iris locating operations become very efficient
without loss of reliability. The total processing time on a
RISC-based CPU for iris detection and localization
to
single-
pixel precision using such operators, starting from a
640
x
480
image, is about one-quarter of a second
(250
msec) with
optimized integer code.
B.
Assessing Image Quality, Eyelid Occlusion,
and Possibility
of
Artifice
The operators previously described for finding an iris also
provide a good assessment of “eyeness,” and of the autofo-
cus performance of the video camera. The normally sharp
boundary at the limbus between the iris and the (white) sclera
generates a large positive circular edge; if a derivative larger
than a certain criterion is not detected by the searching operator
using the contour integral defined in
(3),
then this suggests
either that no eye is present, or that it
is
largely obscured
by eyelids, or that it is in poor focus or beyond resolution.
In practice the automatic identifying system that has been
built continues
to
grab image frames in rapid succession until
several frames in sequence confirm that an eye is present and
in focus, through large values being found by operator
(3),
and through large ratios of circular contour integrals being
found on either side of the putative limbus boundary. Exces-
sive eyelid occlusion
is
alleviated in cooperating Subjects by
providing live video feedback through the lens of the video
camera into which the Subject’s gaze is directed, by means of
a miniature liquid-crystal
TV
monitor displaying the magnified
image through a beamsplitter in the optical axis.
A
further test for evidence that a living eye is present
exploits the fact that pupillary diameter relative
to
iris diameter
in a normal eye is constantly changing, even under steady
illumination
[
11,
[
111.
Continuous involuntary oscillations in
pupil size, termed hippus or pupillary unrest, arise from normal
fluctuations in the activities of both the sympathetic and
parasympathetic innervation of the iris sphincter muscle
[
11.
These changes in pupil diameter relative to iris diameter over
a sequence of frames are detected by the discrete operators
(4)
and
(3),
respectively, in order
to
compute a “hippus
measure” defined as the coefficient of variation (standard
deviation divided by mean) for the fluctuating time series of
these diameter ratios. Together with the accompanying elastic
deformations in the iris texture itself arising either from normal
hippus or from a light-driven pupillomotor response, these
fluctuations could provide a test against artifice (such as a
fake iris painted
onto
a contact lens) if necessary in highly
secure implementations of this system.
(Go
((n
-k)
AT) -Go
((n
-
k
-
1)Ar))
I[
(k
AT
cos(mA0)
+z.o),
(k
Ar
sin(mA0)
+YO
)]
m
(3)
DAUGMAN: HIGH CONFIDENCE VISUAL RECOGNITION OF PERSONS
BY
A
TEST
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1151
C.
Two-Dimensional Gabor Filters
An
effective strategy for extracting both coherent and inco-
herent textural information from images, such as the detailed
texture of an iris, is the computation of
2-D
Gabor phasor
coefficients. This family of
2-D
filters were originally proposed
in
1980
by Daugman
[8]
as a framework for understanding the
orientation-selective and spatial-frequency-selective receptive
field properties of neurons in the brain's visual cortex, and
as useful operators for practical image analysis problems.
Their mathematical properties were further elaborated by
the author in
1985 [9],
who pointed out that such
2-D
quadrature phasor filters were conjointly optimal in providing
the maximum possible resolution both for information about
the orientation and spatial frequency content of local image
structure ("what"), simultaneously with information about
2-
D position ("where"). The complex-valued family of
2-D
Gabor filters uniquely achieves the theoretical lower bound
for conjoint uncertainty over these four variables, as dictated
by an inescapable uncertainty principle
[9].
These properties are particularly useful for texture analysis
[2], [4]-[7], [lo], [14]-[16], [18], [23], [29]-[31]
because of
the
2-D
spectral specificity of texture as well as its variation
with
2-D
spatial position.
A
rapid method for obtaining
the required coefficients on these elementary functions for
the purpose
of
representing any image completely by its
2-D
Gabor Transform, despite the non-orthogonality of the
expansion basis, was given in
[lo]
through the use of a
relaxation network.
A
large and growing literature now exists
on the efficient use of this nonorthogonal expansion basis and
its applications (e.g., [2],
[14], [23], [28]).
Two-dimensional Gabor filters over the image domain
(2,
y
)
have the functional form
G(z,
y)
e-K[(z-zO
)'
+(Y-YO
)2
/a2]
1
(5)
.e-2ri[llo
("-20
)+I10
(Y
-Yo
)]
where
(z0,yo)
specify position in the image,
(cr,p)
specify
effective width and length, and
(UO,
?IO)
specify modulation,
which has spatial frequency
WO
=
dGi
and direction
60
=
arctan(
UO/UO).
(A
further degree-of-freedom included
below but not captured above in
(5)
is the relative orientation
of the elliptic Gaussian envelope, which creates cross-terms
in
q.)
The
2-D
Fourier transform
F(u,
U)
of a 2-D Gabor
filter has exactly the same functional form, with parameters
just interchanged or inverted
[9]:
F(U,
U)
=
e-"[~"-"O~~"*+~"-"0~~8']e-2~i[zO~U-UO~+YO~w-~O)l~
(6)
The real part of one member of the
2-D
Gabor filter family,
centered at the origin
(50,
yo)
=
(0,O)
and with aspect ratio
P/a
=
1
is shown in Fig. 2, together with its
2-D
Fourier
transform
F(u,
U).
