A surface Laplacian reflects the application of a Laplacian operator that has been restricted to a two-dimensional surface topography. Although the general volume-conduction relationship indicated in Eq. 3 may be simplified for one-dimensional intracranial implementations by the proportionality indicated in Eq. 4, the volume implied by a spherical (or more complex) three-dimensional model is clearly not represented by the surface Laplacian. However, the Laplacian operator retains its usefulness for any spatial data set, providing an efficient filter that reliably sharpens images by enhancing edges (e.g., Chanda and Majumder, 2006). Coupled with the reference-independence of the measure, these advantages attracted considerable interest when CSD was first popularized, whether it be the capacity to localize visual (Srebo, 1985) or somatosensory processes (Crammond et al., 1985) or to simplify the topography of EEG rhythms (Koles et al., 1989; Law et al., 1993a; Tenke and Kayser, 2005). The same properties also make the surface Laplacian attractive as a solution to practical problems common in brain computer interfaces (BCI; Babiloni et al., 2001; Cincotti et al., 2003; Pfurtscheller, 2003; Pineda et al., 2003; Wolpaw and McFarland, 1994).
