BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CSL-TR-93-560
       ENTRY:: November 08, 1994
ORGANIZATION:: Stanford University, Computer Systems Laboratory
       TITLE:: The Cramer Rao Bound for Discrete-Time Edge Position
        TYPE:: Technical Report
      AUTHOR:: Gatherer, Alan
        DATE:: February 1993
       PAGES:: 24
    ABSTRACT:: The problem of estimating the position of an edge from a
               series of samples often occurs in the fields of machine
               vision and signal processing. It is therefore of interest to
               assess the accuracy of any estimation algorithm. Previous
               work in this area has produced bounds for the continuous time
               estimator. In this paper we derive a closed form for the
               minimum variance bound (or Cramer Rao bound) for estimating
               the position of an arbitrarily shaped edge in white Gaussian
               noise for the discrete samples case. We quantify the effects
               of the sampling rate, the bandwidth of the edge, the shape of
               the edge and the size of the observation window on the
               variance of the estimator. We describe a maximum likelihood
               estimator and show that in practice this estimator requires
               fewer computations than standard correlation.
       NOTES:: [Adminitrivia V1/Prg/19941108]
         END:: STAN//CSL-TR-93-560