Detection and smoothing of edge contours in images by one-dimensional Kalman techniques

An edge model is developed along with the associated edge detection and contour determination algorithms. An edge point along any scan direction is defined as a sufficient jump in the mean of a time series that is assumed to be white Gaussian around the edge point with the same variance on either side. An edge contour is defined as a sequence of such edge points, each point denoted by the two coordinates of the image plane. Each coordinate sequence is modeled as first-order autoregressive Gaussian over and above a straight line sequence of arbitrary, finite slope and intercept. The first stage of the overall algorithm examines the time series along each row and each column, forms a window around each potential edge point, detects the location and estimates the variance of the error in the location of the edge point, by pattern recognition techniques. The second stage forms noisy edge contours by graph searching techniques. The third stage is smoothing of an edge contour, formulated as a well-defined Kalman smoothing problem. It is shown that the parameters of the system and noise can all be estimated from the data itself. Experimental results on a simple image are discussed