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BACKGROUND OF THE INVENTION
This invention is in th e field of Signature Verification. The invention is
more particularly directed towards a method of determining whether or not
an individual signing his name is the same individual who signed the same
name which was provided as a reference signature by this individual.
According to this invention the movement of the writing instrument as the
name is signed is used to provide a series of data points represents of
that person's signature.
Related applications which describe a method of reading typed text which
are commonly assigned and are hereby incorporated by reference are as
follows. Ser. No. 115,986, filed Jan. 28, 1980, Inventor, Warner C. Scott;
Inventor Warner C. Scott; Ser. No. 153,342, filed May 27, 1980, Inventor,
Warner C. Scott; Ser. No. 501,037, filed June 1, 1983, Inventor, Warner C.
Scott; Ser. No. 527,152, filed Aug. 26, 1983, Inventor, Warner C. Scott;
Ser. No. 527,702, filed Aug. 26, 1983, Inventors, Warner C. Scott, Keith
A. Blanton, Steven Petersen and Ramon Helms; Ser. No. 527,151, filed Aug.
26, 1983, Inventors, Steven Petersen, Keith Blanton and Ramon Helms; Ser.
No. 527,155, filed Aug. 26, 1983, Inventors Keith Blanton, Steven Petersen
and Ramon Helms; Ser. No. 527,731, filed Aug. 26 1983, Inventors, Keith
Blanton, Steven Petersen and Ramon Helms; Ser. No. 527,150, filed Aug. 26,
1983, Inventors, Steven Petersen, Keith Blanton and Ramon Helms; Ser. No.
546,782, filed Oct. 27, 1983, inventor, Warner C. Scott; Ser. No. 546,752,
filed Oct. 27, 1983, C. Scott filed concurrently herewith.
It is desirable for a different application to verify that an individual
signing a particular name is in fact the individual whose name he is
signing. One method of determining whether or not the identity of the
person matches the name he has signed is the use of signature
verification. According to this invention an individual provides a
reference signature by signing his name a plurality of times to enroll his
signature. A signature selected from those provided is a reference
signature representative of that persons signature when they sign their
own name. At a later point in time when an individual purports to be the
same individual who provided the reference signature that individual is
required to replicate the reference signature. This replication is known
as the sample or data signature and provides a series of data points for
comparison with a reference signature which it purports to match. The
sample signature and reference signature are compared with each other and
an indication is given whether or not the same individual signed both of
the signatures.
This invention would find use in the banking industry, where a person could
simply sign his name to indicate his identity and the signature of the
name alone would be sufficient verification of identity to allow the bank
to dispense funds. This could be done through an automatic teller machine
or other device, thus saving considerable funds in hiring extra tellers to
provide this service. Additionally, this could find use in many other
applications, such as, access to particular locations, use of credit
cards, or other times when the identity of the individual signing the name
must be verified.
This invention uses unique factors and a combination of unique factors to
determine whether or not handwritten signatures belong to the same
individual. The approach of this invention is to gather data as the text
is written. In this embodiment the writing is performed on a data tablet
which records the location of the pen at a point in time on the clock
pulse. The data tablet provides the X and Y coordinate of the pen at the
point in time that the data is sampled. The X and Y coordinate of each
data point is used to produce a one-dimensional waveform of the character
as it was written. The waveform of the character has as the abscissa the
path length of the pen and as the ordinate the direction of movement. This
one-dimensional array of the data is an important beginning to a
simplification of an individual's signature. It is important to note that
the abscissa of the plot as shown in the accompanying figures is path
length and not time. This means that individual handwriting speed, writing
part of the letter faster than another part and other variations thereon
do not affect performance in any way.
The X-Y data tablet indicates the location of the writing instrument at a
predetermined clock pulse rate as the signature is written. A number
string is generated which indicates the relationship between sequentially
determined locations of the writing instrument as it moves to different
locations on the X-Y data tablet. The quantity of numbers within the
number string is an indication of the distance between sequentially
determined locations and the value of the numbers within the number string
is an indication of the direction of movement between sequentially
determined locations. Series of number strings form a waveform
representative of the signature as written by the individual. The waveform
of the sample signature is compared with the waveform of a reference
signature and an output is provided indicating whether or not the sample
signature and the reference signature were made by the same individual.
