We present \emph{SPHEAR}, an accurate, differentiable parametric statistical
3D human head model, enabled by a novel 3D registration method based on
spherical embeddings. We shift the paradigm away from the classical Non-Rigid
Registration methods, which operate under various surface priors, increasing
reconstruction fidelity and minimizing required human intervention.
Additionally, SPHEAR is a \emph{complete} model that allows not only to sample
diverse synthetic head shapes and facial expressions, but also gaze directions,
high-resolution color textures, surface normal maps, and hair cuts represented
in detail, as strands. SPHEAR can be used for automatic realistic visual data
generation, semantic annotation, and general reconstruction tasks. Compared to
state-of-the-art approaches, our components are fast and memory efficient, and
experiments support the validity of our design choices and the accuracy of
registration, reconstruction and generation techniques.

我们提出了一种准确、可微分的参数化统计 3D 人头模型 SPHEAR，通过基于球形嵌入的新型 3D 注册方法实现。SPHEAR 不仅可以采样不同的合成头部形状和面部表情，还可以表示凝视方向、高分辨率彩色纹理、表面法线图和具体的发型切割，可用于自动逼真的视觉数据生成、语义注释和通用重建任务，与最先进的方法相比，我们的组件快速且存储效率高，实验证明了我们设计选择的合理性以及注册、重建和生成技术的准确性。

SPHEAR：球面头部注册用于完整统计三维建模

SPHEAR: Spherical Head Registration for Complete Statistical 3D Modeling

When dealing with a parametric statistical model, a Riemannian manifold can
naturally appear by endowing the parameter space with the Fisher information
metric. The geometry induced on the parameters by this metric is then referred
to as the Fisher-Rao information geometry. Interestingly, this yields a point
of view that allows for leveragingmany tools from differential geometry. After
a brief introduction about these concepts, we will present some practical uses
of these geometric tools in the framework of elliptical distributions. This
second part of the exposition is divided into three main axes: Riemannian
optimization for covariance matrix estimation, Intrinsic Cram\'er-Rao bounds,
and classification using Riemannian distances.

当处理参数统计模型时，将参数空间赋予费舍尔信息度量可以自然地产生一个黎曼流形，由该度量引导的参数几何称为费舍尔 - 瑞奥信息几何。有趣的是，这为利用微分几何中的许多工具提供了一个视角。介绍这些概念后，我们将在椭圆分布框架中呈现这些几何工具的一些实际用途，这部分内容主要包括协方差矩阵估计的黎曼优化、内在克拉默 - 瑞奥界限以及使用黎曼距离的分类。