Abstract:
A method and apparatus designed for verifying the identity of a person, for credit card authorization and other purposes, involves the measurement of the thickness of the knuckles and also the longitudinal distance between knuckles. The apparatus simultaneously takes a series of length and width measurements, and feeds them to a computer which is programmed to process the raw data and make comparisons to a standard previously recorded. Techniques for increasing the accuracy of the determination are also disclosed.

Description:
This invention relates to the field of personal identity verification, and is particularly suitable for use in preventing credit card fraud. 
     BRIEF SUMMARY OF THE INVENTION 
     There are a number of situations in which it is necessary or desirable to determine the identity of an unknown person, or to screen out persons who fraudulently claim to be someone else. One example of the latter type of situation is the protection of secured areas in an industrial plant, to which access is restricted for reasons of trade secrecy. Another, and even more common, example is preventing the use of stolen or lost credit cards for unauthorized purchase of goods. 
     A wide variety of methods have been used to verify personal identity in such situations. Many of these methods involve the use of bodily characteristics as the criterion of identity, such as fingerprints. Fingerprint systems are reliable, but are also difficult and expensive to implement. In many ordinary applications a lesser degree of reliability is acceptable, and more cost-effective. 
     Accordingly, some workers have attempted to devise systems which are less expensive and technologically less demanding, but which are reliable enough for ordinary applications such as everyday credit card authorization. In some of these systems it is the measurement of finger proportions which is relied on as an indication of identity. In Ernst U.S. Pat. No. 3,576,537, Miller U.S. Pat. No. 3,576,538, Schwend U.S. Pat. No. 3,585,594, Jacoby U.S. Pat. No. 3,648,240 and Thurman U.S. Pat. No. 3,721,128, for example, the length of an individual&#39;s fingers along its longitudinal axis is measured and used as a test of personal identity for credit card authorization purposes 
     The present invention, on the other hand, employs measurements of the width of the individual&#39;s fingers along a transverse axis as the criterion of personal identity. This measurement has proven to be adequately reliable for credit card authorization, and can be performed inexpensively. 
     In accordance with this invention, the identity of an unknown person is verified by measuring the thickness of one or more joints of a test finger of a known person, and optionally also the distance between the finger joints; then storing the measurement(s), measuring the same dimension(s) of the test finger of an unknown person, comparing the dimension(s) relating to the known and unknown persons to determine the degree of similarity therebetween, and deciding whether that degree of similarity is acceptable as an indication of identity. 
     In one form of the invention, the thicknesses of a selected one of the finger joints along two different axes are measured and compared and used as a basis for the decision. 
     As a refinement, the thickness of a selected one of the finger joints is measured and compared and used as a basis for decision, and a procedure may be used for compensating for short-term changes in joint thickness which employs the thickness another finger joint as a check. 
     Another procedure may be used for compensating for long-term changes in finger dimensions. This involves calculating the difference(s) between the measured dimension(s) and the corresponding stored dimension(s), and modifying the stored dimension(s) by algebraically adding thereto at least a selected fraction of the difference(s). 
     In measuring the thickness of a selected joint of a selected finger of a known person and of an unknown person, a preferred procedure is to measure the thickness at a plurality of data points including the location of the selected finger joint and a range of locations in front of and behind that joint, and to measure the displacement of each of the locations along the longitudinal axis of the test finger. Then the comparison step may include calculating a first curve of a selected type which fits the data points best for each of the persons, establishing criteria of closeness between the curves and the data points, discarding any of the data points which do not meet those criteria, calculating a second curve of a selected type which fits the remaining data points best for each of the persons, determining a peak value for each of the second curves as an indication of the thickness of the selected finger joint for each of the persons, and comparing the peak values to determine the degree of similarity therebetween. 
     In a particular implementation of the invention, at least one of the curves employed is a parabola. The method of least square fit may be used to fit the parabola to its constituent data points. 
