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In this paper, we propose to use B-Splines to represent digital curves. We have developed an efficient algorithm to locate corners and at the same time encode curve segments between them using B-Splines. Used in conjunction with our subpixel edge detector, , it allows us to obtain accurate position of the corners, as needed in many registration problems such as stereo matching and motion parameter estimation. In addition to corners, we detect points of significant curvature between them. The resulting representation is a good approximation of the original, in the sense that it makes interesting points explicit, and achieves significant data compression.