用可学习 B 样条体表示三维人脸
Representing 3D Faces with Learnable B-Spline Volumes
把 B 样条体的控制点换成高维可学习控制特征，并用小型 MLP 预测残差位移，得到一种连续、局部可编辑的三维人脸表示；可直接作为从点云或单目图像回归三维人脸的解码器，替代常用的 PCA 或线性基底。
原文依据 CUBE is parametrized by a lattice (e.g., 8 x 8 x 8) of high-dimensional control features, increasing the model's expressivity.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论本文提出 CUBE（基于控制的统一 B 样条编码），一种新的人脸几何表示，它将 B 样条体与可学习特征相结合，并展示了其作为解码器用于三维扫描配准和单目三维人脸重建的用途。与现有使用三维控制点的 B 样条表示不同，CUBE 由高维控制特征构成的格点（例如 8×8×8）参数化，从而提升了模型的表达能力。这些特征通过一个中间特征空间，定义了从三维参数域到三维欧氏空间的连续两阶段映射。首先，高维控制特征使用 B 样条基函数进行局部混合，得到一个高维特征向量，其前三个值定义了一个三维基础网格。随后，一个小型 MLP 处理该特征向量，预测相对于基础形状的残差位移，从而得到最终精化的三维坐标。为了在稠密语义对应下重建三维表面，CUBE 在从固定模板网格采样的三维坐标处被查询。关键在于，CUBE 保留了传统 B 样条表示的局部支撑性质，使得通过更新单个控制特征即可进行局部表面编辑。我们通过训练基于 transformer 的编码器，从非结构化点云和单目图像预测 CUBE 的控制特征，展示了该表示的优势，与近期基线相比取得了最优的扫描配准结果。
英文原文摘要 1472 字符
We present CUBE (Control-based Unified B-Splinie Encoding), a new geometric representation for human faces that combines B-spline volumes with learned features, and demonstrate its use as a decoder for 3D scan registration and monocular 3D face reconstruction. Unlike existing B-spline representations with 3D control points, CUBE is parametrized by a lattice (e.g., 8 x 8 x 8) of high-dimensional control features, increasing the model's expressivity. These features define a continuous, two-stage mapping from a 3D parametric domain to 3D Euclidean space via an intermediate feature space. First, high-dimensional control features are locally blended using the B-spline bases, yielding a high-dimensional feature vector whose first three values define a 3D base mesh. A small MLP then processes this feature vector to predict a residual displacement from the base shape, yielding the final refined 3D coordinates. To reconstruct 3D surfaces in dense semantic correspondence, CUBE is queried at 3D coordinates sampled from a fixed template mesh. Crucially, CUBE retains the local support property of traditional B-spline representations, enabling local surface editing by updating individual control features. We demonstrate the strengths of this representation by training transformer-based encoders to predict CUBE's control features from unstructured point clouds and monocular images, achieving state-of-the-art scan registration results compared to recent baselines.