An Identity-Authentication System
`Using Fingerprints
`
`ANIL K. JAIN, FELLOW, IEEE, LIN HONG, SHARATH PANKANTI, ASSOCIATE MEMBER, IEEE,
`AND RUUD BOLLE, FELLOW, IEEE
`
`Fingerprint verification is an important biometric technique for
`personal identification. In this paper, we describe the design and
`implementation of a prototype automatic identity-authentication
`system that uses fingerprints to authenticate the identity of an
`individual. We have developed an improved minutiae-extraction al-
`gorithm that is faster and more accurate than our earlier algorithm
`[58]. An alignment-based minutiae-matching algorithm has been
`proposed. This algorithm is capable of finding the correspondences
`between input minutiae and the stored template without resorting to
`exhaustive search and has the ability to compensate adaptively for
`the nonlinear deformations and inexact transformations between
`an input and a template. To establish an objective assessment of
`our system, both the Michigan State University and the National
`Institute of Standards and Technology NIST 9 fingerprint data
`bases have been used to estimate the performance numbers. The
`experimental results reveal that our system can achieve a good
`performance on these data bases. We also have demonstrated that
`our system satisfies the response-time requirement. A complete
`authentication procedure, on average, takes about 1.4 seconds on
`a Sun ULTRA 1 workstation (it is expected to run as fast or faster
`on a 200 HMz Pentium [7]).
`Keywords—Biometrics, dynamic programming, fingerprint iden-
`tification, matching, minutiae, orientation field, ridge extraction,
`string matching, verification.
`
`I.
`
`INTRODUCTION
`There are two types of systems that help automatically
`establish the identity of a person: 1) authentication (verifica-
`tion) systems and 2) identification systems. In a verification
`system, a person desired to be identified submits an identity
`claim to the system, usually via a magnetic stripe card,
`login name, smart card, etc., and the system either rejects
`or accepts the submitted claim of identity (Am I who I claim
`I am?). In an identification system, the system establishes
`a subject’s identity (or fails if the subject is not enrolled
`in the system data base) without the subject’s having to
`claim an identity (Who am I?). The topic of this paper is
`
`Manuscript received October 31, 1996; revised April 26, 1997.
`A. K. Jain and L. Hong are with the Department of Computer Sci-
`ence, Michigan State University, East Lansing, MI 48824 USA (e-mail:
`jain@cps.msu.edu; honglin@cps.msu.edu).
`S. Pankanti and R. Bolle are with the Exploratory Computer Vision
`Group, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598
`USA (e-mail: sharat@watson.ibm.com; bolle@watson.ibm.com).
`Publisher Item Identifier S 0018-9219(97)06635-8.
`
`a verification system based on fingerprints, and the terms
`verification, authentication, and identification are used in a
`loose sense and synonymously.
`Accurate automatic personal identification is becoming
`more and more important to the operation of our increas-
`ingly electronically interconnected information society [13],
`[20], [53]. Traditional automatic personal
`identification
`technologies to verify the identity of a person, which use
`“something that you know,” such as a personal identifica-
`tion number (PIN), or “something that you have,” such as an
`identification (ID) card, key, etc., are no longer considered
`reliable enough to satisfy the security requirements of
`electronic transactions. All of these techniques suffer from
`a common problem of inability to differentiate between
`an authorized person and an impostor who fraudulently
`acquires the access privilege of the authorized person [53].
`Biometrics is a technology that (uniquely) identifies a per-
`son based on his physiological or behavioral characteristics.
`It relies on “something that you are” to make personal
`identification and therefore can inherently differentiate be-
`tween an authorized person and a fraudulent
`impostor
`[13], [20], [53]. Although biometrics cannot be used to
`establish an absolute “yes/no” personal identification like
`some of the traditional technologies, it can be used to
`achieve a “positive identification” with a very high level
`of confidence, such as an error rate of 0.001% [53].
