Euler's elastica and curvature based nonlinear mesh denoising method

In the paper, we extend a new nonlinear variational model based on the general Euler's elastica and curvature for triangulated surfaces. The new model intrinsically combines the gradient operator and the curvature operator in a multiplicative manner. By introducing the total variation norm restricted to triangles, we discretize the Euler's elastica and curvature model on triangulated surface into the triangle-based and edge-based formulations, respectively. A two-stage mesh denoising method is proposed using the general Euler's elastica and curvature model: first filtering the facet normals based on the Euler's elastica and curvature model and then updating the vertex positions. Through an efficient relaxation, the nonlinear and non-differentiable optimization problem is solved iteratively based on the operator splitting and alternating direction method of multipliers (ADMM). The proposed denoising method is evaluated in terms of parameters sensitivity, quantitative comparisons with several state-of-the-art techniques, and computational costs. Numerical experiments confirm that our approach produces competitive results when compared to several existing denoising algorithms at reasonable costs. It achieves promising results by preserving sharper features, restoring more details and structures, and alleviating the staircase effect (false edges). Moreover, the quantitative errors further verify that the proposed algorithm is robust numerically.