We propose a new paradigm for curve detection in which an autonomous and atomic description is computed between measurements on the image and global curves. The description takes the form of a discrete tangent field, i.e.. an estimated representation of quantized tangents and curvatures at each possible trace point. We then present a new algorithm for inferring global curves through this tangent field. by inferring a covering of the global curve. The elements of the covering are short splines, each of which moves according to a potential distribution computed from the tangent field. Both stages of the algorithm are parallel and both bear some analogy to biological mechanisms for curve detection