GB2237917A  Signature verification  Google Patents
Signature verification Download PDFInfo
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 GB2237917A GB2237917A GB9024411A GB9024411A GB2237917A GB 2237917 A GB2237917 A GB 2237917A GB 9024411 A GB9024411 A GB 9024411A GB 9024411 A GB9024411 A GB 9024411A GB 2237917 A GB2237917 A GB 2237917A
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 United Kingdom
 Prior art keywords
 signature
 finite state
 state machine
 values
 measurements
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Classifications

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06K—RECOGNITION OF DATA; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
 G06K9/00—Methods or arrangements for reading or recognising printed or written characters or for recognising patterns, e.g. fingerprints
 G06K9/62—Methods or arrangements for recognition using electronic means
 G06K9/6296—Graphical models, e.g. Bayesian networks
 G06K9/6297—Markov models and related models, e.g. semiMarkov models; Markov random fields; networks embedding Markov models

 G—PHYSICS
 G07—CHECKINGDEVICES
 G07C—TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE
 G07C9/00—Individual entry or exit registers
 G07C9/00126—Access control not involving the use of a pass
 G07C9/00134—Access control not involving the use of a pass in combination with an identitycheck
 G07C9/0015—Access control not involving the use of a pass in combination with an identitycheck by means of a handwritten signature
Abstract
Description
IMPROVEMENTS IN METHODS AND APPARATUS FOR SIGNATURE VERIFICATION The present invention relates to methods and apparatus for signature verification both automatically and as an aid to verification carried out by a person.
Automatic signature verification has uses in financial transactions, for example with cheques and smart cards, and in providing access to facilities, such as computers, or premises.
There are of course many other instances of signature use both past and future which benefit from automatic signature recognition.
In known signature verification apparatus the signatory signs on an electronic input device, numerous types of which are known operating on several different principles. Some operate on the principle described in U.K. Patent No. 1,310,683 and U.S. Patent No. 3,885,097 to provide x,y coordinates of points in the signature, others interrupt light to a sensor as opaque lines on a writing surface are crossed, as described in U.K. Patent Application No. 8626411 (Publication No. 2183071) and corresponding United States Applications Nos. 076209, 137676 and 548192) to provide such features as variations in speed at which different parts of a signature are written, and in other cases a noise generated while the signature is written provides information for signature recognition.
Hidden Markov modelling is a technique that has been used for modelling events that are assumed to have been generated by a statistical process. Hidden Markov Models (HMMs) have been used to model many systems. For example, biological populations, musical styles but in particular HMMs have been used to model speech and natural language. A suggestion that HMMs might be used for signature recognition has been made in the paper "Handwritten Script Recognition Using HMMs" by R. Nag, K.H. Wony and F. Fallside, ICASSP 86, Tokyo, pages 132 to 135. This paper is mainly concerned with recognising handwritten characters by constructing HMMs based on the inclination of script at different points in the characters.
HMMs for signature recognition are also briefly mentioned in the above mentioned U.K. Specification No. 2183071.
An HMM is a class of finite state machine in which the output from a particular state is chosen by sampling from possible values with probability governed by probability distribution function(s) (pdf). Such a machine generates a series of outputs, each of which is dependent tpon its current internal state. The transition from one state to another is dependent on a set of transition probabilities.
According to a first aspect of the present invention there is provided a method of automatic signature verification comprising, for each signatory, the steps of forming a finite state machine particular to the signatures of that signatory based on corresponding measurements of a plurality of signatures from that signatory, at least one of the measurements on each signature being of a feature which is only apparent from values occurring at the time the signature was written, and using the finite state machine to verify signatures alleged to be written by the signatory.
According to a second aspect of the present invention there is provided apparatus for signature verification comprising means for deriving and storing a finite state machine for the signature of each person whose signature is to be recognised by the apparatus, each said machine being based on corresponding measurements on a plurality of signatures from that person, and at least one of the measurements of each signature being of a feature which is only apparent from values occurring at the time the signature was written, and means for verifying signatures based on the stored finite state machines.
Usually the finite state machines are HMMs.
By deriving at least some of the states of the HMMs from dynamic signature features, that is features apparent from values occurring at the time a signature is written, forgery is made much more difficult since in addition to achieving a signature which appears correct, the forger has to mimic dynamic features which are unknown to him.
The HMM states may, for example, be based on Cartesian components of the velocity at which the tip of a pen used in signing travels as different segments of the signature are written, each segment corresponding to a state in the HMM. Thus in each HMM the state pdfs may represent distributions of pen velocity components occurring in writing signatures. Static features may be combined with dynamic features in constructing the HMMs.
The invention also relates to methods and apparatus for deriving finite state machines representing signatures wherein at least one of the states of the machine for a signature is based on a dynamic feature of that signature. Methods and apparatus for verifying signatures from stored finite state machines, where each of the said machines is based on a dynamic feature of a signature, form further aspects of the invention.
