Identification of multidimensional time series and its application in computer graphics

This paper extends the well-known technique of linear signal analysis by predictive filtering to the case where the signals are multidimensional. The properties of the simplest possible multidimensional filter, with a 2-dimensional input and of first order, are examined in detail. It is shown that such filters generate linearly deformed logarithmic spirals, including conies as a special case. The technique can be used to identify segments of such curves drawn freehand in a computer graphics environment; and a system which incorporates it is described. One of the most useful features of the system is its ability to transform the curve by controlling the amount of spiralling, rotation, scaling and translation, on command from the user; this is easy to do because the geometric properties can be calculated from the predictive filter coefficients.