...(n)
It is interesting to note that the interpolation and finite-difference filters developed by Karrenbach (1995) from a general approach of self-similar operators reduce to a localized form of Lagrange polynomials.
...borders
I provide the elevation image only for reference. It has not been used in the interpolation experiment.
A similar filter appears in velocity estimation with the differential semblance method Symes and Carazzone (1991); Symes (1999).
An analogous technique applied to the case of wavefield depth extrapolation with the wave equation would lead to the famous 45-degree implicit finite-difference operator Claerbout (1985).
...user-specified
Developing a method for automatic estimation of the appropriate tension parameter from the input data is a challenging open problem. It goes beyond the scope of this work.
...chapter
To my knowledge, the first derivation of the revised offset continuation equation was accomplished by Joseph Higginbotham of Texaco in 1989. Unfortunately, Higginbotham's derivation never appeared in the open literature.