In an embodiment of the invention, signatures can be written using a pen which interrupts light to a sensor as opaque lines on a writing surface are crossed, as described in the above mentioned U.K. Patent Application No. 8626411.
Each person whose signature is to be recognised writes his signature several times using a pen such as that mentioned in the previous paragraph, and a programmed computer derives an HMM by dividing each signature into segments and using the forwardbackward algorithm to reestimate an initial HMM based on orthogonal components of pen velocity in the segments. Preferably each signature is divided into between thirty and a hundred segments, typically fifty, in deriving the corresponding HMM. The number of states in the HMM usually equals the number of segments used to derive it. An HMM for each person's signature is stored for use when signatures are to be recognised.
To verify a signature, the signature is automatically matched against the stored HMM derived from signatures of the person alleged to be the author of the signature by calculating the logarithm of the likelihood of the model generating the signature to be verified. The likelihood value is calculated by a forward probability or "alpha" pass through the model.
According to a third aspect of the invention there is provided a method of verifying a signature comprising regenerating a signature from a finite state machine model of the signature, and comparing the regenerated signature with a trial signature to be verified in rejecting or accepting the trial signature.
According to a fourth aspect of the invention there is provided apparatus for use in signature verification comprising means for storing data defining the states of a finite state machine model of a signature, and means for generating a display of a representation of the signature from at least some of the said data, whereby a signature to be verified can be compared with the said representation.
The comparison between the displayed representation and the signature to be verified can be carried out either by a person or automatically.
Certain embodiments of the invention will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of apparatus according to the invention, Figure 2 Is a diagram of part of an HMM used to represent a signature, Figure 3 is a flow diagram of an algorithm for generating HMMs from sample signatures, and Figure 4 is a flow diagram of an algorithm for regenerating a signature from an HMM.
Apparatus is first described which, in general, can be used for signature recognition or generating HMMs for signature recognition.
In the apparatus of Figure 1 a pen 10 is used to write a signature 12 on a region 13 of a document 14 such as, in signature recognition, a cheque. The region 13 has closely ruled horizontal and vertical lines and the signature 12 is written over these lines. The pen may be in the form which provides analogue signals for a computer 11, if the computer is capable of analysing such signals to produce pulses which correspond to line crossings in the signature, or the pen itself may include some form of analoguetodigital converter which provides pulses which correspond to line crossings. The horizontal lines in the area 13 are a different colour from the vertical lines in that area and the pen 10 generates two analogue or digital signals, each corresponding to line crossings of one respective colour.Thus the computer 11 is able to derive two signals representative of the number of vertical and horizontal lines, respectively, crossed in unit time. The computer therefore has available digital signals representative of vertical and horizontal components of pen velocity as the signature is written. In addition the pen includes a pressure sensitive switch which indicates whether or not the pen tip is in contact with a surface on which the signature is written and, in this way, a "contact" signal is also supplied to the computer 11.
Many other types of graphical input tablet may be used to supply signals which can be analysed to derive vertical and horizontal components of pentip velocity (x and y velocities) and an indication of whether the tip is in contact with a writing surface or not. For example an input tablet which provides a stream of digital signals representative of the coordinates of the position of the pen tip when in contact with a writing surface may be used.
In order to generate an HMM of a signature the number of sample signatures, typically five, are written on a graphical input tablet, for example in the area 13 of Figure 1, and digital signals representing vertical and horizontal velocity components for the whole signature are stored together with a digital "contact" signal.
These signals are used to generate an HMM of the signature by dividing each of the signals into, typically, 50 uniformlength segments and generating a 50 state HMM. The Bakis form of HMM is used in which, in this example, each of the states has three associated Gaussian probability density functions (pdfs), one for each input data dimension (that is x and y velocities and writing surface contact indicator). Each pdf is represented by a mean value and a variance and the Bakis form also requires transition probabilities between states to be zero except for transitions from a state to Itself, and transitions from a state to two other specified states.
A diagrammatic representation of such an HMM is partially shown in Figure 2 with states represented by circles 20 to 23, 49 and 50.
Nonzero transitions are represented by arrows, some of which, such as the arrow 30, point back to the state itself and represent transitions from a state to itself. Other arrows, such as the arrows 31 and 32, which join one state to another, represent transitions between states.
The computer 11 is programmed to hold a number of matrices, one of which is known as matrix A and has dimensions 50 x 3. This matrix contains real valued natural logarithms of probabilities of transitions from state i to state j where i and j index the matrix.
