The local Hjorth algorithm7 (Hjorth, 1975) applies the nearest neighbor strategy of the linear intracranial CSD to a two-dimensional surface (i.e., subtracting the linearly-weighted potential of the nearest neighbors). Such local estimates fail at the edges of a two-dimensional montage (cf. Tenke et al., 1998), effectively reducing the number of channels with available CSD data. Likewise, just as the consecutive points in a one-dimensional calculation may be smoothed across additional points (e.g., 5-point smoothing; Freeman and Nicholson, 1975), a wider spatial filter may be applied to a two-dimensional array as well. At this point it becomes intuitively apparent that smoothed scalp Laplacian estimates will begin to fail when smoothed across long distances if the curvature of the scalp is not accounted for, and conversely may be improved or stabilized (i.e., filtered) by various spline-fitting methods (e.g., Koles et al., 1989; Carvalhaes and Suppes, 2011). The impact of activity at more distant sites is greater when estimates are fit using a rigid spline, while local influences will increase with a flexible spline. Likewise, a spherical geometric model provides both a parsimonious simplification (Perrin et al., 1989; Law et al., 1993a, 1993b) and consistent estimates across all channels of the EEG montage.
