Modified Fluid 1 (MF1)

MF1 utilises prior knowledge of regions whose intensity information we do not wish to contribute to driving the registration. These regions will be passive in the registration. A binary array is provided whose pixels, corresponding to those in the source, are flagged as passive or active. It is subjected to the same deformations as the source image and is supplied to a Euclidean Distance Transform (EDT) which specifies the distance x from the passive regions. At each timestep in the fluid algorithm, forces at each pixel in the source are computed as in [8] from source-target intensity differences and from intensity gradients in the source. Prior to solution of the PDE, the forces are multiplied by the weighting function (6), which smoothly reduces them to zero in the neighbourhood of the passive regions.

$$w(x;a,b) = \left\{ \begin{array}{r@{\quad:\quad}l} 0 & x \leq... ...-a}}\right)\right) & a<x<b \\ 1 & x \geq b \end{array} \right.$$ (4)

We used a=1 and b=13 and found the 4SED algorithm [9] to be an adequate approximation to the Euclidean distance.