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In addition to a pair of images and a particular transformation, the cost
function requires that a method of interpolation be defined. That is,
some method of calculating what the intensity is in the floating image
at points in between the original voxel (or grid) locations. This is
necessary in order to know the intensity at corresponding points in the
images after the geometrical transformation has been applied to the
floating image.
Interpolation methods that are commonly used are: trilinear (also
called linear or, in 2D, bilinear), nearest neighbour, sinc (of
various kernel sizes and with or without various windowing functions;
e.g. Blackman), spline and Fourier.
The choice of method has some impact on cost function smoothness,
although all interpolation methods except nearest neighbour are
continuous. However, the choice of method becomes most critical for
motion correction as the transformed image intensities are needed for
later statistical analysis.
Peter Bannister
2002-05-03