1
vote
1answer
227 views

Monge Ampere and Calculus

I am learning about mass transportation theory and the Monge-Ampere equation, to transport a function $f$ toward $g$ by a change of variable $T$. In particular, in order to solve for : $$ \min \int ...
14
votes
1answer
411 views

Gradient flow of a surface

I found the following definition in a book (S. Osher, R. Fedkiw, "Level Set Methods and Dynamic Implicit Surfaces", p. 140): [the context is reconstruction of surfaces from unorganized point sets] ...
7
votes
2answers
1k views

Euler-Lagrange, Gradient Descent, Heat Equation and Image Denoising

For an image denoising problem, the author has a functional $E$ defined $$E(u) = \iint_\Omega F \;\mathrm d\Omega$$ which he wants to minimize. $F$ is defined as $$F = \|\nabla u \|^2 = u_x^2 + ...