We propose a new model-based algorithm solving the inverse rig problem in facial animation retargeting, exhibiting higher accuracy of the fit and sparser, more interpretable weight vector compared to SOTA. The proposed method targets a specific subdomain of human face animation - highly-realistic blendshape models used in the production of movies and video games. In this paper, we formulate an optimization problem that takes into account all the requirements of targeted models. Our objective goes beyond a linear blendshape model and employs the quadratic corrective terms necessary for correctly fitting fine details of the mesh. We show that the solution to the proposed problem yields highly accurate mesh reconstruction even when general-purpose solvers, like SQP, are used. The results obtained using SQP are highly accurate in the mesh space but do not exhibit favorable qualities in terms of weight sparsity and smoothness, and for this reason, we further propose a novel algorithm relying on a MM technique. The algorithm is specifically suited for solving the proposed objective, yielding a high-accuracy mesh fit while respecting the constraints and producing a sparse and smooth set of weights easy to manipulate and interpret by artists. Our algorithm is benchmarked with SOTA approaches, and shows an overall superiority of the results, yielding a smooth animation reconstruction with a relative improvement up to 45 percent in root mean squared mesh error while keeping the cardinality comparable with benchmark methods. This paper gives a comprehensive set of evaluation metrics that cover different aspects of the solution, including mesh accuracy, sparsity of the weights, and smoothness of the animation curves, as well as the appearance of the produced animation, which human experts evaluated.

翻译：我们提出一种基于模型的新算法，用于解决面部动画重定向中的逆绑定问题，与现有最先进方法相比，该算法在拟合精度上表现更优，且权重向量更稀疏、更具可解释性。该方法针对人类面部动画的特定子领域——电影与电子游戏制作中采用的高真实感Blendshape模型。本文构建了一个优化问题，充分考虑了目标模型的所有需求。我们的目标函数超越了线性Blendshape模型，采用正确拟合网格细节所必需的二次修正项。研究表明，即便使用SQP等通用求解器，所提问题的解也能实现高精度的网格重构。虽然SQP求解结果在网格空间上精度极高，但在权重稀疏性与平滑性方面表现不佳。为此，我们进一步提出一种基于MM技术的新型算法。该算法专为求解前述目标函数设计，在满足约束条件的同时实现高精度网格拟合，并生成便于艺术家操作与解读的稀疏平滑权重集。我们将所提算法与最先进方法进行基准测试，结果表明该方法在整体性能上具有优越性：在保持权重基数与基准方法相当的前提下，均方根网格误差相对降低高达45%，实现平滑动画重构。本文提供了一套涵盖解的多维度的综合评价指标，包含网格精度、权重稀疏性、动画曲线平滑性，以及由人类专家评估的生成动画视觉表现。