     Calculating one of the curves may comprise the steps of determining a peak data point from among all the data points, and selecting the curves to pass through the peak value data point. The step of determining a peak data point from among all of the data points may comprise the steps of selecting a preliminary peak data point, selecting a predetermined number of the data points on either side of the preliminary peak data point, calculating the average coordinates of the preliminary peak data points and the selected points on either side thereof, and employing the average coordinates as the coordinates of the peak data point through which the curve passes. 
     In addition to measuring and comparing the thickness of a first finger joint, the invention contemplates measurement and comparison of the thicknesses of a second joint of the fingers of the known and unknown persons, and optionally also the respective distances between the first and second joints of the fingers of the known and unknown persons. Such a multi-faceted comparison improves the reliability, at relatively low incremental cost. 
     The apparatus aspects of the invention contemplate means for measuring the finger dimension(s), means for storing the dimension(s) of the known person, means for comparing the dimension(s) of the unknown person to the corresponding stored dimension(s) to determine the degree of similarity therebetween, and means for determining whether the degree of similarity is acceptable as an indication of identity between the known and unknown persons. 
     The measuring means may comprise a pair of jaw means, means movably mounting at least part of the jaw means for opening and closing movement, means for opening the moveable jaw means to admit the finger therebetween, means yieldably biasing the moveable jaw means toward a closed position whereby to follow the contours of the finger as it is moved longitudinally between the jaw means, and transducer means responsive to the moveable jaw means for providing an electrical jaw displacement signal representing the instantaneous displacement of the moveable jaw means during the finger movement, whereby the profile of the jaw displacement signal during the time of the finger movement represents the thickness contour of the finger. 
     The moveable jaw means may comprise a slide member, in which case the mounting means comprises guideway means slideably mounting the slide member for linear motion of the moveable jaw means toward and away from the other of the jaw means, the transducer means if of the type requiring a rotary drive, and includes rotary drive gear means, and the moveable jaw means has coupled thereto linear drive rack means in driving engagement with the rotary drive gear means for operation of the transducer means by the linear motion of the moveable jaw means. 
     Solenoid means may be magnetically coupled to the slide member, and alternating current energization may be supplied to the solenoid means to apply a magnetic dither impulse to the slide member whereby to reduce frictional inaccuracies in the joint thickness measurement. 
     Preferably there is data processing means responsive to the jaw displacement signal and arranged to determine a peak value attained by the thickness contour whereby to determine the thickness of one of the finger joints, and the data processing means is arranged to compare the peak values relating to the known and unknown persons respectively whereby to determine the degree of similarity between the thicknesses of one of their finger joints. 
     The data processing means may be arranged also to determine second peak values of the thickness contour and to compare the second peak values relating to the known and unknown persons respectively, to determine the degree of similarity between the thicknesses of another of their finger joints. 
     There may also be means for sensing the degree of insertion of a finger into the apparatus, and transducer means responsive to the finger insertion sensing means for providing an electrical signal proportional to the degree of finger insertion; and the data processing means may be arranged to receive the finger insertion signal, to determine the finger displacements which are correlated with each of the peak values of the thickness contour, and to subtract one of the finger displacement values from the other whereby to calculate the distance between the finger joints of one of the persons. In that case the data processing means would be further arranged to compare the joint separation values relating to the known and unknown persons respectively, to determine the degree of similarity. 
     The insertion sensing means may comprise finger support means, and means mounting the finger support means for linear motion in response to insertion of a finger into the apparatus, and the insertion-responsive transducer means may be of the type requiring a linear drive, and including linear drive means coupled to the finger support means for linear movement therewith. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a front perspective view of the finger measurement station of a personal identification device in accordance with this invention. 
     FIG. 2 is a similar view, showing the insertion of a finger into the device for measurement purposes. 
     FIG. 3 is a partially schematic, partially rear elevational view of a somewhat different embodiment of a personal identification device in accordance with this invention. 