The two waveforms are compared to each other by size normalizing the
waveforms, aligning the buoys of the waveforms with each other,
determining the integral of the difference between the waveforms for
various buoy alignments and providing an integral of the difference of the
waveforms for their entire length. The integral is then divided by the
number of data points within the signature so that an average difference
between the two waveforms is provided. The average difference between the
two waveforms provides an indication whether or not the same individual
signed both signatures.
Signatures can be compared both qualitatively and quantitatively to
determine the degree of match between the signatures. A person or
handwriting expert reading the text may perform qualitative analysis and
look for similarities in a qualitative manner. However, it is difficult
for a computer to perform qualitative analysis. One object and advantage
of this invention is the placing of handwritten signatures having numerous
qualitative features into a quantitative form. This in effect quantitizes
the numerous qualitative features. The quantitative form may then be
analyzed by a computer and a quantitative output of the computer or
microprocessor takes into account numerous qualitative features which is
achieved through use of the waveforms and various comparison techniques.
The applicant has also provided a way of placing a handwritten signature in
polar coordinates having length and direction, (r, .theta.), to describe
the movement of the pen in a sequence the ignature is written. The use of
polar coordinates and having the magnitude of the polar coordinate being
the abcissa and the direction the ordinate is most useful in this
invention and is one of the steps of this invention which permits
quantitative comparison of qualitative data. This effectively produces a
continous history of pen movement as indicated by polar coordinates. The
direction of the polar coordinate, .theta., is determined as the direction
of movement from on equential point to another on the X-Y data tablet. The
magnitude, r, is determined as the distance of one location to the next.
In the embodiment described herein the polar coordinates are determined
using an X-Y data tablet in conjunction with a look-up table as stored in
the microprocessor memory. The polar coordinates could also be determined
using numerous other techniques. It can be seen looking at FIGS. 4 and 5
that .theta. is determined from FIG. 5 and r is determined from FIG. 4 to
make up the polar coordinate for each point of the waveform. The polar
coordinate could be separately determined using different techniques if
desired. This method of reducing handwritten signatures to data for
comparison with other handwritten signatures is to be contrasted with
numerous other techniques as a sequential continuous history of movement
of the writing instrument.
Numerous other novel features of this invention are also used in
combination with the waveform to produce a novel technique of
quantitatively analyzing a handwritten signature.
An apparatus for carrying out this invention can be provided with a
relatively inexpensive X-Y data tablet and a microprocessor chip with an
appropriate output and memory. This is an extremely inexpensive
implementation and yet is used in such a manner as to permit signature
verification of many individuals.
It is an object of this invention to provide a method of verifying whether
or not the same individual has signed two signatures which are provided.
It is a further object of this invention to provide a method of
implementing a signature verification apparatus which is relatively
inexpensive.
It is a further method of this invention to implement a signature
verification method which is extremely quick and accurate.
It is a further object of this invention to provide data representative of
an individual signature which is a one-dimensional array without time
being a factor within the array.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1a-b a reference signature with the respective reference waveform.
FIGS. 2a-b, show a signature written by the same individual at a later time
with respective waveform.
FIGS. 3a-b illustrate a signature by a person other than the ref individual
attempting to forge the referenced individual's name and the respective
waveform of the attempted forgery.
FIG. 4 is a look-up table indicating the number of unit vectors which would
represent the distance from a given point to a second point.
FIG. 5 is a look-up table which indicates the direcion of the vector
between two points. FIG. 6a-c illustrae size normalization of two
waveforms with each other.
FIGS. 7a-d represents one method of aligning waveforms of two signatures
for comparison.
FIGS. 8a-c represent a second embodiment for aligning digital waveforms of
two signatures and the use of dynamic programming to aid in the aligning
of the waveforms.
FIGS. 9a-b show an example of producing a waveform from handwritten text.
FIG. 10 illustrates removing relative slant from the waveform.
