Orientation

The orientation selectivity of a cell is defined by two different measures - circular variance and bandwidth.

1) Circular variance is calculated from orientation tuning curves as follows:

CV = 1 - |R|, where R = sum(rkexp(i2thetak))/sum(rk) and rk is the response (mean firing rate in spikes/s) @ angle thetak (in radians). Angles should be spaced at equal intervals of 15 deg. If they are not, the data is interpolated and smoothed (see below), and then resampled at 15 deg intervals.

2) Bandwidth at 1/sqrt(2) is calculated as follows. The data is interpolated at 1 deg intervals and then smoothed with a Hanning window filter of a certain half-width @ half-height. Location of a peak is determined and orientations closest to the peak for which the response equals 1/sqrt(2) (70.7%) of the peak response on either side is estimated. The bandwidth is the one-half of the difference between these two angles (denoted by vertical dashed lines).

References:

Orban (1994) ...
Ringach et al. (2002) Orientation selectivity in macaque V1: diversity and laminar dependence. J Neurosci 22: 5639-5651
Schiller et al. (1976)...