Abstract:
A method of analyzing and recognizing fingerprint images that utilizes vector processing of a vector field that is defined as the tangential vector of the fingerprint ridge curves is disclosed. The raw fingerprint image is divided into blocks, filtered to remove noise, and the orientation direction of each block is found. This allows the ridge curves to be enhanced and approximated by piece-wise linear approximations. The piece-wise linear approximations to the ridge curves allow the minutiae to be extracted and classified and a fingerprint minutiae template to be constructed. An enrollment process gathers multiple fingerprint images, creates fingerprint minutiae templates corresponding to the acquired fingerprint images, and stores the templates and other data associated with the respective individual or the enrolled fingerprint in a fingerprint database. In an identification process, an unknown raw fingerprint image is obtained via a fingerprint scanner and processed similarly to the enrollment process such that the fingerprint minutiae template of the unknown fingerprint is compared to one or more previously enrolled fingerprint minutiae templates. The identity of the individual associated with the unknown fingerprint is thereby ascertained. In addition, live finger detection can be accomplished in conjunction with the verification or identification process through analysis of the fingerprint image thus enhancing the security of the overall system.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Serial No. 60/293,487 filed May 25, 2001 and U.S. Provisional Patent Application Serial No. 60/338,949 filed Oct. 22, 2001. 
     
    
     
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
         [0002]    N/A  
         BACKGROUND OF THE INVENTION  
         [0003]    A biometric is defined as a biological characteristic or trait that is unique to an individual and that can be accurately measured. A biometric that can be stored and accessed in an efficient manner can be used to identify an individual or to verify the identity of an individual. A biometric commonly used to identify human beings is one or more fingerprints belonging to the particular human being.  
           [0004]    Fingerprint identification of a human being consists of two stages: enrollment and verification/identification. Enrollment of a fingerprint involves taking a fingerprint image (FPI) of an individual and storing the FPI itself or a plurality of data that is representative of the FPI in an FPI database. Identification of a fingerprint involves taking an FPI of an unknown individual and comparing the unknown FPI to the FPIs or FPI data that is stored in the FPI database. An identification is made when a match between the unknown FPI and an FPI stored in the FPI database is found that has a sufficient reliability that the probability of a false positive is below a predetermined threshold. Fingerprint verification or authentication matches an individual to a fingerprint that has been previously enrolled by that individual. Thus, identification involves searching for a match between a single unknown FPI with many stored FPIs. The verification process involves the matching an unknown or unconfirmed fingerprint minutiae template to a single previously enrolled fingerprint minutia template. Accordingly, the verification process is a one-to-one matching technique.  
           [0005]    The use of biometrics to restrict access to secure entities such as computer networks, cryptographic keys, sensitive data, and physical locations is well known. In addition, smart cards, cards that have a biometric, such as a fingerprint, encoded thereon can be used to provide transaction security as well. A smart card allows a user to provide the biometric encoded on the card, wherein the encoded biometric data is compared to the biometric measured on the individual. In this way, a smartcard can positively authenticate the identity of the smartcard user.  
           [0006]    However, traditional FPI data is based on the set of singularities that can be classified according the type of singularity, e.g., deltas, arches, or whorls. In addition, FPIs contain fingerprint minutiae that are the end point of a ridge curve or a bifurcation point of a ridge curve. FPI images can be classified and matched according to data associated with the fingerprint minutiae. This data can include the position of the minutiae, the tangential direction of the minutiae, and the distance to other minutiae. These types of FPI data can lead to a high false acceptance or identification rate when the unknown FPI has only a few minutiae or if the unknown FPI is only a partial FPI that may or may not include the number of minutiae needed to accurately verify or identify the unknown FPI.  
           [0007]    Therefore what is needed is a method and apparatus to collect, analyze, and store FPI data such that an unknown or unverified FPI can be accurately verified or identified in the FPI or whether the FPI is only a partial print.  
