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：我们提出了一种新的基于模型的算法，用于解决面部动画重定目标中的逆向绑定问题，相较于现有最先进技术，该算法在拟合精度、权重稀疏性和可解释性方面表现更优。本方法针对人类面部动画的一个特定子领域——电影和游戏制作中使用的高真实感混合变形模型。本文构建了一个优化问题，全面考虑了目标模型的所有需求。我们的目标函数超越了线性混合变形模型，采用了正确拟合网格细微细节所必需的二次修正项。研究表明，即便使用通用求解器（如序列二次规划算法），所提问题的解也能实现高精度网格重建。虽然使用序列二次规划算法在网格空间中获得的结果高度精确，但在权重稀疏性和平滑性方面缺乏优势，为此我们进一步提出了一种基于最大最小化技术的新型算法。该算法专门适用于求解所提出的目标函数，能在满足约束条件的同时实现高精度网格拟合，并生成易于艺术家操控和解读的稀疏平滑权重集。我们的算法与现有最先进方法进行了基准测试，结果显示其全面优越性：在保持与基准方法相当的基数条件下，均方根网格误差实现了相对提升高达45%的平滑动画重建。本文提供了一套涵盖解决方案不同维度的综合评估指标，包括网格精度、权重稀疏性、动画曲线平滑度，以及经人类专家评估的动画产出视觉效果。