Digital objects and digital surfaces are isothetic structures per se. Such surfaces are thus not adapted to direct visualization with isothetic quads, or to many geometry processing methods. We propose a new regularization technique to construct a piecewise smooth quad-rangulated surface from a digital surface. More formally we propose a variational formulation which efficiently regularizes digital surface ver-tices while complying with a prescribed, eventually anisotropic, input normal vector field estimated on the digital structure. Beside visualiza-tion purposes, such regularized surface can then be used in any geometry processing tasks which operates on triangular or quadrangular meshes (e.g. compression, texturing, anisotropic smoothing, feature extraction).