The Bakis form requires only 150 nonzero matrix elements, three for each of the 50 states. The matrix B having dimensions of 50 x 3 contains mean and variance values of the state pdfs. A further matrix 0, for input data, has dimensions 3 x a number equal to the number of digital signals expected from a signature of maximum length. The matrix 0 holds and stores the incoming input signals.
The input signals representing a signature can be regarded as being in a number of frames, each containing 3 input signal values, x and y velocity and contact value, and one frame occurring each time values of these three signals are provided.
The HMM is generated by reestimation from an initial model which, as mentioned above, has typically 50 states corresponding to 50 segments. All the transitions of the Bakis model have initial values of unity and the pdfs are represented by the means and variances of each of the x and y velocities and the contact value calculated for each of the initial 50 segments. Although the latter can in practice only take up the values "1" and "0" it is believed that the mean and variance values obtained are useful. At this point the HMM is stored in matrices A and B.
Thus in Figure 3, the flow diagram for HMM generation, the first three operations are to segment the three input signals of one of the sample signatures into 50 segments (operation 40) and calculate the mean and variance for each segment of each input (operation 42). The 11forward" or "alpha" probability values and the "backward" or "beta" probability values are calculated frame by frame, in an operation 43, using the BaumWelch or forwardbackward algorithm as described, for example, by L.A. Liporace in "Maximum likelihood estimation for multivariate stocastic observations of Markov sources", IEEE Transactions on Information Theory, 28: 729734, 1982. Log probabilities are used and it is therefore necessary to add terms in many of the equations. This necessitates the use of an "addlog" function as described by Kingsbury (see appendix B of the paper by S.J.Cox "Hidden Markov Models for Automatic Speech Recognition: Theory and Application, RSRE Memorandum No. 4135, Procurement Executive, Ministry of Defence, RSRE Malvern, Worcestershire, U.K.). The forwardbackward algorithm is also described by Cox and by J.N. Holmes in his book "Speech Synthesis and Recognition", Van Nostrand Reinhold (UK) Co.
Ltd. (1988), see Chapter 8. J.N. Holmes also mentions Kingsbury.
The references to Liporace, Cox, Holmes and Kingsbury are hereby incorporated into this specification.
The forward and backward probabilities are stored in two matrices C and D, respectively, and the dimensions of these matrices are the number of states (usually 50) x the number of frames in a signature, that is one matrix element for the forward and backward probability of each state and each frame. Using these matrices an expected value for each of the transition probabilities and each of the means and variances for each state is calculated (operation 44) and stored in two further matrices known as exptrans (dimensions 50 x 3) and expB (dimensions 50 x 6). Storing these values is shown as an accumulation operation 45 since the operation is later repeated for the other signature samples when storing is replaced by accumulation.
The operations 43 to 45 are repeated using the three input signals from another sample signature. The expected values obtained are added in the operation 45 to the corresponding values in matrices exptrans and expB. The process of repeating the operations 43 to 45 is repeated with the three input signals from each remaining sample signature in turn until a test 46 determines that all the signature samples have been used.
The accumulated values are then used to calculate reestimates of the values of the transitions, means and variances in an operation 47, this being a process akin to normalisation, the results being stored in the A and B matrices. The forward pass of the forwardbackward algorithm is carried out in an operation 48 using the transition probabilities, means and variances from the operation 47, and then a test 51, which is explained below, is carried out. At this stage the test 51 causes a jump back to the operation 43. In repeating the operations 43 to 46, each sample signature is used again in turn by reading its three input signals into the matrix 0.The operations 43 to 48 are repeated until, as indicated by the test 51, the increase in the likelihood of the data being produced by the model between successive iterations is below a value such that further iterations do not provide a worthwhile improvement. At this point the parameters stored in the A and B matrices define the final HMM. At each stage the likelihood of the data being produced by the model is given by the value in the last cell of the C matrix (forward probabilities), that is the matrix element corresponding to the last state in the HMM.
Having described the generation of HMMs for signatures, signature verification will now be considered.
The signatory signs on using, for example, an apparatus of the type shown in Figure 1 or another apparatus from which x and y velocity signals and contact signals can be generated. Although in signature verification for largescale applications such as in banking only the pen 10 and the area 13 need to be specially provided since a general purpose computer such as one already installed for such applications can be used to calculate the probability of an unknown signature being genuine.
For verification, the parameters of HMM derived from the sample signatures are stored in equivalents of the A and B matrices but the arrays expB, exptrans and D are not required.
The probability of the new or trial signature data having been generated by the stored HMM is now calculated and can be expressed as P(OIM) which means the probability of the set of observations O occurring given values defining a Markov model M.
If 01, 2 ~~~~ OT are observations corresponding to frames of the input signals and N is the number of states in the model, then the probability of the joint event of emitting the partial observation sequence 01, 2 t Ot and occupying state Sj at time t is given by at(j) = P(01, 2 , Ot, (state Sj at time t)lM) Then the completed forward probability pass yields <img class="EMIRef" id="02717812800090001" />