     FIG. 4 is an enlarged rear elevational view, with parts broken away for clarity of illustration, of a portion of the device of FIG. 3. 
     FIG. 5 is a sectional view taken along the lines 5--5 of FIG. 4. 
     FIG. 6 is a fragmentary side elevational view of a portion of the finger measurement station of either embodiment. 
     And FIG. 7 is a partial rear perspective view of a portion of the finger measurement station of either embodiment. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 illustrates a finger measurement device incorporating a front panel 10 formed with an opening 12 which defines a finger measurement station. Just behind the opening 12 are a pair of jaws in the form of two horizontally opposed rollers 14 which are operable to receive between them the finger of a human being for the purposes of measuring the horizontal thickness thereof. An optional third roller 16 may be provided for measurement of the vertical thickness, in the event that this additional measurement is incorporated into the procedure for personal identification. 
     Between the horizontal measurement rollers 14, and below the vertical measurement roller 16, is a finger support plate 18 on which the finger to be measured is placed, in the manner illustrated in FIG. 2. The support plate is suitably mounted for longitudinal movement in a direction perpendicular to the panel 10, least one of the rollers 14 is suitably mounted for horizontal movement toward and away from the other (as indicated by arrow 21), and the roller 16 is suitably mounted for vertical movement toward and away from the support plate 18 (as indicated by arrows 23). 
     Consequently, finger 20 and the support plate 18 can be moved forward together, as indicated by arrow 22, to introduce the finger 20 into the panel opening 12 and insert it between the rollers 14, and also between the roller 16 and the support plate 18. Rubber pads 24 are affixed to the upper surface of the plate 18 to assure the requisite frictional engagement between the finger 20 and the plate. As the finger is inserted into the panel opening 12, the moveable roller 14 moves horizontally away from the stationary roller 14 to accommodate the horizontal width of the finger 20, and the roller 16 moves upwardly to accommodate the vertical width of the finger. 
     Thus the total displacement of the rollers 14 from each other at any particular moment is a measure of the horizontal thickness of the particular part of finger 20 which is between those rollers at that moment, and the vertical displacement of the roller 16 at any particular moment is a measure of the vertical thickness of the particular part of finger 20 which is between that roller and the support plate 18 at that moment. 
     Moreover, as the finger 20 moves further into the panel opening 12, the displacements of the rollers 14 and 16 continuously trace the horizontal and vertical thickness contours respectively of the finger 20 as a function of the length of the finger. These thickness contours of course widen to relative peaks at each of the knuckles of the finger 20. 
     Therefore, by continuously or repeatedly measuring the displacements of the rollers 14 and 16 as the finger is being inserted into the panel opening 12, one can obtain data on the finger thickness contours. Then, by suitable processing of that data, the relative peaks in the thickness contours which represent the knuckles can be located, and conclusions as to the thicknesses and locations of the knuckles can be drawn which are usable as criteria of personal identity. 
     In order to mount the finger support plate 18 for longitudinal movement, the rear portion thereof is captured between two upper rollers 30 and a lower roller 32 which are journaled on respective pins 34 so that they roll as the plate 18 moves longitudinally. The pins 34 in turn are supported between the vertical walls 36A of an upright channel member 36. The forward portion of the support plate 18 rests upon an upright post 40, which is connected to the wiper of a linear potentiometer 42 and moves therewith as the finger 20 is inserted into the panel opening 12. Consequently the resistance of potentiometer 42 varies as a function of finger insertion, to facilitate electrical measurement of finger displacement. 
     The upright channel member 36 is supported upon an inverted channel member 44, and the linear potentiometer 42 is affixed to the underside of the channel member. The channel member in turn is affixed to the panel 10. The linear potentiometer post 40 protrudes upwardly from the potentiometer 42 through a slit 44A formed in the channel member 44. A return spring 46 is secured at its rear end to the potentiometer post 40, and at its forward end to the panel 10 in any suitable manner (not illustrated), so as to bias the potentiometer post, and with it the finger support plate 18, forwardly (opposite to the direction indicated by arrow 22) to establish their initial positions before any finger measurements are taken. 
