Systems and methods are provided for interactive construction of an object boundary by minimizing a sum of costs, including costs associated with inconsistency of the image data and costs associated with undesired curve shape properties. A particle filter optimization algorithm is implemented that incorporates a variable strength, intrinsic preference for boundary smoothness. The particle filter generates alternative sequences of random moves, constructed in parallel, to avoid becoming stuck in local minima. Approximate optimization algorithms are utilized, keeping computational burden low, freeing resources to analyze intrinsic costs associated with local curvature. In one embodiment, a user may construct a curve by launching a particle stream, and by choosing visually satisfactory locations on the stream from which to relaunch particles. The user can also provide other input, such as drop down dams to redirect the stream at T-junctions. Additionally, a facility is incorporated to break the smoothness constraint automatically at corners of the object boundary.