DETAILED DESCRIPTION OF THE INVENTION
Disclosed is an apparatus and method for generating data from pen
movements. The generated data is then used to provide a quantitative
analysis of the pen movement. The data can be used in numerous
applications. One application is in signature verification to determine if
two signatures were made by the same individual as more fully discussed
and claimed herein. An additional application is character recognition of
handwritten text, both printed and cursive as described and claimed in
TI-9218. An additional application is to provide a printing system which
prints characters directly from handwritten text as claimed in TI-10204.
The printer is particularly useful for Chinese and Japanese characters
because this eliminates the need for a keyboard input and permits direc t
printing of these complex handwritten characters.
An apparatus which could be used to perform signature verification is
preferably comprised of an X-Y data tablet which provides an output
indicating the X and Y location of a writing instrument on the tablet and
a microprocessor or computer for analyzing the information from the data
tablet. An X-Y data tablet is provided with five mil. resolution. The
graphic tablet indicates the X and Y coordinate at which the pen is
presently located and also indicates whether the pen is up from the paper
or down on the paper. This type of data tablet is commonly available and
the particular tablet used in one embodiment of this invention is a
Demi-Pad 5tm manufactured by GTCO Corp. of Rockville, Maryland. The
graphics tablet as used in this embodiment has a five mil. resolution,
however, it is to be understood that any resolution may be used and a
different resolution might be desirable depending on the particular use of
this invention. The graphics table described herein also uses a wire
connected to the pen to indicate whether the pen is up or down on the
paper. It is to be understood that numerous different types of data
tablets and writing instruments, refered to as pens herein, could be used
and all that is necessary is an indication of the location of the pen on
the paper. This may be done using a resistor array, a light sensor, an
optical scanner magnetic wands or any other tablet and pen which may be
used together to follow the motion of the pen as text is written.
The use of an X-Y data tablet is preferred in many instances because of the
very low cost with which they can be provided. Additionally, the pressure
sensitive X-Y data tablet described herein is sufficiently accurate and
yet is very simple and has a minimum amount of hardware. In the embodiment
described herein the hardware of the data tablet is performing very few of
the functions required for signature verification. It may be possible to
use a more elegant data tablet which provides directly the polar
coordinates, provides data at set distances rather than on a clock pulse
rate or other features which have been described herein as being performed
by a microprocessor.
An X-Y data tablet of finer or coarser resolution could be used depending
on the desired application. If the data tablet has finer resolution, for
example, in the range of one mil, the waveform would be correspondingly
more detailed and would more accurately represent the exact movement of
the pen from one location to another. This would be in conjunction with
the clock rate which samples the location of the pen. A coarser resolution
may be desirable in some applications when as detailed a waveform is not
required. It may also be desirable to use a data tablet with direct polar
coordinates rather than using the microprocessor to perform polar
coordinate conversion as will be described herein.
The X-Y data tablet provides an output at each clock pulse. The clock pulse
for this embodiment is at approximately 90 Hz. This means that 90 times
each second the data tablet the curren and Y location of the pen on the
tablet if the pen is touching the tablet or else indicate that the pen is
not touching the tablet by sending the appropriate data signal. When a
person is writing very quickly across the page fewer data points will be
received then if the same line were drawn very slowly across the page. The
final result, however, would be two lines which are identical to each
other without respect to the speed with which were written. The clock rate
in combination with the resolution of the data tablet will determine the
number of data points in the waveform. If the clock rate is extremely fast
and a fine resolution is used a large number of data points will be
determined while the pen is being moved on the paper. This will provide
considerable more data points for comparison of the waveform with other
waveforms. However, the comparisons will take much longer due to the
larger number of data points. If the pen is not moving on the paper the
location will not change from one clock pulse to the next and no data will
be supplied to produce the waveform. This is because there will be no
distance moved and no direction of movement which are the only two factors
used in determining the waveform. The clock pulse rate may be slower to
adapt to particular circumstances and for speed.
Data compression may also be desirable for specific applications. It is
possible to represent several identical data points or number string
comprised of many numbers by only a few numbers. It is also possible to
decrease the clock rate in conjunction with data compression so that the
waveform comparison may be performed more quickly.
