Abstract
Partitioning Magnetic-Resonance-Imaging (MRI) data into salient anatomic structures is a problem in medical imaging that has continued to elude fully automated solutions. Implicit functions are a common way to model the boundaries between structures and are amenable to control-theoretic methods. In this paper, the goal of enabling a human to obtain accurate segmentations in a short amount of time and with little effort is transformed into a control synthesis problem. Perturbing the state and dynamics of an implicit function's driving partial differential equation via the accumulated user inputs and an observer-like system leads to desirable closed-loop behavior. Using a Lyapunov control design, a balance is established between the influence of a data-driven gradient flow and the human's input over time. Automatic segmentation is thus smoothly coupled with interactivity. An application of the mathematical methods to orthopedic segmentation is shown, demonstrating the expected transient and steady state behavior of the implicit segmentation function and auxiliary observer.