THE RECURSIVE ESTIMATOR 

In order to estimate the position of the pen tip at each time step, we use a particular form of a recursive estimator, a Kalman Filter. Such an estimator can be used based on the assumptions that: 

  • The dynamics of the system whose state is to be estimated can be modeled. 
  • Measurements of the system's outputs with direct or indirect information on the system's state can be made. 
  • Given a prediction of the system's state a prediction of the system's outputs can be made. 
    •  Furthermore: 
  • We have an (albeit simple) dynamical model of the system whose state consists of the position, velocity and acceleration of the pen tip. 
  • The detection of the most likely position of the pen tip at each given frame is obtained by template correlation. The position of maximum correlation will provide the measurements for our recursive estimator.
    •  Given the simple dynamical model of the pen tip motion, we can use the original Kalman Filter formulation, that  assumes the system is linear, and that inaccuracies in the dynamical model and measurement noise can be modeled as gaussian processes. In our case, the assumption of gaussian noise is clearly unrealistic, since the innovation of the filter shows a lot of structure. We are working on implementing better models of handwriting generation that will fit the experimental results. Also, in order to speed up the estimator to run at real-time rates, a sequential measurement update scheme is used. 

    Return to the pen interface page. 

    Mario Enrique Munich - mariomu AT vision DOT caltech DOT edu