The term "signature trace" as used herein refers to the course or path
followed by the writing instrument as the signature is written. "Trace"
has a standard meaning as defined by the dictionary.
The method of this invention will now be described. An overview of the
steps used in this invention will now be given which may prove helpful in
identifying which portions of the particular details fit at which point in
the method. First, an individual provides a reference signature which is
stored in a template memory as the ideal or reference signature of that
individual. The signature is stored with the necessary identification as
to which individual has signed that name. This may be stored on a magnetic
card such as a common credit card rather than in a template memory. It is
only necessary that the reference signature be provided to a
microprocessor for comparison with specific individuals. If the reference
signature was stored magnetically on a credit card the person putting the
credit card into the machine would be required to match the reference
signature on that credit card in order to continue use of the credit card
service or banking machine. Alternatively, if the reference signature was
stored on a template memory the person who is going to provide the sample
signature will have the desired reference signature retrieved from the
template memory.
A next step in the method of this invention is the providing of the sample
signature. The sample signature is provided by the unknown individual who
is attempting to sign the name which will match the desired reference
signature. The waveform for the sample signature is then generated to a
waveform using the techniques as more fully described herein.
When the pen is placed on the X-Y data tablet to begin writing the
signature the X-Y data tablet sends the X and Y location of this point as
the reference location. The X-Y data tablet continues to send the X and Y
location of the pen as it moves across the data tablet at a predetermined
clock pulse rate. As the pen moves to different locations on the X-Y data
tablet the distance and direction of movement between sequential locations
is determined. The distance and direction of movement is used to provide a
waveform which is an indication of the path followed by a pen in making a
signature. The abscissa of this waveform is cumulative path length and the
ordinate is direction of movement. It is important to note that the
waveform is specifically designed to remove the function of time from the
data.
It is desirable to indicate the beginning and ending points of the
signature. This can be done by the person providing the sample signature
pressing an input key and at the next point at which the pen touches the
pad will be indicated as the beginning of the signature. At the end of the
signature a person may lift the pen from the data pad and place it at a
particular location on the data pad to indicate the signature is over or
alternatively press an end button to indicate that the end of the
signature has been reached. The microprocessor can be programmed to ignore
data points for any signal noise which is recieved after the signature is
ended or prior to the signature being made.
After the waveform for the sample signature is determined the next step in
this invention is the comparison of the two waveforms with each other.
This is a quantitative comparison as more fully described herein with a
numerical output as the result indicating the degree of similarity. Prior
to making the quantitative comparison the waveforms are usually aligned
with each other. It is, of course, possible to compare the waveform with
no alignment whatsoever, however, the quantitative output will be somewhat
different than those in which various alignment techniques were used.
Alignment techniques are described herein with considerable detail.
Depending on the alignment technique which is used the quantitative
comparison will be considerably different for the sample reference
waveforms. The preferred alignment technique described herein uses dynamic
programming which is a method by which an extremely large number of
alignments are tested and the quantitative comparison made and then
alternative alignments are made with quantitative comparisons and that
alignment having the most favorable quantitative comparison is selected as
described herein with respect to dynamic programming. The next step after
performing the aligning using any one of the many techniques described
herein is to perform the actual quantitative comparison. This is done by
determining the integral of the difference between the waveforms in this
embodiment and providing a number proportional to the average integral
which is used to indicate indicating the similarity between the two
waveforms. The next step in the method of this invention is to output
whether or not the sample signature was made by the same person who
produced the reference signature. This output provides the average
integral between the waveforms and the relative data count between the two
waveforms.
The data count is an indication of the speed with which the pen was moved
as it was pressed against the paper. The combination of the integral score
and the data count score is an indication as to whether or not the same
person signed each of the names and is provided as the final output for
this machine or in place thereof merely a "yes" or a "no" indicating that
"yes" the person may proceed because the same person has provided both
signatures or "no", the person may not proceed because the signatures do
not match. The steps which have just been described will now be described
with more particular detail.
WAVEFORMS
It is very common in handwritten text for different parts of each letter to
be written at considerably different speeds. For example, the first part
of a curve or a straight line down may be made very quickly and the
transition from one letter to the next may be made at a much slower speed.