         BRIEF SUMMARY OF THE INVENTION  
         [0008]    A method of analyzing and recognizing fingerprint images that utilizes vector processing of a vector field that is defined as the tangential vector of the fingerprint ridge curves is disclosed. The raw fingerprint image is divided into blocks, each block is filtered to remove noise and the orientation direction of each block is found. This allows the ridge curves to be enhanced and approximated by piece-wise linear approximations. The piecewise linear approximations to the ridge curves allow the minutiae to be extracted and classified and a fingerprint minutiae template to be constructed. An enrollment process gathers multiple fingerprint images, creates fingerprint minutiae templates corresponding to the fingerprint images, and stores the templates and other data associated with the respective individual or the enrolled fingerprint in a fingerprint database. In an identification or verification process an unknown raw fingerprint image is obtained via a fingerprint scanner and processed similarly to the enrollment process described above. The fingerprint minutiae template of the unknown fingerprint is compared to one or more previously enrolled fingerprint minutiae templates to identify or verify the identity of the individual associated with the unknown fingerprint. In addition, live finger detection can be accomplished in conjunction with the identification or verification processes through analysis of the fingerprint image thus enhancing the security of the overall system.  
           [0009]    Other forms, features, and aspects of the above-described methods and system are described in the detailed description that follows.  
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING  
       [0010]    The invention will be more fully understood from the following detailed description taken in conjunction with the accompanying drawings in which:  
         [0011]    [0011]FIG. 1 is a flow chart of a method for acquiring and enrolling fingerprint minutiae templates;  
         [0012]    [0012]FIG. 2 is a flow chart of a method for extracting minutiae from a raw fingerprint image and forming a fingerprint minutiae template;  
         [0013]    [0013]FIG. 3 is a schematic diagram of a direction filter suitable for use in the present fingerprint analysis method;  
         [0014]    [0014]FIG. 4 is a flow chart of a method for identifying/verifying the identity of an individual using the presently described fingerprint analysis method;  
         [0015]    [0015]FIG. 5 is a flow chart of a method for comparing an unknown fingerprint minutiae template with a previously enrolled fingerprint minutiae template;  
         [0016]    [0016]FIG. 6 is block diagram for a system to control physical access using the fingerprint analysis methods described herein;  
         [0017]    [0017]FIG. 7 is a block diagram for a system to control computer network access using the fingerprint analysis methods described herein;  
         [0018]    [0018]FIG. 8 is a block diagram for a system to control access to a web page across the internet using the fingerprint analysis methods described herein;  
         [0019]    [0019]FIG. 9 is a flow chart for a method of using the presently described fingerprint analysis methods in conjunction with a smartcard;  
         [0020]    [0020]FIG. 10 is a flow chart for a method of detecting a live finger by analyzing the binary fingerprint image;  
         [0021]    [0021]FIG. 11 is a flow chart for a method of detecting and classifying singularities found in the finger print image; and  
         [0022]    [0022]FIG. 12 is a flow chart for a method of estimating the resolution of a raw fingerprint image. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]    A fingerprint image (FPI) acquisition, analysis, storage, and recognition system is disclosed in which FPIs are acquired and a fingerprint template based upon the acquired FPI is created. The fingerprint template is stored and can be used to both identify an unknown FPI and to verify the identity of an FPI.  
         [0024]    [0024]FIG. 1 is block diagram of the enrollment process used to acquire an FPI and to store the corresponding fingerprint template. In particular, the raw FPI is acquired from a fingerprint sensor or scanner or a scanned FPI, as depicted in step  102 . As used herein a raw FPI is defined as an original fingerprint image captured by a fingerprint sensor or scanner or a raw fingerprint can be a digitally scanned image of a paper and ink fingerprint. A raw FPI includes a plurality of ridge curves and valleys interspersed between the various ridge curves corresponding to the ridges and valleys of the original fingerprint. The ridge curves and valleys form various structures that include singularities such as whorls, deltas, arches, and also include fingerprint minutiae that are the ending point of ridge curves or bifurcation points of ridge curves. Each of the minutiae has data associated therewith that is indicative of the position of the minutiae, the tangential direction of the minutiae, and the type of minutiae.  
