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A relaxation process is described and is applied to the detection of smooth lines and curves in noisy, real world images. There are nine labels associated with each image point, eight labels indicating line segments at various orientations and one indicating the no-line case. Attached to each label is a probability. In the relaxation process, interaction takes place among the probabilities at neighboring points. This permits line segments in compatible orientations to strengthen one another, and incompatible segments to weaken one another. Similarly, no-line labels are reinforced by neighboring no-line labels and weakened by appropriately oriented line labels. This process converges, in only a few iterations, to a condition in which points lying on long curves have achieved high line probabilities, while other points have high no-line probabilities, There is some tendency, under this process, for curves to thicken; however, a thinning procedure can be incorporated to counteract this. The process is effective even for curves of low contrast, and even when many curves lie close to one another.