DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields

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 DDM, an efficient, effective, robust, and differentiable distance metric for 3D geometry data. Specifically, we construct DDM 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 DDM, 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 DDM achieves significantly higher accuracy under all tasks. As a generic distance metric, DDM has the potential to advance the field of 3D geometric modeling. The source code is available at https://github.com/rsy6318/DDM. © 2025 IEEE.