`
`A. Overview of Biometrics
`Theoretically, any human physiological or behavioral
`characteristic can be used to make a personal identification
`as long as it satisfies the following requirements [13]:
`
`1) universality, which means that every person should
`have the characteristic;
`2) uniqueness, which indicates that no two persons
`should be the same in terms of the characteristic;
`3) permanence, which means that
`the characteristic
`should be invariant with time;
`4) collectability, which indicates that the characteristic
`can be measured quantitatively.
`
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`Table 1 Comparison of Biometric Technologies
`
`In practice, there are some other important requirements
`[13], [53]:
`
`1) performance, which refers to the achievable identifi-
`cation accuracy, the resource requirements to achieve
`an acceptable identification accuracy, and the working
`or environmental factors that affect the identification
`accuracy;
`2) acceptability, which indicates to what extent people
`are willing to accept the biometric system;
`3) circumvention, which refers to how easy it is to fool
`the system by fraudulent techniques.
`
`Biometrics is a rapidly evolving technology that has been
`widely used in forensics, such as criminal identification and
`prison security, and has the potential to be widely adopted
`in a very broad range of civilian applications:
`
`1) banking security, such as electronic fund transfers,
`ATM security, check cashing, and credit card trans-
`actions;
`2) physical access control, such as airport access control;
`3) information system security, such as access to data
`bases via login privileges;
`4) government benefits distribution, such as welfare dis-
`bursement programs [49];
`5) customs and immigration, such as the Immigration
`and Naturalization Service Passenger Accelerated
`Service System (INSPASS) which permits faster
`immigration procedures based on hand geometry
`[35];
`6) national ID systems, which provide a unique ID to the
`citizens and integrate different government services
`[31];
`7) voter and driver registration, providing registration
`facilities for voters and drivers.
`
`Currently, there are mainly nine different biometric tech-
`niques that are either widely used or under investigation,
`
`including face, fingerprint, hand geometry, hand vein, iris,
`retinal pattern, signature, voice print, and facial thermo-
`grams [13], [18], [20], [53], [68]. A brief comparison of
`these nine biometric techniques is provided in Table 1.
`Although each of these techniques, to a certain extent,
`satisfies the above requirements and has been used in
`practical systems [13], [18], [20], [53] or has the potential
`to become a valid biometric technique [53], not many of
`them are acceptable (in a court of law) as indisputable
`evidence of identity. For example, despite the fact that
`extensive studies have been conducted on automatic face
`recognition and that a number of face-recognition systems
`are available [3], [62], [70], it has not yet been proven that
`1) face can be used reliably to establish/verify identity and
`2) a biometric system that uses only face can achieve an
`acceptable identification accuracy in a practical environ-
`ment. Without any other information about the people in
`Fig. 1, it will be extremely difficult for both a human and a
`face-recognition system to conclude that the different faces
`shown in Fig. 1 are disguised versions of the same person.
`So far, the only legally acceptable, readily automated, and
`mature biometric technique is the automatic fingerprint-
`identification technique, which has been used and accepted
`in forensics since the early 1970’s [42]. Although signatures
`also are legally acceptable biometrics, they rank a distant
`second to fingerprints due to issues involved with accuracy,
`forgery, and behavioral variability. Currently, the world
`market for biometric systems is estimated at approximately
`$112 million. Automatic fingerprint-identification systems
`intended mainly for forensic applications account for ap-
`proximately $100 million. The biometric systems intended
`for civilian applications are growing rapidly. For example,
`by the year 1999, the world market for biometric systems
`used for physical access control alone is expected to expand
`to $100 million [53].
`The biometrics community is slow in establishing bench-
`marks for biometric systems [20]. Although benchmark
`results on standard data bases in themselves are useful only
`to a limited extent and may result in excessive tuning of the
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`Fig. 1. Multiple personalities: all of the people in this image are the same person. (From The New
`York Times Magazine, Sept. 1, 1996, sect. 6, pp. 48–49. Reproduced with permission of Robert
`Trachtenberg.)