The x velocity, y velocity and contact signals from the trial signature and the stored HMM parameters are used in a forward pass of the forwardbackward algorithm to calculate P(OM) and the last element in the matrix C provides this value when the forward pass is complete.The probability found is tested against a threshold and the signature is rejected or accepted as a result of this test.
Whether a signature should be accepted at a given level of probability is one which will depend on the application concerned; for example in banking it may be more acceptable to have a threshold probability for acceptance which allows a small percentage of forgeries to be accepted but gives a lower percentage of false rejections. Forgeries are, on the whole, unlikely and in any case most would be discovered by such a threshold level while false rejections create bad feeling against a system if they occur often with genuine users. In another application, such as access to security premises, a lower threshold of pulse acceptances might be better since false rejections can be tolerated by suitably instructed staff. Thus setting the probability threshold for acceptance is a matter of the application concerned but it is also necessary to set the threshold heuristically.
Another aid to recognition is the possibility of regenerating a representation of a genuine signature so that it can be displayed, for example, on a computer screeen. Such a display is useful where acceptance or rejection of a signature is not to be carried out entirely on the basis of the results of calculation but is partly at the discretion of the person present at the time the signature is written or produced. The regenerated signature may also be used as a convenient method of electronic signature storage and in such circumstances authorisation of a signature may be made solely by a person present on the basis of the regenerated signature.
In reproducing the signature it is assumed that the states are arranged in a linear chain and the duration of each state is proportional to the reciprocal of transition back to that state.
These durations are calculated and stored before regeneration, together with the total signature time which is the sum of the state durations.
A signature can be regenerated from the mean values of x velocity, y velocity and surface contact held by the HMM for that signature; that is in the B matrix. A test 52 is then carried out to determine whether the mean value of the contact signal of the first state of the HMM is equal to, or greater than one. If so the pen is in contact with the writing surface and a line joining a start point to a next point in the signature can be displayed, when calculated. For this purpose the means of the x velocity, y velocity for that state are retrieved and the position of the next point is calculated (operation 53) and a line joining the start point and the next point is displayed (operation 54). A test 55 now determines whether the next state shall be used to determine the next point for line construction on the basis of the stored duration of the current state.If a change is to be made an operation 56 retrieves the mean values of the next state. A test 57 now follows to decide if the current duration t of the regenerated signature is greater than the calculated total duration T and if not a return to the test 52 occurs. Each time this test indicates that the pen is not in contact with the writing surface, the x coordinate of the start of the next line to be displayed is incremented by a convenient amount (operation 58). If the test 52 indicates contact between pen and writing surface the operations 53 and 54 occur and the next line forming the regenerated signature is displayed. In this way by moving through the HMM states by means of the tests 52, 55 and 57, and the operations 53, 54, 56 and 58, lines forming the whole regenerated signature are eventually displayed.
When a signature is regenerated in this way and a break appears the position chosen to continue the signature is usually incorrect. However, a good idea of the original can be obtained, especially by a person with a little experience. The signature to be authenticated may also be modelled by an HMM and regenerated in the same way so that the two regenerated signatures can be compared by eye or automatically. The problem of breaks in regenerated signatures can be overcome when absolute position of the pen tip is also known, for example when the input tablet is in a form which provides x and y coordinates since mean values of x and y positions are available to determine the position of the next point after a break.
As an alternative to displaying lines, the regenerated signature may be made up by displaying only the points calculated.
Having described several specific embodiments of the invention, it will be clear that the invention can be put into practice in many other ways. For example other dynamic features of a signature may be used in providing variables for the pdfs and nondynamic features such as pen position may also be included. One pen tip velocity component, only, may be used, preferably in combination with another dynamic or static feature of the signature.
The HMM rodel may be simplified from the Bakis form by allowing only probabilities from a state to itself or to the next state in the model and different techniques may be used to form the HMM from the sample signatures.
A known alternative to the BaumWelch algorithm for HMM reestimation is the Viterbi algorithm and this algorithm may therefore be used both for deriving the HMM model itself and for calculating probability in verification.
Claims (29)
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GB898925479A GB8925479D0 (en)  19891110  19891110  Improvements in methods and apparatus for signature verification 
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GB9024411D0 GB9024411D0 (en)  19910102 
GB2237917A true GB2237917A (en)  19910515 
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GB9024411A Withdrawn GB2237917A (en)  19891110  19901109  Signature verification 
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Cited By (4)
Publication number  Priority date  Publication date  Assignee  Title 

