Variational principles, surface evolution, PDEs, level set methods, and the stereo problem

Variational principles, surface evolution, PDEs, level set methods, and the stereo problem

We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (= or >2). It is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The Euler-Lagrange equations that are deduced from the variational principle provide a set of partial differential equations (PDE's) that a...

Variational principles , Surface Evolution , PDE ' s , level set methods and the Stereo

1 Variational principles, Surface Evolution, PDE's, level set methods and the Stereo Problem Olivier Faugeras and Renaud Keriven Abstract We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the de nition of a variational principle that must be satis ed by the surfaces of the objects in the scene an...

Level set methods and the Stereo

We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the deenition of a variational principle that must be satissed by the surfaces of the objects in the scene and their images. The Euler-Lagrange equations which are deduced from the variational principle provide a set of PDE's which are used to def...

Surface Evolution Equations — a level set method —

LTCC Course Variational and Computational Methods for PDEs

∆u = ∂2u ∂x1 + ∂2u ∂x2 where x = (x1, x2) ∈ R2 are Cartesian coordinates. Even though the Poisson equation looks very special it is an important model case representing several problems from physics and engineering, e.g. electrostatics, stationary heat transfer and other diffusion problems. Variations of the techniques we will study apply to a wide class of second order so-called elliptic probl...