The problem of extracting continuous structures from noisy or cluttered images is a difficult one. Successful extraction depends critically on the ability to balance prior constraints on continuity and smoothness against evidence garnered from image analysis. Exact, deterministic optimisation algorithms, based on discretized functionals, suffer from severe limitations on the form of prior constraint that can be imposed tractably. This paper proposes a sequential Monte-Carlo technique, termed JetStream, that enables constraints on curvature, corners, and contour parallelism to be mobilized, all of which are infeasible under exact optimization. The power of JetStream is demonstrated in two contexts: (1) interactive cut-out in photo-editing applications, and (2) the recovery of roads in aerial photographs.