         [0025]    The raw FPI is processed to enhance the contrast between the ridge curves and valleys contained in the FPI, as depicted in step  104 . As depicted in step  106 , the quality of the enhanced FPI is evaluated and if the quality of the FPI is sufficiently high, the minutiae from the FPI are extracted and control is passed to step  108 . If not, control passes to step  102  and another FPI is acquired. As depicted in step  108 , the number of minutia are examined and if there are sufficient minutiae, control is passed to step  110  where the minutiae are extracted from the FPI and an FPI template is formed. In general the number of minutiae that are required is dependent upon the level of security that is required. A low security application may only require six minutiae that are able to be matched, while a high security application may require 12 or more minutiae that are able to be matched.  
         [0026]    As used herein a fingerprint template is an undirected graph of minutiae extracted from an FPI. Each node in the fingerprint template is an individual minutia and each connecting segment in the graph connects two minutiae (i.e., graph nodes). Each connecting segment also includes data associated therewith, for example, cross points of the connecting segment with ridge curves, and the angles between the direction of the connecting segment and the tangential direction of the ridge curve at the intersecting point. In addition, the template can include data on the core and deltas associated with the FPI. For example, the FPI template can include data associated with a core or delta such as the position and direction of respective core and delta.  
         [0027]    The fingerprint template is associated with the individual and then stored in a fingerprint template database, as depicted in step  112 . If there are a not sufficient number of minutiae, control passes to step  102  and another RAW FPI is acquired.  
         [0028]    [0028]FIG. 2 is a flowchart that describes the various steps necessary to perform the image processing of the raw FPI, the minutiae extraction, and the FPI template formation. The steps depicted in FIG. 2 can be used to process raw FPIs for enrollment purposes, and raw FPIs for identification or identity verification purposes.  
         [0029]    As depicted in FIG. 2, a raw FPI is acquired from a fingerprint scanner or from scanning a paper and ink fingerprint, or from a previously digitized FPI, as depicted in step  202 . The raw FPI is separated into an array of non-overlapping blocks, as depicted in step  204 . The block size can be selected based upon various parameters such as the size of the FPI, the amount of data contained therein, and the processor speed. Preferably, the block size is selected as a function of the resolution of the FPI such that within each block, the ridge curves can be approximated by straight lines. In one preferred embodiment, the block size is given by {fraction (R/25)} and rounded to the closest power of 2, where R is the resolution of the FPI in dots/inch. In the ilustrated embodiment, the resolution of a typical fingerprint scanner is approximately 500 dpi and is divided into 256 blocks in a 16×16 block pattern of equal size blocks. In another embodiment, the block size may be varied within an FPI depending upon the size of the object within the FPI that is to be processed.  
         [0030]    The blocked image is processed to provide one or more regions of interest, as depicted in step  206 . A region of interest in the FPI is a portion or portions of the FPI containing the ridge curves and valleys of the FPI, the remaining portion or portions of the FPI do not contain any significant fingerprint data. To determine the regions of interest, the FPI is separated into foreground blocks and background blocks, as depicted in step  206 . In one embodiment, the mean and variance of the pixel intensities are determined for each block. A predetermined mean threshold and variance threshold are selected and a k-nearest neighbor clustering algorithm is used to classify all blocks within the K-nearest neighbors as a foreground block or a background block. In a preferred embodiment, a convex hull is formed that includes all of the blocks determined to be foreground blocks. A second check of all background blocks is made to ensure that noise or other interference has not inadvertently switched a foreground block into a background block. A check is made to determine if the center of a previously determined background block is contained within the convex hull formed by the foreground blocks. If so, the background block is converted into a foreground block.  
         [0031]    The regions of interest in the FPI are filtered to remove random noise in order to form a clearer filtered mage, as depicted in step  208 . Random noise is typically high frequency noise and accordingly a low pass filter is used to smooth out the high frequency noise from the foreground blocks of the blocked image. In one embodiment, the low pass filter is a Gaussian filter. The Gaussian filter can be a 2-dimensional filter mask that when convolved with each pixel, within each of the foreground blocks, removes the high frequency noise contained within the FPI.  
