D.A. Shub

In the most of data analysis systems the data reception occurs in unequal intervals of time while for data processing and analysis it is convenient and often necessary to have the sequence of uniform-by-time readout. Necessity of solving such problem occurred during development of program system of handwriting input, storing, analysis and visualization. In this program system during the handwriting analysis it is used temporal characteristics of pen movement - time intervals between the written curve points, speed and acceleration of pen movement. The temporal characteristics of handwriting are got by means of graphic tablets. The graphic tablets generate readouts through unequal intervals of time, whereas to use most of input data analysis algorithms (such as DTW, HMM, GMM) the sequence of uniform-by-time readout is required. To gain readout values, concerning time moments between known readouts, it is offered to use interpolation. To solve similar problems, piecewise-linear and spline interpolation are widely used. In the given work Hermite spline interpolation is used. It provides not only smooth interpolating function, but also equality of its derivative to given values. As in considered case exact values of tangent angles in measurement points are unknown, it is more convenient to use Catmull-Rom spline interpolation, being particular case of Hermite spline interpolation. In case of Catmull-Rom spline interpolation it is enough to know values of readouts between which the interpolated readout lays and values of previous and next readout. To do this, gaining interpolated sequence algorithm was developed. The developed algorithm is implemented in DA 3D+ Handwriting program system. This program system is used for automated analysis, input and visualization of handwriting and signature.