Our approach is to define a novel, single, external bidirectional force field which has the ability to dynamically update itself while the contour evolves. This is significantly different from other works and we emphasise that it does not involve the introduction of any extra forces to mobilise the force field.
In brief, we hypothesise electric currents flowing through both the object boundary and the active contour. The magnetic fields generated by each of the currents will interact and cause a force between them. This magnetic vector force field behaves as an external force to push or pull the active contour towards the object boundary. Although the magnetic field caused by the image gradient is stationary, the force it imposes on the snake is dependent on the snake’s evolution. Thus the force field is dynamically changing along with the snake. We show that by using this electromagnetic interaction analogy between image gradients and active contours, the snake is then much less sensitive to its initial position and much more robust towards complex geometries and topologies.
Next, we present the basic theory of magnetostatics which is used to provide the analogy for our magnetostatic active contour MAC. The Level Set method is then used to implicitly represent and evolve MAC.