The joint bilateral filter is a variant of the standard bilateral filter, where the range kernel is evaluated using a guidance signal instead of the original signal. It has been successfully applied to various image processing problems, where it provides more flexibility than the standard bilateral filter to achieve high quality results. On the other hand, its success is heavily dependent on the guidance signal, which should ideally provide a robust estimation about the features of the output signal. Such a guidance signal is not always easy to construct. In this paper, we propose a novel mesh normal filtering framework based on the joint bilateral filter, with applications in mesh denoising. Our framework is designed as a two-stage process: first, we apply joint bilateral filtering to the face normals, using a properly constructed normal field as the guidance; afterwards, the vertex positions are updated according to the filtered face normals. We compute the guidance normal on a face using a neighboring patch with the most consistent normal orientations, which provides a reliable estimation of the true normal even with a high-level of noise. The effectiveness of our approach is validated by extensive experimental results.The definitive version is available at

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for interactive applications. Local-global solvers developed in recent years can quickly compute an approximate solution to such problems, making them an attractive choice for applications that prioritize efficiency over accuracy. However, these solvers suffer from lower convergence rate, and may take a long time to compute an accurate result. In this paper, we propose a simple and effective technique to accelerate the convergence of such solvers. By treating each local-global step as a fixed-point iteration, we apply Anderson acceleration, a well-established technique for fixed-point solvers, to speed up the convergence of a local-global solver. To address the stability issue of classical Anderson acceleration, we propose a simple strategy to guarantee the decrease of target energy and ensure its global convergence. In addition, we analyze the connection between Anderson acceleration and quasi-Newton methods, and show that the canonical choice of its mixing parameter is suitable for accelerating local-global solvers. Moreover, our technique is effective beyond classical local-global solvers, and can be applied to iterative methods with a common structure. We evaluate the performance of our technique on a variety of geometry optimization and physics simulation problems. Our approach significantly reduces the number of iterations required to compute an accurate result, with only a slight increase of computational cost per iteration. Its simplicity and effectiveness makes it a promising tool for accelerating existing algorithms as well as designing efficient new algorithms.

3D face reconstruction from a single image is a classical and challenging problem, with wide applications in many areas. Inspired by recent works in face animation from RGBD or monocular video inputs, we develop a novel method for reconstructing 3D faces from unconstrained 2D images, using a coarse-to-fine optimization strategy. First, a smooth coarse 3D face is generated from an example-based bilinear face model, by aligning the projection of 3D face landmarks with 2D landmarks detected from the input image. Afterwards, using local corrective deformation fields, the coarse 3D face is refined using photometric consistency constraints, resulting in a medium face shape. Finally, a shape-from-shading method is applied on the medium face to recover fine geometric details. Our method outperforms stateof- the-art approaches in terms of accuracy and detail recovery, which is demonstrated in extensive experiments using real world models and publicly available datasets.

apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.