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# Signature Verification Based on Complete Accelerometry

IP.com Disclosure Number: IPCOM000088345D
Original Publication Date: 1977-May-01
Included in the Prior Art Database: 2005-Mar-04
Document File: 3 page(s) / 51K

IBM

## Related People

Herbst, NM: AUTHOR [+2]

## Abstract

Recent work [1] and [2] has demonstrated an operating signature verification system based on the motion of the stylus during the signature as measured by two accelerometers. This work tacitly assumed that the motion of the pen point could be determined by means of a tablet or a pair of accelerometers mounted within the pen.

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Signature Verification Based on Complete Accelerometry

Recent work [1] and [2] has demonstrated an operating signature verification system based on the motion of the stylus during the signature as measured by two accelerometers. This work tacitly assumed that the motion of the pen point could be determined by means of a tablet or a pair of accelerometers mounted within the pen.

Measurements on a large number of actual signatures has revealed that many signatures contain substantial rotational or pitching motions, as well as pure translations. Thus a complete description of the pen motion must include rotations of the pen about the point (pitch) as well as translations.

The practical importance of this became clear when several individuals were observed writing almost exclusively with finger motions, by rocking the pen back and forth. The two-accelerometer pen gave no output for these signatures, although the motions were appreciable.

By classical mechanics, the complete description of a rigid body in 3-space requires 6 measurements. Some simplifications are possible because of the nature of the signature. Fig. 1 shows the pen schematically located in space. Accelerometers are mounted at A and B. The acceleration q at any point on the pen is given by the well-known equation q = w x r + wx(wxr) + Lambda/-1/ (f + g) where f is the translational force of the pen origin in space coordinates, g is the force of gravity, r the location of q relative to the pen origin, and Lambda is the transformation from body to space coordinates. The essence of this structure is to use f and w, or approximations thereto, as measurements for signature verification.

A six accelerometer pen is not overly practical. Since the pen is in contact with the writing surface and axial rotations of the pen appear to be very significant, the disclosed system has only four important degrees of freedom. Thus four accelerometers yield a useful approximate solution.

Such a pen is shown in Fig. 2. Four miniature semiconductor accelerometers 12, 0.125 in. diameter, are mounted in parallel tubes symmetrically placed about the pen axis. The pen also contains a pressure gauge 14. As shown, the pen is a ball-point pen with an ink cartridge 16. The pen is approximately 1/2'' in diameter. The necessary wires leading from the pen's five individual sensing elements are not shown. General form

In its most general form, the pen must contain 6 noncolinear accelerometers. The 6 accelerations are then processed along classical lines of inertial navigation
[3]. 1. Determine [w] algebraically. 2. Integrate to find [w]. 3. Solve the ordinary differential equation Lambda = Lambda w for the direction cosines. 4. Solve the remaining 3 equations for [g + f]. The initial conditions can be determined by tracking the pen from its re...