     The embodiment of FIGS. 3-5 is similar in all respects to that of FIGS. 1-2 and 6-7, except that the vertical measurement roller 16 is omitted, and the device depicted therein is suitable for use with a personal identification algorithm which employs only horizontal finger thickness measurements. 
     The horizontal measurement rollers 14 are journaled on respective shafts 50, which are captured between the tines of respective fork members 52. One of the fork members is fixedly secured to a mounting block 54, which in turn is affixed to the front plate 10. The other fork member 52, however, is secured to a slide member 56 by means of a post 58 which is received within a socket formed in one end of the slide member 56 and secured in place by a set screw 60. The other end of the slide member 56 is slideably received within an opening formed in a mounting block 62 which in turn is affixed to the front plate 10. This permits the slide member 56 and its associated fork member 52 and roller 14 to slide horizontally as a unit to accommodate the thickness of the finger 20 as the latter is inserted into the panel opening 12. 
     A rotary potentiometer 70 is secured to an auxiliary mounting plate 72, which is part of the frame of the personal identification device, and is mechanically coupled to the horizontal movement of the moveable roller 14 by means of the potentiometer shaft 74, a pair of gears 76 and 78, a pinion 80 and a rack 82. The rack is received within a socket formed in the slide member 56, and secured therein by set screws 84. As the roller 14 and slide member 56 move horizontally, the rack moves therewith, and thereby drives the pinion 80. The pinion and the gear 78 are both keyed to a common shaft 86 which is journaled on the mounting block 62. Consequently, the gear 78 rotates with the pinion, and thereby drives the gear 76 and the potentiometer shaft 74 which is secured thereto. 
     This arrangement causes the resistance of the potentiometer 70 to vary as a function of the horizontal displacement of the moveable roller 14, which in turn is a function of the horizontal width of the portion of the finger 20 which is passing between the rollers 14 at any particular moment. In this way, the illustrated apparatus derives an electrical output which varies continuously as a function of horizontal finger width. 
     If it is decided to include the vertical measurement roller 16 in this apparatus, as illustrated in FIGS. 1 and 2, a similar but vertically displaceable mechanism may be employed in conjunction with the vertical measurement roller in order to derive an electrical output which varies continuously as a function of vertical finger width. 
     The initial position of the moveable roller 14 prior to insertion of the finger 20 is established by a biasing spring 88 secured to a cable 90 which is wrapped around the potentiometer shaft 74. The tension in the spring 88 causes the shaft 74 to rotate in the direction to bias the moveable roller 14 toward the fixed roller 14. 
     When making a horizontal finger width measurement, a lever 92 may be conveniently used to retract the moveable roller 14 from its initial position, in order to facilitate initial insertion of the finger 20. The lever is fulcrumed by a pivot pin 94 secured to the front plate 10, and is pivotably secured to the fork member 52 by a pin 96. As the lever 92 is moved in the direction indicated by arrow 98, this connection causes the fork 52, slide member 56 and moveable roller 14 to be retracted so as to open up the jaws formed by the two rollers 14, permitting the finger 20 to be inserted easily therebetween. 
     Thereafter, the lever 92 may be released, allowing the biasing spring 88 to return the moveable roller 14 toward its initial position. This causes the moveable roller to come into contact with the finger 20, and thereafter, as the finger 20 is withdrawn from between the rollers 14 it causes the moveable roller to remain in contact with the finger to provide a continuous electrical measurement corresponding to the thickness contour of the finger. 
