Say I have a set of sample measurements of a one dimensional curve in the image plane $f(x)$. What is the purpose of minimizing the following functional $$E(S) = \int \left[\lambda(S''(x))^2 + (f(x) - S(x))^2 \sum_k \delta (x - x_k)\right]dx$$
I believe it has something to do with energy minimization and snakes.