Alternatively, different parts of the same letter may be made quickly as
changes in directions are made or slowly for the same change of direction
at a different part of the letter. This invention specifically overcomes
the problems of writing the characters at different speeds as explained
herein. The waveform will be identical for written signatures which follow
the same path without respect to the speed. As can be seen by the
description of the waveform herein the waveform is specifically designed
to be identical in all respects whether the signature is written quickly
or slowly. This is because the waveform is a combination of the path
travelled and the direction of travel and is not determined using a
function of time.
The function of time and the speed with which a signature is written for a
different portion of this invention is determined independent of the
waveform. As a signature is made the X-Y data tablet will provide a number
of discrete data points which is a direct indication of the amount of time
taken to sign the name while the pen was moving on the data tablet. If the
pen is off of the data tablet or is stationary during clock pulses no new
data points will be provided and this will not increase the data point
count for that particular signature. In this way the number of data points
is directly related to the speed at which the pen is moved across the data
tablet while the signature is being made. It is not related to the amount
of time while the pen is off of the data tablet. The number of data points
received for the reference signature is determined and stored for use as
described herein.
The method by which the waveform is determined will now be described with
particular detail. The X-Y data tablet provides an output indicating the X
and Y location of the pen at any point during which the other is being
made. The microprocessor generates the polar coordinates of the pen from
the rectangular coordinates as given by the data tablets. The polar
coordinates are determined by placing the last location at the center and
the next location with respect to a first location being the center as
will now be described in particular detail. As the pen moves from one X
and Y location to the next X and Y location a vector connecting those two
points can be determined. The vector will have a magnitude and a
direction. Because the X-Y data tablet used in this embodiment provides an
output after certain time intervals the length of the vector will be
directly related to the speed with which the pen moved. If the pen was
moving very rapidly the two adjacent data points would be far apart on the
XY graphics tablet, however, if the pen moves very slowly the locations
may be adjacent squares on the X-Y data tablet. If there was no motion at
all the data point will be the same and the XY graphics tablet will
continue to provide the same X and Y locations for the pen each clock
pulse until the pen is moved. The data output from the X-Y data tablet is
made time independent.
The data output from the X-Y data tablet is made time independent in the
following manner. FIG. 4 shows a chart with the beginning X and Y location
at the center square. Squares which are considered to be one vector length
away are labeled with one. Squares of two, three, four and etc. unit
vectors away are labeled accordingly. A unit vector is defined in this
example as the distance across one square of the graphics tablet. It can
be seen that a diagonal movement across a square will be longer than a
horizontal or vertical movement across the square. Each square in FIG. 4
is individually labeled to represent the number of unit vectors from the
center square to that square. The data from the X-Y graphics tablet is fed
to a microprocessor or in the alternative to a large computer for
processing of the data.
One embodiment uses look-up tables to determine the length of the vector
between location and the direction of the vector. This has been found to
be an efficient way to quickly determine the length and direcion of the
vector betwen the points. It is possible to determine the waveform using
only look-up tables or using other methods to determine vector directions
and lengths, as is well known.
The table of FIG. 4 is stored in memory available to the microprocessor for
access as data points are read. When the microprocessor receives the
second data point it locates that square on the grid shown on FIG. 4 for
which the second point corresponds using the first point as the center.
When this point is located the microprocessor then determines the number
of unit vectors which correspond with the number which would reach the
partcular square. For example, if the reference location one were at the
center and the next location were to the right six squares and up five
squares this would correspond to an eight being in that square on FIG. 4.
The microprocessor would then produce a number string comprised of eight
unit vectors having equal magnitude and all having equal direction so that
the addition of these vectors would provide a result from point one to
point two on FIG. 4. This is illustrated in FIGS. 9a-b. It can be seen
that in this embodiment the microprocessor not actually determine the
vectors and their directions. The microprocessor merely counts the number
of squares in the X direction and the number of squares in the Y direction
which represents the difference between the reference location and the
next location. The microprocessor then addresses the appropriate portion
of the look-up table in memory to determine the number of unit vectors
which would be the distance corresponding to this X and Y location from
the reference location.