     In order to permit the moveable roller 14 to respond more accurately to the changes in thickness as the finger is withdrawn, magnetically induced dither is used to free the horizontal movement of the slide member 56 from frictional hang-up. A solenoid winding 100 is provided, through the center of which loosely protrudes an extension 56A of the slide member 56. The solenoid is energized, via a circuit breaker 102, by ordinary 60 Hz A.C., half-wave rectified by a diode 104. This causes the solenoid to vibrate the slide member 56 rapidly, and thereby prevent it from becoming frictionally locked by minute surface irregularities within the interior of the mounting block 62. A switch 106 is provided, however, to allow the operator of the apparatus to turn off the dither feature if desired. 
     A computer, preferably a microcomputer, schematically illustrated at 110, is connected to receive the electrical information concerning depth of finger insertion provided by the potentiometer 42, and also the electrical information regarding the finger thickness contour provided by the potentiometer 70, and it is suitably programmed to carry out a personal identification algorithm using this information as raw data. In successful tests of this invention, for example, an Apple II personal computer, programmed in Basic, was used, and the potentiometers were connected to the computer&#39;s paddle control inputs. 
     The first step in the personal identification procedure is to do a finger measurement on a selected test finger (e.g. the index or middle finger) of a known person, and store the data relating to that person on a magnetic disk. Subsequently, when an unknown person claims to be the known person, a second identical finger measurement is performed upon the test finger of the unknown person, the data relating to the known and unknown persons are compared, and a computer-assisted decision is made, based on some suitable decision algorithm, as to whether the data are sufficiently similar to justify treating the unknown person as the known person, e.g. by honoring that individual&#39;s credit card for the purchase of merchandise. 
     One decision algorithm which has been used with success in tests of this invention employs the well known least square regression analysis to fit one or more parabolic curves to the measured finger thickness contours, and the dimensions of the parabolas thus obtained are used as refined data on which to base the comparison between the known and unknown persons. If an arbitrarily selected number of measurements of the known and unknown persons are within an arbitrarily selected numerical distance of each other, then that is taken as an indication of personal identity. If those criteria are not met, then that is taken as an indication of non-identity. 
     The choices of these arbitrary criteria depend entirely upon the desired trade-off between the degree of security required and the number of false negatives which can be tolerated. This will depend on the circumstances (e.g. the amount of money at stake) and the personal judgment of the individual charged with designing the system. 
     The minimum amount of information required for operation of the invention is a comparison between either the horizontal or vertical thicknesses of one selected knuckle on one test finger of the known and unknown persons. Alternatively, more accurate determinations can be made by comparing the horizontal or vertical thicknesses of two selected knuckles on one or more test fingers of the known and unknown persons. Another way of increasing the accuracy is to include a comparison of both the vertical and horizontal thickness measurements of at least one knuckle of both persons, employing both the horizontal measurement rollers 14 and the vertical measurement roller 16 discussed above. 
     The preferred method, however, is to compare the thickness of at least two knuckles of one finger plus the distance between those two knuckles. As the test finger is withdrawn the potentiometer which is coupled to the thickness measurement roller presents to the computer a smoothly varying electrical resistance curve representing the thickness contour of the finger, and the potentiometer which is coupled to the finger support plate presents to the computer a continuous electrical resistance ramp which representing the changing degree of finger insertion. By plotting one value against the other, the computer obtains information about the variation of the thickness of the finger along its length. The peak values of the thickness contour represent the two knuckles of the finger, and the separation between the peaks represents the distance between those knuckles. 
     The computer is programmed to sample the potentiometer resistance at frequent intervals during finger withdrawal, thereby collecting a series of raw data point pairs (length and thickness). The program then processes this raw data to find the two peak values representing the knuckles of the test finger. But instead of using the raw peak values, the program preferably calculates a refined peak for each knuckle by taking a selected number of finger width values (e.g. ten of them) which are closest in magnitude to each raw peak, and averaging them together to reduce measurement errors. This average value is then used as the peak thickness for each knuckle, and serves as the reference point about which to fit a smooth curve which best fits the raw data points. 