`
`system parameters to “improve” the system performance,1
`they constitute a good starting point for comparison of the
`gross performance characteristics of the systems.
`No metric is sufficiently adequate to give a reliable and
`convincing indication of the identification accuracy of a
`biometric system. A decision made by a biometric system
`is either a “genuine individual” type of decision or an
`“impostor” type of decision, which can be represented
`by two statistical distributions, called genuine distribution
`and impostor distribution, respectively. For each type of
`decision, there are two possible decision outcomes, true or
`false. Therefore, there are a total of four possible outcomes:
`1) a genuine individual is accepted, 2) a genuine individual
`is rejected, 3) an impostor is rejected, and 4) an impostor is
`accepted. Outcomes 1) and 3) are correct, whereas 2) and 4)
`are incorrect. In principle, we can use the false (impostor)
`acceptance rate (FAR), the false (genuine individual) reject
`rate (FRR), and the equal error rate (EER)2 to indicate the
`identification accuracy of a biometric system [18], [19],
`[53]. In practice, these performance metrics can only be
`estimated from empirical data, and the estimates of the
`performance are very data dependent. Therefore, they are
`meaningful only for a specific data base in a specific test
`environment. For example, the performance of a biometric
`system claimed by its manufacturer had an FRR of 0.3%
`and an FAR of 0.1%. An independent test by the Sandia
`National Laboratory found that the same system had an
`FRR of 25% with an unknown FAR [10]. To provide a
`more reliable assessment of a biometric system, some more
`descriptive performance measures are necessary. Receiver
`operating curve (ROC) and
`are the two other commonly
`used measures. An ROC provides an empirical assessment
`
`1 Several additional techniques, like data sequestering [51] and third-
`party benchmarking [9], may also help in obtaining fairer performance
`results.
`2 Equal error rate is defined as the value where FAR and FRR are equal.
`
`of the system performance at different operating points,
`which is more informative than FAR and FRR. The statis-
`tical metric
`gives an indication of the separation between
`the genuine distribution and impostor distribution [19]. It is
`defined as the difference between the means of the genuine
`distribution and impostor distribution divided by a conjoint
`measure of their standard deviations [19]
`
`(1)
`
`where
`and
`are the means and standard deviations of the genuine
`distribution and impostor distribution, respectively. Like
`FAR, FRR, and EER, both ROC and
`also depend heavily
`on test data and test environments. For such performance
`metrics to be able to generalize precisely to the entire pop-
`ulation of interest, the test data should 1) be large enough
`to represent the population and 2) contain enough samples
`from each category of the population [19]. To obtain fair
`and honest test results, enough samples should be available,
`and the samples should be representative of the population
`and adequately represent all the categories (impostor and
`genuine). Further, irrespective of the performance measure,
`error bounds that indicate the confidence of the estimates
`are valuable for understanding the significance of the test
`results.
`
`B. History of Fingerprints
`Fingerprints are graphical flow-like ridges present on
`human fingers (see Fig. 2). Their formations depend on
`the initial conditions of the embryonic mesoderm from
`which they develop. Humans have used fingerprints as a
`means of identification for a very long time [42]. Modern
`fingerprint techniques were initiated in the late sixteenth
`century [25], [53]. In 1684, English plant morphologist N.
`
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`(a)
`
`(b)
`
`(c)
`
`(d)
`
`(e)
`
`(f)
`
`Fig. 2. Fingerprints and a fingerprint classification schema of six categories: (a) arch, (b) tented
`arch, (c) right loop, (d) left loop, (e) whorl, and (f) twinloop. Critical points in a fingerprint, called
`core and delta, are marked on (c).
`
`Grew published a paper reporting his systematic study on
`the ridge, furrow, and pore structure in fingerprints, which is
`believed to be the first scientific paper on fingerprints [42].
