Inequality-Constrained and Robust 3D Face Model Fitting
Inequality-Constrained and Robust 3D Face Model Fitting
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DOI：
10.1007/978-3-030-58545-7_25
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发表时间：
2020
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影响因子：
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通讯作者：
E. Sariyanidi;C. Zampella;R. Schultz;B. Tunç
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文献类型：
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作者：
E. Sariyanidi;C. Zampella;R. Schultz;B. Tunç
在各种工业和研究应用的推动下，在面部上拟合3D变形模型（3DMMs）是一个研究得很好的问题。3DMM将3D面部形状表示为基函数的线性和。然而，只有当基系数在有限的区间内取值时，得到的形状才是合理的面。基于无约束优化的方法通过对系数进行加权惩罚来解决这个问题;然而，确定这种惩罚的权重是困难的，并且普遍适用的单一权重的存在是值得怀疑的。我们提出了一个新的配方，不需要调整任何权重参数。具体来说，我们制定3DMM拟合作为一个不等式约束的优化问题，其中的主要约束是，基础系数不应超过区间时，学习3DMM构造。我们采用额外的限制，利用稀疏的地标检测器，迫使面部形状是一个可靠的检测器的误差范围内。为了使操作“在野外”，我们使用一个强大的目标函数，即梯度相关。我们的方法使用深度学习（DL）方法对具有不精确地面实况的“野外”数据进行了验证，并且在具有精确地面实况的更多受控数据上优于DL方法。由于我们的公式不需要任何学习，它具有多功能性，允许它与任意大小的多个框架一起操作。这项研究的结果鼓励进一步研究3DMM拟合与不等式约束优化方法，这是未经探索相比，无约束的方法。
Fitting 3D morphable models (3DMMs) on faces is a well-studied problem, motivated by various industrial and research applications. 3DMMs express a 3D facial shape as a linear sum of basis functions. The resulting shape, however, is a plausible face only when the basis coefficients take values within limited intervals. Methods based on unconstrained optimization address this issue with a weightedpenalty on coefficients; however, determining the weight of this penalty is difficult, and the existence of a single weight that works universally is questionable. We propose a new formulation that does not require the tuning of any weight parameter. Specifically, we formulate 3DMM fitting as an inequality-constrained optimization problem, where the primary constraint is that basis coefficients should not exceed the interval that is learned when the 3DMM is constructed. We employ additional constraints to exploit sparse landmark detectors, by forcing the facial shape to be within the error bounds of a reliable detector. To enable operation “in-the-wild”, we use a robust objective function, namely Gradient Correlation. Our approach performs comparably with deep learning (DL) methods on “in-the-wild” data that have inexact ground truth, and better than DL methods on more controlled data with exact ground truth. Since our formulation does not require any learning, it enjoys a versatility that allows it to operate with multiple frames of arbitrary sizes. This study’s results encourage further research on 3DMM fitting with inequality-constrained optimization methods, which have been unexplored compared to unconstrained methods.