IEEE Trans Image Process. 2013 Nov;22(11):4170-81. doi: 10.1109/TIP.2013.2271115. Epub 2013 Jun 26.
Establishing a dense vertex-to-vertex anthropometric correspondence between 3D faces is an important and fundamental problem in 3D face research, which can contribute to most applications of 3D faces. This paper proposes a sparse facial deformable model to automatically achieve this task. For an input 3D face, the basic idea is to generate a new 3D face that has the same mesh topology as a reference face and the highly similar shape to the input face, and whose vertices correspond to those of the reference face in an anthropometric sense. Two constraints: 1) the shape constraint and 2) correspondence constraint are modeled in our method to satisfy the three requirements. The shape constraint is solved by a novel face deformation approach in which a normal-ray scheme is integrated to the closest-vertex scheme to keep high-curvature shapes in deformation. The correspondence constraint is based on an assumption that if the vertices on 3D faces are corresponded, their shape signals lie on a manifold and each face signal can be represented sparsely by a few typical items in a dictionary. The dictionary can be well learnt and contains the distribution information of the corresponded vertices. The correspondence information can be conveyed to the sparse representation of the generated 3D face. Thus, a patch-based sparse representation is proposed as the correspondence constraint. By solving the correspondence constraint iteratively, the vertices of the generated face can be adjusted to correspondence positions gradually. At the early iteration steps, smaller sparsity thresholds are set that yield larger representation errors but better globally corresponded vertices. At the later steps, relatively larger sparsity thresholds are used to encode local shapes. By this method, the vertices in the new face approach the right positions progressively until the final global correspondence is reached. Our method is automatic, and the manual work is needed only in training procedure. The experimental results on a large-scale publicly available 3D face data set, BU-3DFE, demonstrate that our method achieves better performance than existing methods.
建立 3D 人脸之间密集的顶点到顶点的人体测量对应关系是 3D 人脸研究中的一个重要而基础的问题，它可以为大多数 3D 人脸应用做出贡献。本文提出了一种稀疏人脸变形模型来自动实现这一任务。对于输入的 3D 人脸，基本思想是生成一个具有与参考人脸相同网格拓扑结构和与输入人脸高度相似形状的新 3D 人脸，并且其顶点在人体测量意义上与参考人脸的顶点相对应。我们的方法中建模了两个约束：1）形状约束和 2）对应约束，以满足三个要求。形状约束通过一种新的人脸变形方法来解决，该方法集成了法向射线方案到最近顶点方案中，以保持变形中的高曲率形状。对应约束基于这样的假设，即如果 3D 人脸的顶点相对应，那么它们的形状信号位于流形上，并且每个人脸信号都可以由字典中的几个典型项稀疏表示。字典可以很好地学习，并包含对应顶点的分布信息。对应信息可以传递到生成的 3D 人脸的稀疏表示中。因此，提出了基于面片的稀疏表示作为对应约束。通过迭代地求解对应约束，可以逐渐调整生成的人脸的顶点到对应位置。在早期迭代步骤中，设置较小的稀疏度阈值，会导致较大的表示误差，但会产生更好的全局对应顶点。在后续步骤中，使用较大的稀疏度阈值来编码局部形状。通过这种方法，新面孔中的顶点逐渐接近正确的位置，直到最终达到全局对应。我们的方法是自动的，仅在训练过程中需要人工工作。在大型公开可用的 3D 人脸数据集 BU-3DFE 上的实验结果表明，我们的方法比现有方法具有更好的性能。