`Since then, a number of researchers have invested a huge
`amount of effort in studying fingerprints. In 1788, a detailed
`description of the anatomical formations of fingerprints was
`made by Mayer [16], in which a number of fingerprint
`ridge characteristics were identified. Starting from 1809, T.
`Bewick began to use his fingerprint as his trademark, which
`is believed to be one of the most important contributions in
`the early scientific study of fingerprint identification [42].
`Purkinje proposed the first fingerprint classification scheme
`in 1823, which classified fingerprints into nine categories
`according to the ridge configurations [42]. H. Fauld, in
`1880, first scientifically suggested the individuality and
`uniqueness of fingerprints. At
`the same time, Herschel
`asserted that he had practiced fingerprint identification for
`approximately 20 years [42]. This discovery established the
`foundation of modern fingerprint identification. In the late
`nineteenth century, Sir F. Galton conducted an extensive
`study of fingerprints [42]. He introduced the minutiae
`features for single fingerprint classification in 1888. An
`important advance in fingerprint identification was made
`in 1899 by E. Henry, who (actually his two assistants from
`India) established the famous “Henry system” of fingerprint
`classification [25], [42], an elaborate method of indexing
`fingerprints very much tuned to facilitating the human
`experts in performing (manual) fingerprint identification.
`By the early twentieth century, the formations of finger-
`
`prints were well understood. The biological principles of
`fingerprints are summarized below.
`• Individual epidermal ridges and furrows (valleys) have
`different characteristics for different fingers.
`• The configuration types are individually variable but
`they vary within limits that allow for systematic clas-
`sification.
`• The configurations and minute details of individual
`ridges and furrows are permanent and unchanging for
`a given finger.
`In the early twentieth century, fingerprint identification was
`formally accepted as a valid personal-identification method
`by law-enforcement agencies and became a standard routine
`in forensics [42]. Fingerprint-identification agencies were
`set up worldwide, and criminal fingerprint data bases were
`established [42].
`Starting in the early 1960’s, the Federal Bureau of Inves-
`tigation (FBI) home office in the United Kingdom and the
`Paris Police Department invested a large amount of effort
`in developing automatic fingerprint-identification systems
`(AFIS’s) [25]. Their efforts were so successful that a large
`number of AFIS’s are currently installed and in operation
`at
`law-enforcement agencies worldwide. These systems
`have greatly improved the operational productivity of these
`agencies and reduced the cost of hiring and training human
`fingerprint experts for manual fingerprint
`identification.
`Encouraged by the success achieved by AFIS’s in law-
`enforcement agencies, automatic fingerprint identification
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`rapidly grew beyond law enforcement into civilian applica-
`tions [25], [53]. In fact, fingerprint-based biometric systems
`are so popular that they have almost become the synonym
`of biometric systems [20]. Although significant progress has
`been made in designing automatic fingerprint-authentication
`systems over the past 30 years, a number of design factors
`(lack of reliable minutiae-extraction algorithms [48], [54],
`difficulty in quantitatively defining a reliable match between
`fingerprint images [43], [45], poor fingerprint classification
`algorithms [12], [14] [39], [46], [57], [74], etc.) create
`bottlenecks in achieving the desired performance [25], [42].
`
`C. Design of a Fingerprint-Verification System
`An automatic fingerprint identity authentication system
`has four main design components: acquisition, representa-
`tion (template), feature extraction, and matching.
`1) Acquisition: There are two primary methods of cap-
`turing a fingerprint image: inked (off-line) and live scan
`(ink-less). An inked fingerprint image is typically acquired
`in the following way: a trained professional3 obtains an
`impression of an inked finger on a paper, and the impression
`is then scanned using a flat-bed document scanner. The live-
`scan fingerprint is a collective term for a fingerprint image
`directly obtained from the finger without the intermediate
`step of getting an impression on a paper. Acquisition of
`inked fingerprints is cumbersome; in the context of an
`identity-authentication system,
`it
`is both infeasible and
`socially unacceptable for identity verification.4 The most
`popular technology to obtain a live-scan fingerprint image
`is based on the optical frustrated total internal reflection
`(FTIR) concept [28]. When a finger is placed on one side
`of a glass platen (prism), ridges of the finger are in contact
`with the platen while the valleys of the finger are not.