US5544257A (en) *  19920108  19960806  International Business Machines Corporation  Continuous parameter hidden Markov model approach to automatic handwriting recognition 
GB2431269A (en) *  20051013  20070418  Hewlett Packard Development Co  Detector for generating a model representing a form of markings for a pattern 
AU2002338814B2 (en) *  20011001  20080717  Kecrypt Systems Limited  A system for identifying a user 
US8553137B2 (en)  20050908  20131008  HewlettPackard Development Company, L.P.  Image data processing method and apparatus 
Families Citing this family (1)
Publication number  Priority date  Publication date  Assignee  Title 

US6655585B2 (en)  19980511  20031202  Citicorp Development Center, Inc.  System and method of biometric smart card user authentication 
Citations (1)
Publication number  Priority date  Publication date  Assignee  Title 

GB2183071A (en) *  19851105  19870528  Nat Res Dev  Apparatus for capturing information in drawing or writing 
Family Cites Families (1)
Publication number  Priority date  Publication date  Assignee  Title 

US3818443A (en) *  19720428  19740618  Burroughs Corp  Signature verification by zerocrossing characterization 

1989
 19891110 GB GB898925479A patent/GB8925479D0/en active Pending

1990
 19901109 GB GB9024411A patent/GB2237917A/en not_active Withdrawn
 19901109 WO PCT/GB1990/001725 patent/WO1991007729A2/en unknown
Patent Citations (1)
Publication number  Priority date  Publication date  Assignee  Title 

GB2183071A (en) *  19851105  19870528  Nat Res Dev  Apparatus for capturing information in drawing or writing 
NonPatent Citations (2)
Title 

IBM Technical Disclosure Bulletin,Vol.20,no.8, January 1978,pages 3355 to 3360 * 
ICASSP 86, Tokyo, pages 2071 to 2074, R. Nag et al, "Script recognition using hidden Markov models" * 
Cited By (6)
Publication number  Priority date  Publication date  Assignee  Title 

US5544257A (en) *  19920108  19960806  International Business Machines Corporation  Continuous parameter hidden Markov model approach to automatic handwriting recognition 
US5636291A (en) *  19920108  19970603  International Business Machines Corporation  Continuous parameter hidden Markov model approach to automatic handwriting recognition 
AU2002338814B2 (en) *  20011001  20080717  Kecrypt Systems Limited  A system for identifying a user 
US7558409B2 (en)  20011001  20090707  Kecrypt Systems Limited  System and method for identifying a user by grading a digital representation of an analogue form entered by the user 
US8553137B2 (en)  20050908  20131008  HewlettPackard Development Company, L.P.  Image data processing method and apparatus 
GB2431269A (en) *  20051013  20070418  Hewlett Packard Development Co  Detector for generating a model representing a form of markings for a pattern 
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Publication number  Publication date 

GB9024411D0 (en)  19910102 
GB8925479D0 (en)  19891228 
WO1991007729A3 (en)  19911031 
WO1991007729A2 (en)  19910530 
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