Thecramerraoboundfor Discrete-time Edge Position Estimation

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. &ev Words ad Phrases: Edge detection, Cramer-Rao Bound, Pattern Recognition, Estimation Theory This work partially funded by the SRC Contract No. 9 1 -MC-5 15 and the National Science Foundation, NSF Contract No. MIPS 8957058. Copyright