What is difference between along the edge and across the edge I am trying to implement a paper called structured tensor based image interpolation. In the paper I came across a concept called tangent direction and normal direction. What they mean is tangent direction is along the edge and normal direction is across the edge. Can anyone help me to find out what the tangent and normal direction the author is talking.
The paper link is below:-
https://arxiv.org/pdf/1402.5564.pdf
This is illustrated for a step edge. If you look at gray-scale values, one often considers that a 1D edge is (relatively) irregular across the edge (from gray to black), and regular along the edge (parallel to the border, the luminance value does not vary). 



You can perceive it better in the 3D view, where the amplitude along with the gray value is represented in 3D. 

In more generic cases, at the appropriate scales, the structure tensor is supposed to capture this behavior.