     Successful results have been obtained employing a parabolic curve fitted by the method of least squares, using in the regression formula about twenty-five data points on each side of the average peak. (For details of the regression formula, see e.g. Sec. 5.6 of &#34;Advanced Engineering Mathematics&#34; by C. R. Wylie, Jr., published by McGraw-Hill.) This parabola is then compared to the raw data points, and all data points which are more than a selected distance from the parabola peak are arbitrarily discarded, on the assumption that they are on a non-parabolic portion of the finger. The curve-fitting process is then repeated, using the remaining data points, to obtain a second, more accurate parabola which passes through the selected set of points with minimum least square error, thus conforming optimally to the retained data points. The magnitude and longitudinal location of the peak of this second parabola is calculated from the resulting equation; and is taken as the thickness and position respectively of the knuckle. 
     The end result of the described data processing is two parabolas, one for each of the two knuckles of the test finger, which give the locations of those knuckles along the longitudinal axis of finger. A straightforward subtraction of one location value from the other then gives the distance between the knuckles. The knuckle thickness values for the two knuckles similarly may be determined simply by examining the peak values of the two parabolas. These values are then stored on disk. 
     Subsequently, when an unknown person is presented for identification, the same measurements are repeated on the same joints of the unknown person, and the same calculations are performed by the computer. The newly acquired knuckle thickness and knuckle separation values are then compared to the corresponding stored values by a straightforward subtraction process to determine the respective absolute values of the differences between the two knuckle thicknesses and the knuckle separations, of the known and unknown persons. If these three absolute values meet an arbitrarily determined criterion, the computer is programmed to reject the unknown person; otherwise the identity of the two individuals is accepted. 
     Alternatively, each calculated parabola may be reduced to the standard equation form y=ax 2  +bx+c, and the coefficients a, b and c for both the known and the unknown persons are compared to determine the degree of similarity between them. 
     One possible source of inaccuracy which inheres in the system, regardless of the number or type of measurements employed, is the fact that the thickness of the finger joints of the same individual may vary over a short term such as the course of a single day, depending upon circadian physiological rhythms. In order to cope with this difficulty, two joints of the same finger, or preferably two corresponding joints of separate fingers (e.g. the index and middle fingers), can be measured on both the known and the unknown individuals. Two joints of one finger are then treated as test joints, and the corresponding joints of the other finger are treated as reference joints and used to correct for short-term variations in joint thickness. 
     The test joint and the reference joint thicknesses of the known person are both measured, processed as described above, and stored. Then the same procedure is performed on the unknown person. But before the results relating to the test joints of the two persons are compared, the reference joint measurements of the two persons are first compared and the difference between the two, if any, is determined by subtraction. This difference is then assumed to be a measurement of the short-term changes in joint thickness, and is algebraically added to the test joint measurement of either the known or the unknown person (i.e. added to or subtracted from it, depending on whether the difference is positive or negative) to correct for the assumed short-term changes. Then it is this corrected test joint measurement which is compared to the test joint measurement for the other person. This procedure is part of the comparison algorithm employed by the computer. 
     It is believed that the impact of short-term daily changes is further reduced by performing all measurements on the non-dominant hand, i.e. the left hand of a right-handed person and vice versa. 
     Another possible source of inaccuracy is long-term changes which take place over the lifetime of the known person as a result of aging. This problem can be dealt with by making periodic corrections of the stored measurements each time the known person successfully re-enters the system for measurement. Thus, each time a request for validation is answered in the affirmative, despite the presence of small discrepancies in the measurements which are within the limits of acceptability, some selected fraction (e.g. one fifth) of the difference is algebraically added to the previously stored measurements of the known person to produce a new permanently stored value which is assumed to reflect a long-term trend resulting from changes in the known person&#39;s physical characteristics as a result of increasing age. 
