Interpolation Method

When using an intensity-based cost function, it is necessary to repeatedly resample one of the images to match the other. This resampling process necessarily requires selection of an interpolation model to be used within the registration algorithm. It is important to understand that the interpolation method used for registration does not have to be the same interpolation method used when applying the optimal registration parameters to compute a final image (see Fig. 1). Because speed is important, simple trilinear interpolation is usually the interpolation model implemented when optimizing intensity-based cost functions. Hajnal et al. [10] suggested that the use of sinc interpolation during registration might lead to improved registration accuracy. Direct comparisons of trilinear and sinc interpolation [7,21] have found that the theoretical advantages of sinc interpolation do not translate into substantial improvements in registration accuracy and that the deterioration of performance in terms of speed is severe with sinc interpolation.

For calculus-based minimization using analytical derivatives, the interpolation of voxel intensities is a critical link between the spatial transformation model (which dictates exactly where in space the interpolated value must be computed) and the derivatives of the cost function based on that image intensity with respect to the formal spatial transformation parameters. A small change in a spatial transformation parameter will slightly alter the position at which the value must be interpolated, and this will in turn alter the intensity itself. Calculus-based methods track these derivatives through the entire process, invoking the chain rule as necessary to reduce the redundant computations. Explicit equations for the derivatives of the trilinear interpolation process are given in [23].

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