Qualifying the discrepancy between 3D geometric models, which could be
represented with either point clouds or triangle meshes, is a pivotal issue
with board applications. Existing methods mainly focus on directly establishing
the correspondence between two models and then aggregating point-wise distance
between corresponding points, resulting in them being either inefficient or
ineffective. In this paper, we propose DirDist, an efficient, effective,
robust, and differentiable distance metric for 3D geometry data. Specifically,
we construct DirDist based on the proposed implicit representation of 3D
models, namely directional distance field (DDF), which defines the directional
distances of 3D points to a model to capture its local surface geometry. We
then transfer the discrepancy between two 3D geometric models as the
discrepancy between their DDFs defined on an identical domain, naturally
establishing model correspondence. To demonstrate the advantage of our DirDist,
we explore various distance metric-driven 3D geometric modeling tasks,
including template surface fitting, rigid registration, non-rigid registration,
scene flow estimation and human pose optimization. Extensive experiments show
that our DirDist achieves significantly higher accuracy under all tasks. As a
generic distance metric, DirDist has the potential to advance the field of 3D
geometric modeling. The source code is available at
https://github.com/rsy6318/DirDist.

本文提出了一种基于方向距离场的 3D 几何数据的高效、有效、鲁棒和可微的距离度量方法 DirDist，通过在同一域上定义其方向距离场的两个 3D 几何模型的差异来建立模型对应关系，并在多个几何建模任务上展示了 DirDist 的优势，包括模板曲面拟合、刚体配准、非刚体配准、场景流估计和人体姿势优化。大量实验证明，在所有任务下，DirDist 的准确性显著提高，作为一种通用的距离度量方法，DirDist 有潜力推动 3D 几何建模领域的发展。