         [0032]    The orientation angle and magnitude of each of the foreground blocks in the filtered image are found, forming an orientation image, as depicted in step  210 . In general, the orientation angle and magnitude are found by determining the gradient in the x and y directions. In one embodiment, a Sobel differential operator is applied to each foreground block to determine the orientation angle and amplitude. In the event that the orientation amplitude is below a predetermined threshold, a Hough transformation is used to estimate the orientation angle.  
         [0033]    The contrast between the ridge curves and the valleys in the orientation image is increased forming a ridge-enhanced FPI, as depicted in step  212 . In particular, a plurality of directional filters each corresponding to a foreground block smoothes out the differences along the ridge curves and intensifies the contrast between the ridge curves and valleys within the corresponding block. In one embodiment, the directional filter is a 2-dimensional mask having an x and y direction. The y direction of the mask is intended to amplify the fingerprint ridge curves and to negatively amplify the valleys. In one embodiment, the directional filter is a Gaussian filter along the ridge direction.  
         [0034]    A directional filter mask is depicted in FIG. 3 in which the filter mask  300  is a square in which the side length is equal to the period of the signal, or the period of the signal plus 1, whichever is an odd number. The middle rows  302  are selected to enhance the ridges, and the side rows  310  are used to negatively amplify the valleys. There may be transition rows  308  between the middle rows  302  and the side rows  308  that have coefficients equal to zero. The center coefficient, a 0 ,  305  of the center row  304  is set to a 0  and the coefficients of the center row  304  are cosine tapered to edge values of a 0 /4 forming a symmetric row. In the illustrated embodiment, a 0  is set to 1000 and the center row  304  is cosine tapered to a value of 250 at each edge. The coefficients of the middle rows  302  are cosine tapered from the value of the center row to a value of a 0,i /1.41, where a 0,i  is the value of the i th  coefficient of the center row  304 . The value of each coefficient of the side rows  310  is given by  
         b   i     =       -     1   2            (       ∑     j   =   1     m                     a     i   ,   j         )                             
 
         [0035]    where i is the i th  coefficient of the side row and m is the number of middle rows. Once the directional filter mask for a block has been determined, the directional filter mask is convolved with the pixels in the corresponding block.  
         [0036]    The ridges and valleys of the ridge-enhanced FPI are then separated into one of two binary values, a first binary value for a ridge pixel and a second binary value for a valley pixel, forming a binary fingerprint image, as depicted in step  214 . In particular, the image binarization is accomplished by establishing a binary threshold and comparing the intensity value of each pixel to the binary threshold. A pixel having a pixel value greater than the binary threshold is set to a first value and a pixel having a pixel value less than the binary threshold is set to a second value. In one embodiment in which the maximum pixel intensity is 255, the binary threshold is one-half the maximum pixel intensity or 128. The first value is equal to 255 and the second value is equal to zero.  
         [0037]    The ridge curves and valleys of the binary FPI are thinned to a predetermined width, which in the illustrated embodiment is a single pixel forming a thinned image, as depicted in step  216 . The thinning may be accomplished with thinning algorithms that are known in the art.  
         [0038]    The thinned ridge curves and valleys in the thinned image are approximated by piece-wise linear segments forming a piecewise linear FPI, as depicted in step  218 . The thinned ridge curves are represented by chain code connecting the start and end points of each ridge curve within a corresponding block. A line segment connecting the start and end points of the respective ridge curve is formed and the maximum distance between the line segment and the ridge curve is determined. If this distance is greater than a predetermined maximum value, two line segments approximate the ridge curve. A first line segment is formed from the start point to the point on the ridge curve having the maximum distance from the original line segment. A second line segment is formed from the end point of the first line segment to the end point of the ridge curve. This process is continued iteratively until the distance between the ridge curve and any point on the piece wise linear approximating segments is less than the predetermined minimum value.  
