Regularization of orthonormal vector sets using coupled PDE’s

We address the problem of restoring, while preserving pos-sible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicitly into account. We develop a variational solution for the general case where each image feature may correspond to multiple n-D orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where discontinu-ities and orthonormal constraints are preserved by means of constrained minimization and -functions regularization, leading to a set of coupled anisotropic diffusion PDE’s. A geometric interpretation of the resulting equations, coming from the field of solid mechanics, is proposed for the 3D case. Two interesting restrictions of our framework are also tackled: the regularization of 3D rotation matrices and the Direction diffusion (the parallel with previous works is made). Finally, we present a number of denoising results and applications. 1