The considerations outlined in this tutorial review show that spatial high-pass properties of the surface Laplacian transform may be tailored to the research objective by the use of spherical splines with appropriate parametric choices for flexibility and regularization (cf. Figs. 8, 9 and 15). In fact, rigid splines and heavy regularization could be used to spatially low pass a topography that is virtually identical to a surface potential topography, however, it would still be reference-free. While this may appear to counter the advantage of the surface Laplacian, it would directly serve the need to maintain low spatial frequencies in the EEG signal, if this was an important concern (e.g., Nunez et al., 1999). Although this objective is incompatible with the maxim of minimizing surface Laplacian estimates with respect to the ‘analytic’ surface Laplacian distribution, which is better for more flexible splines (i.e., m = 2 or m = 3; Babiloni et al., 1995), the recommendation to use the surface Laplacian as a supplement to surface potential analysis implies an even greater discrepancy by prioritizing reference-dependent topographies without regard for the