The microprocessor must then determine a direction of the vectors. In the
example given wherein the second square is six to the right and five up
from the first square the direction of the vectors is 28 as shown in FIG.
5. FIG. 5 shows the table which may be stored in memory available to the
microprocessor having the directions for all possible directions stored
therein as a look-up table. This provides fast access by the
microprocessor and an easy way to determine the direction of the unit
vectors. The microprocessor will therefore give each of the eight vectors
a magnitude of one and a direction of 28. It can be seen from FIG. 5 that
the number of directions goes from zero to 255. Zero is represented as
being due east, 64 as north, 128 as west and 192 as south. The use of 256
units to a circle was selected with digital prooessing in mind, however,
the invention could be just as easily carried out using 360 units, 512
units or any other convenient number. It has been found that the use of
256 units is sufficiently detailed to provide the desired waveforms. This
process is a rectangular to polar coordinate conversion.
The microprocessor has now determined a portion of the waveform of a
handwritten text which is independent of time, that is, the speed with
which it was written. The waveform from the example given would result in
a straight line eight units long at exactly 28. This is a single number
string made up of eight numbers. The number of units, which in this
example is eight, represents the distance between the two points and not
the speed with which they were drawn. If the first point had been produced
by placing the pen at the reference location and then lifting the pen off
of the data tablet for a few moments then placing the pen down at the next
location the digital waveform would look identical to drawing a line to
this data point. The total distance moved is eight units and the direction
of movement is 28. Without respect to the movement of the pen in between
the determination of data points.
As has been stated herein data points are determined at a clock pulse rate.
The location of the pen on the clock pulse will be the only data used in
composing the waveform. The movement of the pen in between clock pulses
will not be reflected. However, it is to be understood that in this
embodiment the clock pulses are sufficiently fast that locations are often
determined for adjacent squares. Accordingly, the path of the pen will be
important because the clock rate is so high that the entire path of the
pen will be traced from one square to the next. However, if the clock rate
is made slower or the pen is moved extremely fast it is possible for the
pen to travel a path other than a straight line betwee sequentially
determined data points.
This becomes apparent and particularly useful when the pen is lifted off of
the tablet dotting an i or crossing a t. The time for which the pen is off
the data tablet will not be counted and no data points will be provided.
Therefore, the last data point when the pen left the tablet and the
location of the next data point when the pen first touches the tablet will
be independent of the paths followed by the pen while up in the air. It
will also be independent of the amount of time taken to move from one
location to another. It will be directly related to the distance between
the two points and the direction of movement from one point to the next
the two points on the data tablet. This is been found to be a particularly
effective technique for signature verification. An individual almost
always signs his signature with exactly the same order of crossing t's and
dotting i's. Furthermore, the movement from one part of the signature to
begin to cross the t and dot the i is always uniform within the person and
will be uniform in direction and in relationship of length to the whole of
the signature. This particular feature is extremely difficult to forge. If
an attempted forger dots the i or crosses the t in any different order the
waveforms will be significantly different because the waveform is
particularly sensitive to the order in which these functions occur due to
the waveform being constructed from sequentially determined data points on
the paper.
Referring now to the two locations as previously stated it can be seen that
the waveform of these two points would be represented by drawing a
horizontal line eight units long approximately between north and east at
exactly a 28 direction mark as shown in FIG. 9a. FIG. 9a shows east is a
zero unit, north is at 64, therefore these two points could be represented
by drawing a horizontal line eight units long approximately halfway
between north and east at exactly a 28 direction mark. A number string as
used herein refers to those data numbers generated to represented movement
from one location to the sequentially adjacent location.
When the pen moves to a third data point the second data point is
referenced as though it were the center of the block of the squares shown
in FIG. 4 and 5. For example, if the next data point were two to the left
and one up from the data point located at 28 in the prior example this
would be represented as two unit vectors having equal length and a
direction of 109. As can be seen from FIG. 5 this direction of 109 is
determined by placing the most recent data point at the center of FIG. 5
and then determining the relationship between the next data point and the
prior data point and if the prior data point were at the center of FIG. 5.
