The estimator described in section 2.2.1 becomes increasingly inaccurate for sub voxel width filter sizes. As the filter width decreases equation 12 becomes increasingly inaccurate until the estimation in equation 14 is no longer valid. An alternative estimate [2] offers a more robust result when evaluating images with small spatial correlation. Consider the following definitions

where is a unit vector along the dimension currently under consideration. is the individual voxel variance, the variance of the difference between each voxel and its edgewise neighbours, and is the correlation of two neighbouring voxels.

The approach outlined in 2.2.1 calculates the quantity

Forman *et al* derive the alternate formula

Mark Jenkinson [4] has provided an extensive derivation for this formula as well as pointing out another, computationally cleaner, variation on the same theme

Equations 20 and 21 remain accurate for relatively small spatial smoothnesses and it is equation 21 that you will find in the FSL code base.