Kinematic theory of signature verification measurements

Previous empirical work on signature verification suggests a theoretical study of appropriate measurements. First, plausible arguments from imagined experiments isolate pen-point accelerations as basic variables. Then, heuristic analysis offers a conjectural form for size and speed variations, while vector-matrix notation permits a brief appraisal of position and velocity measurements. Recent test instrumentation of Herbst and Liu motivates a broad investigation of accelerometer data. Then, recovery of the pen-point acceleration requires determination of the complete pen trajectory, and theorems about ordinary differential equations preclude degeneracies of the assumed instrument configuration. Also, block triangularization of a nondegenerate system provides effective reduction to known computational methods, and spatial alignment of the point trajectory permits numerical solution with incomplete initial conditions. An analytic solution for certain degenerate cases shows the specific pathologies of such instrumentation. A hypothetical constraint on handwriting motion yields an iterative solution from fewer measurements. Some final remarks evaluate data-reduction proposals. © 1980.