The determination of a portion of the waveform is shown in FIG. 9a. The
chart shown in FIG. 5 is used to determine the direction of the unit
vectors for sequentially located data points. After the unit vectors are
determined they will be added one at a time as shown in FIG. 9a to
determine a waveform. For example, if the fourth point located as the
signature was written were five to the left and two down from point three
as shown in FIG. 9b this would have a direction of 144. The direction of
144 can be determined by using point three as the center square in FIG. 5
and moving left in the X direction five and down in the Y direction two to
reach the square 144. The length of the distance between points three and
four in unit vectors can be determined from FIG. 4 by going five to the
left in the X direction and two in the Y direction and the number five in
this square indicates that there are five unit vectors between points
three and four. Therefore a number string of five numbers would be
generated. The waveform in FIG. 9a illustrates the movement of the pen
from three to four by drawing a path length which is five units long at a
direction of 144. The next point located is the signature written shown as
point five in FIG. 9b. This point is ten points to the right in the X
direction and four points down in the Y direction from point four. When
FIGS. 5 and 4 are used to determine the number of unit vectors and the
direction the distance between points four and five is so great that the
look-up tables do not allow this determination.
In determining the waveform between points four and five the path length is
broken into two vectors having an approximately equal length the result
will be one vector between points four and five. In the example given this
could be accomplished by using two vectors each five units to the right on
the X direction and two units down on the Y direction. A vector of this
length can be found on FIG. 5 having the direction of 240. FIG. 4 shows
that the path length is equal to five unit vectors for the vector between
point four and the halfway point and is also equal to five unit vectors
for the path length between the halfway point in point five. The waveform
produced from this line drawn from point four to point five is shown
illustrated in FIG. 9a.
The movement of a writing instrument as described and shown in FIG. 9b
would produce the waveform as described and shown in FIG. 9a. As clearly
illustrated on FIG. 9a the path length is the abcissa and the direction is
the ordinate. It is to be understood that the waveform of 9a is greatly
exaggerated and is an expanded version of the waveform which would
normally be produced by a writing instrument. The resolution of the X-Y
data tablet will be sufficiently great that there will not be many sharp
steps of significant direction changes unless there is an extremely sharp
change of direction. Handwriting of an individual is usually much smoother
than that shown in FIG. 9b and the digital waveform produced thereby would
be correspondingly smoother and have fewer distinct steps. However, in any
handwriting when a sudden change in direction occurs, especially a
complete reversal of direction the digital waveform will reflect the
sudden change of direction with the step increase or decrease from one
direction to the next.
If the pen is moved very quickly or is off the paper between points it is
possible for adjacent located points to be further than a threshold number
of unit vectors apart. This is because the location is sampled at a
constant clock rate to determine the location of the pen and movement
greater than the threshold number of unit vectors during the time interval
would place the pen outside the look-up table which has been provided in
FIG. 4. As can be seen on FIG. 4 the threshold value that would require
splitting of the vector is nine but may be as high as 13 depending on the
direction. The vector is too large if the second location of the pen would
not be shown by FIG. 4 by placing the first location at the center. When
this occurs the microprocessor automatically splits the vector into two or
more equal vectors each of which is less than the threshold value of unit
vectors from the prior adjacent point and the sum of which is equal to the
original single vector. Each of the two vectors are then analyzed in the
described fashion to determine the appropriate unit vectors and their
direction and are made part of the vector sum to determine the waveform.
Examples of waveforms are shown in FIGS. 1b, 2b and 3b. These waveforms
were produced on a plotter to illustrate the digital waveforms used as
produced by the microprocessor in this invention. As can be seen, when the
same direction is maintained for a great path length a straight,
horizontal line is produced in the waveform. When the pen is raised from
the paper and then put down at a new location the microprocessor treats
these as two adjacent locations and computes the waveform in the described
manner. This will be illustrated in the waveform as a horizontal line
representing the distance between the two points in the direction a vector
between the the two points would have. When the direction of motion is
sharply changed a straight vertical line results as shown in the digital
waveforms. It is to be understood that the digital waveforms illustrated
in the figures, including FIGS. 6a-c, 7a-d and 9a are greatly enlarged to
show particular details and to make understanding of the waveform and
comparison techniques easier.