         [0039]    The fingerprint minutiae are extracted from the piece-wise linear FPI, as depicted in step  220 . In general, minutiae are classified as either ending minutiae or bifurcation minutiae.  
         [0040]    Ending minutiae are defined as the end point of a ridge curve in an FPI and bifurcation minutiae are defined as a crossing point of two ridge curves in an FPI. In particular, a connection number is computed for each pixel in a corresponding block, wherein the connection number is indicative of whether a pixel is a fingerprint minutia and if so, what type of minutia the corresponding pixel is. The connection number is equal to  
         CN   =     (       ∑     i   =   1     7                       1   2                 P   i     -     P     i   +   1                  )       ,                         
 
         [0041]    where P i  and P i+1 , are the values of the 8 pixels surrounding the pixel of interest. The connection number corresponds to the properties detailed in Table 1:  
                   TABLE 1                       Connection number, CN, value   Property                   0   Pixel is an isolated point       1   Pixel is an end point       2   Pixel is a continuing point       3   Pixel is a branching point       4   Pixel is a crossing point                  
 
         [0042]    For a CN value of 1 or 3, the angle of the ending point or the branching point to the associated ridge curve is determined. The minutiae type, the x-y position of the minutiae, and the angle of the minutiae associated with the respective ridge curve are determined and stored.  
         [0043]    The extracted minutiae are further processed to remove false minutiae leaving true minutiae as depicted in step  222 . As can be appreciated, a large number of false minutiae can be created and detected during the processing steps prior to this step. These minutiae may be due to small ridge segments, ridge breaks, boundary minutiae, and noise.  
         [0044]    For every minutiae extracted in step  220 , the minutiae is analyzed to see if the minutiae belongs to a broken ridge curve, a noisy link, or if the extracted minutiae is a boundary minutiae. A broken ridge curve occurs when two minutiae are within a predetermined distance of one another and the directions of the respective minutiae are opposite to one another. If the number of minutiae within a specified area exceeds a predetermined threshold, the minutiae are considered to be part of a noisy link. If minutiae occur along the boundary of the FPI, it is considered to be boundary minutiae. In the event that the extracted minutiae belong to one of these three classes, the minutiae is deleted from the extracted minutiae list.  
         [0045]    A fingerprint minutiae template is then formed from the true minutiae, as depicted in step  224 . In particular, a fingerprint minutiae template is an undirected graph in which the true minutiae are the corresponding nodes and line segments connected between two-node points form the edges of the graph. Each of the true minutiae is only connected to other true minutiae within a predetermined distance of it. Data associated with the intersection between a graph edge and any of the ridge curves in the FPI is also stored. This data can include the location of the intersection, i.e., the intersection points, and the angles between the graph edge and tangential direction of the ridge curve.  
         [0046]    [0046]FIG. 4 depicts a block diagram of an embodiment of the verification/identification process. A raw FPI is acquired from a finger print sensor or scanner, as depicted in step  402 . The acquired FPI is processed, as depicted in step  404 , and if the image is suitable for minutiae extraction as depicted in step  406 , the number of minutiae that exist in the FPI is determined, as depicted in step  408 . If sufficient minutiae exist in the FPI, the minutiae are extracted and a fingerprint minutiae template is formed as described with respect to FIG. 2, as depicted in step  410 . If the image is not suitable to extract minutiae then control passes to step  402  and a new raw FPI is acquired.  
         [0047]    If the fingerprint minutiae template is formed, one or more of the previously enrolled templates are compared to the fingerprint minutiae template of the raw FPI, as depicted in step  412 . In the verification process, a single enrolled template that is known a-priori may be compared to the template of the raw FPI in a one to one matching scheme, where the alleged identity of the individual to be verified is known. In the identification process, many of the enrolled templates are compared to the template of the raw FPI in a one to many matching scheme. As discussed in more detail below, the enrolled templates and the template of the raw FPI may be classified according to various characteristics such as the presence of singularities in the FPI to reduce the number of enrolled fingerprint templates to be searched. The number of minutiae that are matched is compared to a predetermined threshold, as depicted in step  414 , and if the number of matched minutiae exceeds the predetermined verification threshold, the enrolled template and the unknown/unverified template of the raw FPI are considered matched, as depicted in step  416 . Accordingly, the person is identified or verified as the individual associated with the enrolled template. If the individual associated with the unknown/unverified FPI is cleared for entry into a secure entity such as a computer, a data network, or a physical space, entry is granted as depicted in step  418 . Otherwise, control is passed back to step  402  for acquisition of another FPI.  
