Geometric interpretation

This proof offers an interpretation of the Lomoplan outputs. When Lomoplan first computes the filter coefficients, it estimates the vector ${\bf p}$. The filter coefficients capture the inverse (dip) spectrum of the local subcube. The application of the filter within the subcube computes at every location the vector product of the overall gradient of the subcube and the gradient at that specific location, $\Vert{\bf p}\Vert \Vert\nabla g\Vert \sin(\alpha) {\bf n}$.($\alpha$ is the angle between ${\bf p}$ and the gradient $\nabla g$;${\bf n}$ is the normal to the plane spanned by ${\bf p}$ and $\nabla g$).