     Of course if the unknown person is rejected because the differences are outside the limits of acceptability, when such differences are assumed to be due to different identities rather than to the aging of a single individual, and therefore no correction for long-term changes is made. 
     Note that it is only the long-term correction which is incorporated into the permanently stored data base, and not the short-term circadian correction. The long-term aging changes are permanent, but the short-term daily variation is temporary. 
     A variety of choices of test joints and reference joints for short-term and long-term change compensation is possible. The preferred system is to use the thicknesses of the two knuckles of the index finger, and the distance between those knuckles, as the test measurements; and the corresponding dimensions of the middle finger of the same hand as the reference dimensions which correct for short- and long-term variations. 
     A specific example of the use of these techniques will now be given. In a preferred embodiment of the invention, a credit card holder first appears at a central station or at a local store which is equipped with apparatus of the type described above for measurement by the apparatus, at which time six raw values are measured, i.e. three different values on each of two fingers. The three values are the thickness of the first and second knuckle joints of the finger in question, and the distance (or separation) between those joints. The fingers employed are the index finger and the middle finger of the credit card holder&#39;s non-dominant hand. These measurements are sent by telephone to the central computer, and stored in the computer&#39;s data base. 
     When the credit card holder, or someone claiming to be the credit card holder, presents the credit card at one of the participating retail stores after having his measurements added to the central computer&#39;s data base, the same six raw measurements are taken again. The credit card number and the six measured values are sent over telephone lines to the central computer for both credit checking and identification, the latter operation being based upon a comparison between the new data and the stored data. 
     The computer first processes the raw data as described above, then uses the processed data to calculate the differences between the reference finger joint thicknesses of the known person and the unknown person, for each of the two knuckles of that finger, and then algebraically adds those differences to the corresponding finger joint thicknesses measured upon the unknown person&#39;s test finger. The resulting corrected test finger joint thicknesses of the unknown person are then compared to the respective corresponding stored test finger joint thickness measurements. This comparison is carried out by subtracting the final test finger joint thickness value of one person from the corresponding final test finger joint thickness value of the other person for each of the two test finger joints. 
     In addition, the computer subtracts the test finger joint separation value and reference finger joint separation value of one person from the corresponding finger joint separation values of the other person. These calculations thus produce four separate error values; one for each of the two test finger joint thicknesses, and one for each of the two finger joint separations. These four error values are then employed in the following decision algorithm to determine whether the combined error values are within acceptable limits for extending credit. 
     An arbitrary, pure numerical constant K is used as a figure of merit, and is initially set equal to zero. This figure of merit is then incremented or decremented according to the results of the comparisons between the processed finger measurements. For this procedure the computer uses an arbitrary unit of length equal to 0.184 millimeters. According to the decision algorithm, if the absolute value of the error for the joint separation value for the middle finger exceeds 4 units (0.736 millimeters), the computer subtracts 1 from K; whereas if the absolute value of that error is less than 2.1 units (0.386 mm), then the computer adds 1 to K. 
     If the absolute value of the error for the joint separation for the index finger is less than 2.1 units (0.386 mm), then 1 is added to K; but if it exceeds 4 units (0.736 mm), then 1 is subtracted from K. 
     If the absolute value of the error for the first test finger joint thickness is less than 5.1 units (0.24 mm), then 1 is added to K; and the same is done with respect to the absolute value of the error for the second test finger joint thickness. 
     If the resulting integral value of K is greater than 1, i.e., if it is at least 2, then credit is extended; but if it is less than 2, credit is denied. While this decision algorithm has worked well in small scale tests, it has the advantage of being &#34;tunable&#34; if further experience indicates that the figure of merit K should be incremented or decremented by different amounts or under different error conditions. 
     For the purposes of further exemplification, this description concludes with the following appendix consisting of a program flow chart of a personal identification algorithm in accordance with the invention, and a corresponding Basic computer program listing, followed by a table of definitions of symbols used in the listing and a description of the program operation: ##SPC1##