         [0048]    [0048]FIG. 5 depicts an embodiment of a matching process suitable for use with the identification/verification methods described herein. Having acquired an enrolled fingerprint template and a fingerprint template to be identified/verified, first find all node pairs (A, B) that are locally matched, as depicted in step  502 , where A is a minutiae node from the enrolled template and B is a minutiae node from the template to be identified/verified. For each identified node pair (A,B) a transformation T(B−&gt;A) is formed, as depicted in step  504 . The transformation T(B−&gt;A) is defined as the translation of B to A and the rotation of B necessary to align B to A. Each node pair (A,B) is further used as an anchor node and a neighborhood match is performed in the neighborhood of the anchor node using the corresponding transformation T(B−&gt;A), as depicted in step  506 . The transformed minutiae nodes in the neighborhood of the node pair (A,B) in each template are compared with one another and if the differences in position and rotation between corresponding minutiae are less than a predetermined matching threshold, the minutiae are considered to be matched, as depicted in step  508 ,  510 , and  512 . For each node pair (A,B), the number of matched minutiae are counted, as depicted in step  514 . The number of matched minutiae are compared to a matching threshold, as depicted in step  516 . If the number of matched minutiae exceeds the matching threshold, the fingerprint templates are considered to be matched, as depicted in step  518 , otherwise, control is returned to step  502 .  
         [0049]    [0049]FIG. 6 depicts a block diagram of a physical access control system  600 . A fingerprint scanner  602  is used to scan a fingerprint. The scanned FPI is provided to a fingerprint server  606  that contains fingerprint templates of enrolled individuals. The fingerprint server  606  creates a fingerprint minutiae template of the scanned FPI and compares the template to the previously enrolled templates corresponding to the individuals cleared for access to the secure location. A positive match between the fingerprint minutiae template of the scanned FPI and one of the previously enrolled fingerprint minutiae templates will positively identify the individual if enrolled. The fingerprint server  606  provides for match/no-match indicia to be provided to the physical access device  604  allowing access into the secured area. Note that the actual identity of the person seeking to gain entrance does not have to be ascertained, although it may be. Only the occurrence of a match between one of the group of enrolled fingerprint templates and the fingerprint minutiae template of the scanned FPI is required. However, in a further embodiment additional conventional identification establishing technologies may be implemented in conjunction with the fingerprint analysis and identification/verification described herein.  
         [0050]    [0050]FIG. 7 depicts a block diagram of a network logon control system  700 . A fingerprint sensor or scanner  702  coupled to a user PC  704  is used to provide scanned fingerprint data across a data network  706  to a fingerprint server  708 . The fingerprint server  708  creates a fingerprint minutiae template of the scanned FPI and compares this template to the previously enrolled fingerprint minutiae templates corresponding to the individuals cleared for access to the computer network. A match between the newly created fingerprint minutiae template and one or more of the previously enrolled fingerprint minutiae templates indicates that the individual is allowed access to the computer network. In addition, the fingerprint server  708  can positively identify the particular individual seeking access and, once verified, provide the identity and the relevant data of the individual to the network server  710 .  
         [0051]    [0051]FIG. 8 depicts a block diagram of an internet logon control system  800 . A fingerprint sensor or scanner  802  coupled to a user PC  804  is used to provide a scanned fingerprint across the internet  806  to a fingerprint server  808  that may be associated with a particular web page or associated with a secure financial transaction that occurs over the internet. The fingerprint server  808  creates a fingerprint minutiae template of the scanned FPI and compares this template to the previously enrolled fingerprint minutiae templates corresponding to the individuals cleared for access to the computer network. A match between the newly created fingerprint minutiae template and the previously enrolled fingerprint minutiae templates indicates that the individual is allowed access to the associated web page or that the financial transaction is properly authorized. In addition, the fingerprint server  808  can positively identify the particular individual seeking access, and once verified, provide the identity of the individual to the application servers  810  along with personal data associated with the particular individual.  