`The rest of the imaging system essentially consists of an
`assembly of a light emitting diode (LED) light source and
`a charge-couple device (CCD) placed on the other side of
`the glass platen. The laser light source illuminates the glass
`at a certain angle, and the camera is placed such that it can
`capture the laser light reflected from the glass. The light
`that is incident on the plate at the glass surface touched by
`the ridges is randomly scattered, while the light incident
`at the glass surface corresponding to valleys suffers total
`internal reflection, resulting in a corresponding fingerprint
`image on the imaging plane of the CCD.
`A number of other live-scan imaging methods are now
`available, based on ultrasound total internal reflection [61],
`optical total internal reflection of edge-lit holograms [21],
`thermal sensing of the temperature differential (across the
`ridges and valleys) [41], sensing of differential capaci-
`tance [47], and noncontact three-dimensional scanning [44].
`These alternate methods are primarily concerned with either
`reducing the size/price of the optical scanning system or
`improving the quality/resolution/consistency of the image
`
`3 For reasons of expediency, MasterCard sends fingerprint kits to its
`credit card customers. The kits are used by the customers themselves to
`create an inked fingerprint impression to be used for enrollment.
`4 Again, MasterCard relies on inked impressions for enrollment.
`
`live-scan
`
`capture. Typical specifications for the optical
`fingerprints are specified in [60].
`2) Representation (Template): Which machine-readable
`representation completely captures
`the invariant and
`discriminatory information in a fingerprint image? This
`representation issue constitutes the essence of fingerprint-
`verification design and has far-reaching implications on the
`design of the rest of the system. The unprocessed gray-
`scale values of the fingerprint images are not invariant over
`the time of capture.
`Representations based on the entire gray-scale profile of
`a fingerprint image are prevalent among the verification
`systems using optical matching [4], [50]. The utility of
`the systems using such representation schemes, however,
`may be limited due to factors like brightness variations,
`image-quality variations, scars, and large global distortions
`present in the fingerprint image because these systems are
`essentially resorting to template-matching strategies for ver-
`ification. Further, in many verification applications, terser
`representations are desirable, which preclude representa-
`tions that involve the entire gray-scale profile fingerprint
`images. Some system designers attempt to circumvent this
`problem by restricting that the representation is derived
`from a small (but consistent) part of the finger [50]. If this
`same representation is also being used for identification
`applications, however, then the resulting systems might
`stand a risk of restricting the number of unique identities
`that could be handled simply because of the fact that the
`number of distinguishable templates is limited. On the
`other hand, an image-based representation makes fewer
`assumptions about the application domain (fingerprints) and
`therefore has the potential to be robust to wider varieties of
`fingerprint images. For instance, it is extremely difficult to
`extract a landmark-based representation from a (degenerate)
`finger devoid of any ridge structure.
`Representations that rely on the entire ridge structure
`(ridge-based representations) are largely invariant to the
`brightness variations but are significantly more sensitive to
`the quality of the fingerprint image than the landmark-based
`representations described below. This is because the pres-
`ence of the landmarks is, in principle, easier to verify [75].
`An alternative to gray-scale-based representation is to ex-
`tract landmark features from a binarized fingerprint image.
