A variational method for the recovery of dense 3D structure from motion

The purpose of this study is to investigate a variational formulation of the problem of three-dimensional (3D) interpretation of temporal image sequences based on the 3D brightness constraint and anisotropic regularization. The method allows movement of both the viewing system and objects and does not require the computation of image motion prior to 3D interpretation. Interpretation follows the minimization of a functional with two terms: a term of conformity of the 3D interpretation to the image sequence first-order spatio-temporal variations, and a term of regularization based on anisotropic diffusion to preserve the boundaries of interpretation. The Euler–Lagrange partial differential equations corresponding to the functional are solved efficiently via the half-quadratic algorithm. Results of several experiments on synthetic and real image sequences are given to demonstrate the validity of the method and its implementation.