         [0052]    [0052]FIG. 9 depicts a flow chart for a method of comparing a fingerprint minutiae template with a fingerprint minutiae template previously stored on a smartcard. A smartcard can be used both at a point of service transaction location or across a network such as the internet to positively identify the individual that is authorized to use the smart card. An FPI is obtained from a fingerprint sensor or scanner, as depicted in step  902 . The FPI is processed, as in step  904 , and if the image is of sufficient quality, as depicted in step  906  and sufficient minutiae are identified as depicted in step  908 . The FPI is analyzed and processed as described above according to FIG. 2 and the minutiae are extracted from the FPI and a fingerprint minutiae template is created, as depicted in step  910 . Otherwise, a new FPI is obtained and control is passed to step  902 . The extracted minutiae and the fingerprint minutiae template formed from the acquired FPI are compared to the fingerprint minutiae template stored on the smartcard, as depicted in step  912 . If a match occurs, as depicted in step  914 , the identity of the smartcard holder is verified, as depicted in step  916 , otherwise control is passed to step  902 , and a new FPI is obtained.  
         [0053]    The verification and identification functions described herein are based on the premise that a finger being presented and scanned by the fingerprint scanner is a live finger and not a prosthetic or severed finger having a false fingerprint. FIG. 10 depicts a flow chart for a live finger detection method that may be used in conjunction with the identification and verification methods described herein. The binary fingerprint image of step  214  in FIG. 2 is further analyzed to detect the presence and size of sweat pores contained within the fingerprint image. The binary image is provided, as depicted in step  1002 . The boundaries of the binary image are traced and chain coded, as depicted in step  1004 . All clockwise closed chains are detected, as depicted in step  1006 , and the area and arc length of the detected closed chains are measured as depicted in step  1008 . Although clockwise closed chains are used to identify sweat pores, counter-clockwise closed chains can also be used. The measured area is compared to a sweat pore threshold and if greater than the sweat pore threshold, the closed chain is a detected sweat pore. If the sweat pore exceeds a certain live finger sweat pore threshold, the finger is flagged as live, as depicted in step  1010 . In the illustrated embodiment in which the fingerprint sensor/scanner has a 500 dpi resolution, the sweat pore threshold is four pixels. Otherwise, the finger is flagged as non-living and no further processing is employed and the identity of the individual is not confirmed. If the finger is living and the measured arc length is compared to a hole threshold and if less than the hole threshold, the chain is removed, as depicted in step  1012 . In this manner, arcs having a arc length less than the hole threshold are considered to be noise and are therefore removed.  
         [0054]    In some circumstances, it may be desirable to classify the FPI according to the location of the cores and deltas, the estimate of the main direction of the cores, and classifying the FPI according to various categories of FPI. FIG. 11 depicts a flow chart of a method of identifying the location of the cores and deltas, estimating the directions, and classifying the FPI. The orientation field corresponding to an FPI from step  210  of FIG. 2 is provided, as depicted in step  1102 . The orientation field is refined, as depicted in step  1104  by subdividing each block into a four sub-blocks, as depicted in step  1106 . The orientation of each sub-block is predicted, using the original orientation direction as the predictor, as depicted in step  1106 . An octagonal core mask is created that is a vector valued  2 -dimensional matrix having as a value a unit vector radial from the center of the corresponding sub-block, as depicted in step  1108 . The center of the core mask is aligned with the corresponding sub-block and is convolved with the sub-blocks in the FPI, as depicted in step  1110 .  