`Landmark-based representations are also used for privacy
`reasons—one cannot reconstruct the entire fingerprint im-
`age from the fingerprint landmark information alone. The
`common hypothesis underlying such representations is the
`belief that the individuality of fingerprints is captured by
`the local ridge structures (minute details) and their spatial
`distributions [25], [42]. Therefore, automatic fingerprint
`verification is usually achieved with minute-detail matching
`instead of a pixel-wise matching or a ridge-pattern matching
`of fingerprint images. In total, there are approximately 150
`different types of local ridge structures that have been iden-
`tified [42]. It would be extremely difficult to automatically,
`quickly, and reliably extract these different representations
`from the fingerprint
`images because 1) some of them
`are so similar to each other and 2) their characterization
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`(a)
`
`(b)
`
`Fig. 3. Ridge ending and ridge bifurcation.
`
`depends upon the fine details of the ridge structure, which
`are notoriously difficult to obtain from fingerprint images
`of a variety of quality. Typically, automatic fingerprint
`identification and authentication systems rely on repre-
`senting the two most prominent structures5: ridge endings
`and ridge bifurcations. Fig. 3 shows examples of ridge
`endings and ridge bifurcations. These two structures are
`background-foreground duals of each other, and pressure
`variations could convert one type of structure into the
`other. Therefore, many common representation schemes
`do not distinguish between ridge endings and bifurca-
`tions. Both the structures are treated equivalently and are
`collectively called minutiae. The simplest of the minutiae-
`based representations constitute a list of points defined by
`their spatial coordinates with respect to a fixed image-
`centric coordinate system. Typically, though, these minimal
`minutiae-based representations are further enhanced by tag-
`ging each minutiae (or each combination of minutiae subset,
`e.g., pairs, triplets) with additional features. For instance,
`each minutiae could be associated with the orientation of the
`ridge at that minutiae; or each pair of the minutiae could be
`associated with the ridge count: the number of ridges visited
`during the linear traversal between the two minutiae. The
`American National Standards Institute–National Institute of
`Standards and Technology (NIST) standard representation
`of a fingerprint is based on minutiae and includes minutiae
`location and orientation [2]. The minutiae-based represen-
`tation might also include one or more global attributes like
`orientation of the finger, locations of core or delta,6 and
`fingerprint class.
`Our representation is minutiae based, and each minutia
`is described by its location (
`coordinates) and the
`orientation. We also store a short segment of the ridge
`associated with each minutia.
`3) Feature Extraction: A feature extractor finds the ridge
`endings and ridge bifurcations from the input fingerprint
`images. If ridges can be perfectly located in an input
`
`5 Many of the other ridge structures could be described as a combination
`of ridge endings and bifurcations [42].
`6 Core and delta are the two distinctive global structures in a fingerprint
`[25]; see Fig. 2(c).
`
`fingerprint image, then minutiae extraction is just a triv-
`ial task of extracting singular points in a thinned ridge
`map. In practice, however, it is not always possible to
`obtain a perfect ridge map. The performance of currently
`available minutiae-extraction algorithms depends heavily
`on the quality of input fingerprint images. Due to a number
`of factors (aberrant formations of epidermal ridges of
`fingerprints, postnatal marks, occupational marks, problems
`with acquisition devices, etc.), fingerprint
`images may
`not always have well-defined ridge structures. Reliable
`minutiae-extraction algorithms should not assume perfect
`ridge structures and should degrade gracefully with the
`quality of fingerprint images. We have developed a modified
`version of the minutiae-extraction algorithm proposed in
`[58] that is faster and more reliable. Our minutiae-extraction
`scheme is described in the Section II.
`4) Matching: Given two (test and reference) representa-
`tions, the matching module determines whether the prints
`are impressions of the same finger. The matching phase
`typically defines a metric of the similarity between two
`fingerprint representations. The matching stage also defines
`a threshold to decide whether a given pair of representations
`are of the same finger (mated pair) or not.
