You've got directional frequencies in 2d - you'd measure it in the direction of some vector. With sinusoids, cos(wx+vy), the "natural" frequency is along the (w

You've got directional frequencies in 2d - you'd measure it in the direction of some vector. With sinusoids, cos(wx+vy), the "natural" frequency is along the (w,v) direction. The 1D frequency along this direction is |(w,v)|^2. It's like how with the gradient, you have directional derivatives.