The determination of a waveform from a signature can be seen by comparing
the example given in FIGS. 1a and 1b. FIG. 1b represents a waveform
produced from the signature made in FIG. 1a. At the start of the W the pen
begins a movement in the direction of approximately 40 as shown by FIG. 5
and continues to curve around to the top of the first curve in the letter
W until it moving in direction of exactly zero. This is shown as the
waveform in FIG. 1b passes through zero at point 42. The pen continues to
move along the paper until it reaches the first vertical portion of the
letter W and moves straight down in making this letter. This vertical
movement has a direction of approximately 192 and continues for a specific
distance during a plurality of clock pulse rates as represented by the
horizontal line 44 in FIG. 1b. A horizontal line in FIG. 1b is an
indication that the pen move the same direction for a specific distance.
It can be seen that the abcissa is distance moved by the writing
instrument and the ordinate is direction of movement. There is no
indication of time in the waveform. The W is formed by curving across the
bottom and going through zero again reaching the top of the center of the
letter W and then suddenly reversing direction to go straight down in the
middle of the W. This sudden reversal of direction is illustrated as line
46 in the waveform of FIG. 1b. This is a vertical line illustrating a
sudden jump from one direction to another due to the reversal of
direction. After the sudden reversal of direction the rest of the letter W
is formed and then passes through the zero direction and wraps around the
waveform as shown in FIG. 1b. The end of the letter W is shown as 47 on
FIG. 1b.
The pen is then lifted from the paper and moved in the air to begin making
the a in Warner. When the pen reappears at the top of the letter a this is
shown as 52 in the waveform of FIG. 1b. The horizontal line 50 represents
the direction of movement from the top of the W to the top and beginning
point on the a. The line is horizontal indicating that the direction of
motion was unchanged for a certain distance. It can be seen that the
waveform reflects the pen movement from one portion of the signature to
another even though the pen is off the paper. The waveform uses the last
location on the W as the first point and the first location on the a as
the next point to determine the movement of the pen from one point to the
next on the data tablet. The waveform is then generated by determining
unit vectors to that distance and the direction of movement between the
two locations. No data points are generated while the pen is off the
paper. It can be seen that the waveform would be identical if the pen were
left on the paper and moved in a uniform direction from the top of the W
to the beginning of the letter a. In this respect the directional
relationship from one letter to another with the pen off the page in
between them is extremely important. The relative relationship between
sequentially located points on the data tablet is determinative of the
direction of the horizontal line. The direction of motion from the top of
the W to the beginning of the a is approximately 230 as can be seen in
FIGS. 5 FIG. 1b. If this direction of motion were slightly offset the
horizontal line may be the same distance in length but the direction of
motion would be considerably different and would be reflected by an
increased integral of the area between the waveform as will be described
herein.
The remainder of the word Warner is written and produces the waveform as
shown in FIG. 1b. The pen is then lifted from the page and the letter C is
made as indicated by the slanting line 53. After the letter C has been
made the "." behind the initial C is made as represented by 56 in FIG. 1b.
The length of the horizontal line just prior to 56 is an indication of the
distance between the C and the ".". The pen is then again lifted from the
paper and moved to begin making a letter S. When the pen is placed on the
paper to begin making a letter S this is indicated as 60 in FIG. 1b. The
direction of motion from the "." to the top of the S is at a direction of
approximately 30 and is horizontal for a specific distance as shown by
line 58. When the pen touches the paper to begin making the S the
direction of travel is reversed as indicated by the vertical lines between
the horizontal line 58 and point 60. The remainder of the word Scott is
then written as shown by the waveform.
The order in which the person signing their name dots the i's, crosses t's,
etc. is crucial in forming the waveform as can be seen from this example.
For example, if the "." after the letter C had been made at the end of
that entire signature this would considerably change the waveform. Even
though the final signature may look identical after it is written. If the
"." were placed after the word Scott had | | |