`In the case of the minutiae-based representations, the
`fingerprint-verification problem may be reduced to a point
`pattern matching (minutiae pattern matching) problem. In
`the ideal case, if 1) the correspondence between the tem-
`plate minutiae pattern and input minutiae pattern is known,
`2) there are no deformations such as translation, rota-
`tion, and deformations between them, and 3) each minutia
`present in a fingerprint image is exactly localized, then
`fingerprint verification is only a trivial task of counting the
`number of spatially matching pairs between the two im-
`ages. Determining whether two representations of a finger
`extracted from its two impressions, possibly separated by
`a long duration of time, are indeed representing the same
`finger is an extremely difficult problem. Fig. 4 illustrates
`the difficulty with an example of two images of the same
`finger. The difficulty can be attributed to two primary
`reasons. First, if the test and reference representations are
`indeed mated pairs, the correspondence between the test and
`reference minutiae in the two representations is not known.
`Second, the imaging system presents a number of peculiar
`and challenging situations, some of which are unique to a
`fingerprint image capture scenario.
`
`1) Inconsistent contact: the act of sensing distorts the
`finger. Determined by the pressure and contact of the
`finger on the glass platen, the three-dimensional shape
`of the finger gets mapped onto the two-dimensional
`surface of the glass platen. Typically, this mapping
`function is uncontrolled and results in different in-
`consistently mapped fingerprint
`images across the
`impressions.
`2) Nonuniform contact: The ridge structure of a finger
`would be completely captured if ridges of the part
`of the finger being imaged are in complete optical
`contact with the glass platen. However, the dryness of
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`CPC EX 2044 - Page 006 ASSA ABLOY AB v. CPC Patent Technologies Pty Ltd.
`IPR2022-01093
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`semipermanently. This may introduce additional spu-
`rious minutiae.
`4) Feature extraction artifacts: The feature extraction
`algorithm is imperfect and introduces measurement
`errors. Various image-processing operations might
`introduce inconsistent biases to perturb the location
`and orientation estimates of the reported minutiae
`from their gray-scale counterparts.
`5) Sensing act: the act of sensing itself adds noise to the
`image. For example, residues are leftover from the
`previous fingerprint capture. A typical finger-imaging
`system distorts the image of the object being sensed
`due to imperfect imaging conditions. In the FTIR
`sensing scheme, for example, there is a geometric
`distortion because the image plane is not parallel to
`the glass platen.
`
`In light of the operational environments mentioned above,
`the design of the matching algorithms needs to establish and
`characterize a realistic model of the variations among the
`representations of mated pairs. This model should include
`the properties of interest listed below.
`
`a) The finger may be placed at different locations on the
`glass platen, resulting in a (global) translation of the
`minutiae from the test representation from those in
`the reference representation.
`b) The finger may be placed in different orientations on
`the glass platen, resulting in a (global) rotation of the
`minutiae from the test representation from that of the
`reference representation.
`c) The finger may exert a different (average) downward
`normal pressure on the glass platen, resulting in a
`(global) spatial scaling of the minutiae from the test
`representation from those in the reference represen-
`tation.
`d) The finger may exert a different (average) shear force
`on the glass platen, resulting in a (global) shear
`transformation (characterized by a shear direction and
`magnitude) of the minutiae from the test representa-
`tion from those in the reference representation.
`e) Spurious minutiae may be present in both the refer-
`ence and the test representations.
`f) Genuine minutiae may be absent in the reference or
`test representations.
`g) Minutiae may be locally perturbed from their “true”
`location, and the perturbation may be different for
`each individual minutiae. (Further, the magnitude of
`such perturbation is assumed to be small and within
`a fixed number of pixels.)
`h) The individual perturbations among the correspond-
`ing minutiae could be relatively large (with respect
`to ridge spacings), but the perturbations among pairs
`of the minutiae are spatially linear.
`i) The individual perturbations among the corresponding
`minutiae could be relatively large (with respect to
`
`(a)
`
`(b)
`
`Fig. 4. Two different fingerprint impressions of the same finger.
`To know the correspondence between the minutiae of these two
`fingerprint images, all of the minutiae must be precisely localized
`and the deformations must be recovered.
`
`the skin, skin dise