A variantional approach to 3D line orientation estimation from motion

A variational approach to estimating 3D line orientation from motion is presented. A 2D motion constraint on 3D lines regularized by a quadratic term is used to set up an objective functional. From its associated Euler-Lagrange equations, we develop a vector-valued diffusion model, with a reaction term based on the 2D motion constraint. Three separate diffusion processes, corresponding to each component of the 3D line orientation, are coupled with each other through the reaction term and evolve simultaneously. Each 3D line orientation is estimated separately. The regularization parameter is estimated by an L-curve, which provides a better estimation. Experimental results from image sequences indicate stability and accuracy of the approach.