2-D
Gabor functions can form a complete self-similar
wavelet expansion basis
[lo],
with the requirements
of
or-
thogonality and strictly compact support
[20]-[21]
relaxed,
by appropriate parameterization for dilation, rotation, and
translation. If we take q(x,y) to be a chosen generic 2-
D Gabor wavelet, then we can generate from this member
SPATIAL FILTER PROFILE
FREQUENCY RESPONSE
Fig.
2.
The real part
of
a
2-D
Gabor
wavelet,
and
its
2-D
Fourier
transform
(from
Daugman
(1980)
[SI).
a complete self-similar family of
2-D
wavelets through the
generating function
lJj'mpgf3(Z,
Y)
=
2-2mQ(d
YO,
(7)
where the substituted variables
(2':
y')
incorporate dilations of
the wavelet in size by
2-",
translations in position
@,
q),
and
rotations through angle
6':
z'
=
2-m[xcos(0)
+
ysin(O)]
-
p
(8)
y'
=
Tm[-xsin(6')
+
ycos(O)]
-
q.
(9)
It is noteworthy
[9]
that as consequences of the similarity
theorem, shift theorem, and modulation theorem
of
Fourier
analysis, together with the rotation isomorphism of the Fourier
transform, all of these effects of the generating function
(7)
applied to a
2-D
Gabor mother wavelet
Q(z,
y)
=
G(z,
y) in
order to generate a
2-D
Gabor daughter wavelet
Qmpq~(z,
y)
have corresponding or reciprocal effects on its Fourier trans-
form
F(u,u)
without any change in functional form. This
family of wavelet filters and their Fourier transforms is closed
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1993
under the transformation group of dilations, translations, ro-
tations, and convolutions
[9].
We will exploit these self-
similarity properties of
2-D
Gabor filters in analyzing iris
textures across multiple scales to construct identifying codes.
D. Doubly Dimensionless Projected Polar Coordinate System
Zones of analysis are established on the iris in a doubly
dimensionless projected polar coordinate system. Its purpose
is to maintain reference to the same regions of iris tissue
regardless both of pupillary constriction and overall iris image
size, and hence regardless of distance to the eye and video
zoom factor. This pseudo polar coordinate system is not
necessarily concentric, since for most eyes the pupil is not
central in the iris. (Typically the pupil is both nasal to,
and inferior to, the center of the iris
[l],
and it is not
unusual for its displacement to be as great as
15%.)
The
stretching of the elastic trabecular meshwork of the iris from
constriction of the pupil is intrinsically modelled by the doubly
dimensionless projected 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
in the iris, regardless of size and pupillary dilation, a pair of
dimensionless real coordinates
(T,
e)
where
T
lies on the unit
interval
[0,1]
and
0
is the usual angular quantity that is cyclic
over
[0,2a].
The remapping of the iris image
I(z,
y)
from raw
coordinates
(x,
y)
to the doubly dimensionless nonconcentric
polar coordinate system
(T-,
0)
can be represented as
where
.(.,e)
and
y(r,e)
are defined as linear combinations
of both the set of pupillary boundary points
(.,(e),
~~(8))
around the circle that was found to maximize operator
(4),
and
the set of limbus boundary points along the outer perimeter of
the iris
(xs
(e),
ys
(e))
bordering the sclera, that was found to
maximize operator
(3):
Z(T,
e)
=
(1
-
.).,(e)
+
T-Xs(O)
(11)
Demarcations of the zones of analysis specified in this
projected doubly dimensionless coordinate system, for two
sample close-up iris images, are illustrated in Figs.
3
and
4.
These zones of analysis are assigned in the same format for all
eyes and are based on a fixed partitioning of the dimensionless
polar coordinate system, but of course for any given eye
their affine radial scaling depends on the actual pupillary
diameter (and possible offset) relative to the limbus boundary
as determined by operators
(3)
and
(4).
The zones of analysis
always exclude a region at the top of the iris where partial
occlusion by the upper eyelid is common, and a
45"
notch at
the bottom where there is a corneal specular reflection from
the filtered light source that illuminates the eye from below.
Fig.
3.
Demarcated zones
of
analysis and illustration
of
a computed iris code.
Fig.
4.
Demarcated zones
of
analysis and illustration
of
a computed iris code.
(Illumination at an angle is desirable to deflect its specular
reflection from eye-glasses, which persons are not asked to
remove. The much greater curvature of the cornea compared
with that of spectacle lenses, however, prevents elimination
of the illuminator's first Purkinje reflection from the moist
lower front surface of the cornea or of contact lenses; this
necessitates the exclusion notch in the zones of analysis near
the 6-o'clock position.)
Rotation invariance to correct for head tilt and cyclover-
gence of the eye within its orbit is achieved in a subsequent
stage of analysis of the iris code itself. The overall recog-
nition scheme is thus invariant under the PoincarC group of
transformations of the iris image: planar translation, rotation
(due to cyclovergence and tilt of the head), and dilation (due
both to imaging distance and video zoom factor). Through the
doubly dimensionless coordinate system, the constructed iris
code is also invariant under the nonaffine elastic distortion (or
projected conic transformation) that arises from variable pupil
constriction.