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A sequential algorithm for edge detection using a line-byline detector of edge elements connected to a recursive edge-following scheme is presented. On each line, edge elements are detected by means of a filtering operation in order to follow the slow variations of the gray level and some sequential and recursive estimators for locating jumps in this level. The edge-following problem is solved by a Kalman filter, the state model corresponding to a noisy straight line. In this first part, the complete edge detection algorithm is presented after a brief survey of edge detection methods available in the literature. Two main examples of applications are given: detection of white and black targets in the landscape in order to perform automatic driving of vehicles and detection of blood vessels in stereographic images of the brain. In the second part, a detailed study of the sequential estimators for change in mean, which are used in the line-by-line detection, will be found.