         [0055]    The convolution result of the core mask and the sub-blocks is normalized, as depicted in step  1112 , and core and delta regions are identified as having large convolution results, i.e. the singularities of the FPI, as depicted in step  1114 . The Poincare index is determined for all areas of the FPI having a convolution result greater than a predetermined curve threshold, as depicted in step  1116 . The Poincare index is found by surrounding each area by a closed curve and a direction integration is performed. If the direction integration equals zero, as depicted in step  1118 , the diameter of the closed curve is reduced, as depicted in step  1120 , and the direction integration is performed again. This step is repeated until the radius is one, as depicted in step  1122 , or the integration is non-zero, as depicted in step  1118 .  
         [0056]    The singularities of the FPI are classified according to the value of the corresponding Poincare index, as depicted in step  1116 . For a Poincare index of 1, the singularities are classified as whorls and are clustered according to the corresponding Euclidean distance from the arbitrary origin. If there is more than one whorl cluster, the biggest cluster is selected and the smaller clusters are deleted. For a Poincare index of 0.5, the singularities are cores, and are clustered according to the corresponding Euclidean distance from the arbitrary origin. If there are more than three clusters of cores, the largest two are kept and the remaining core clusters are deleted. For a Poincare index of −0.5, the singularities are classified as deltas and are clustered according to the corresponding Euclidean distance from the arbitrary origin. If there is one whorl cluster and 3 or more delta clusters, the largest two delta clusters are kept and the remaining delta clusters are deleted. If there is no whorl cluster and 1 or more delta clusters, the largest two delta clusters are kept and the remaining delta clusters deleted.  
         [0057]    For any cores detected in step  1116 , the direction of the cores are estimated, as depicted in step  1118 . The core mask from step  1106  is convolved with the core singularity and the direction estimated from the results in that the displacement from the core center to the mass center of all zero sub-blocks is along the main direction of the core.  
         [0058]    If no cores or whorl clusters are identified then cores near the boundary of the FPI are estimated. The cores near the boundary are estimated by treating as a core singularity sub-blocks near the boundary having a convolution value in the top 20% of values. The cores are processed as described above.  
         [0059]    The FPI is then classified as a whorl, right loop, left loop, arch, or double loop. An FPI having a single whorl cluster is classified as a whorl. An FPI having a core cluster, and one or less delta clusters is a loop. If the cross product of the vector from the core to the delta with the main direction of the core is along the normal direction of the fingerprint plane, the fingerprint is a right loop. Otherwise, if the cross product is against the normal, the fingerprint is a left loop. If the cross product is nearly zero, the fingerprint is an arch. If there are two core clusters and two or less delta clusters, the fingerprint is a double loop. If there is no core then the fingerprint is an arch.  
         [0060]    In some circumstances, the raw fingerprint images from which one or more fingerprint minutiae templates are formed are obtained from fingerprint scanners or sensors that have different resolutions. Generally, the automated fingerprint identification/verification process described herein assumes that all of the raw FPIs are of the same resolution. Although this may be true for most fingerprint scanners, if the FPI has been previously digitized from film, the resolution information may not have been included with the FPI. Without a-priori knowledge of the resolution of the FPI, extra processing is required to ensure that the images being processed are of similar resolution.  
         [0061]    [0061]FIG. 12 depicts a method for use with the methods described herein to determine the resolution of an FPI having an unknown resolution. The raw FPI acquired in step  1202  is divided into  16  blocks, as depicted in step  1204 . For each block, the Fourier transform is computed as depicted in step  1206 . The magnitude of the Fourier coefficients is determined, as depicted in step  1208 . The Fourier coefficients are classified according to the corresponding spatial frequency, as depicted in step  1210 . The average magnitude of the components for each spatial frequency is determined, as depicted in step  1212 . The spatial frequency having the largest average magnitude is an estimation of the ridge distance of the raw FPI, as depicted in step  1214 , and may be used to adjust the processing to allow for FPIs of similar resolution to be compared.  
         [0062]    Those of ordinary skill in the art should further appreciate that variations to and modification of the above-described methods for identifying and verifying fingerprints can be made. Accordingly, the invention should be viewed as limited solely by the scope and spirit of the appended claims.