Fig. 1: Illustration of scale invariance.
a RF width (y-axis) is inversely proportional to fo (x-axis) in a model of scale invariance. Points that are common to any of the five blue diagonal lines are part of a scale invariant family. Four example Gabor’s are shown at the four locations indicated by open circles. Prior studies have typically modeled V1 RFs as sitting along the solid blue line (Eq. (1)). b SF bandwidth (y-axis) is proportional to fo (x-axis) in a model of scale invariance. Each location represents a 2D Gaussian that is constrained by the Fourier transform of the Gabors in a. Each blue line in b is calculated from the Fourier transform of the family of Gabor’s along each line of a. Also, the 2D Fourier transform of the four Gabors shown in a are overlayed, where the x-axis (cyc/°) is along the preferred orientation. The green ellipse indicates the distribution of 2D spectral energy. Along a line of scale invariance (e.g. solid blue), orientation bandwidth (“σϴ”, top right) does not change.
