Gauss-Newton method

The Gauss-Newton method is a standard approach to (approximately/locally) solving non-linear equations. Assume that me aim to minimize a (squared) L2 norm $$||r(x)||$$ w.r.t. $$x$$. The super-simplified pseudo-algorithm of the Gauss-Newton method is :


 * Given a starting guess for $$x$$
 * Repeat
 * 1) Linearize $$r$$ near current guess
 * 2) Compute new guess, which is the linear LS solution on the linearized $$r$$
 * Until convergence

The Gauss-Newton method is used frequently for 3DMM fitting and 2D-2D image alignment. In particular, it is used by the 3DI method as well.