# DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields arXiv: https://arxiv.org/abs/2401.09736 ยท HTML: https://mlsanity.com/paper/2401.09736/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 34 of its 63 references that are in the map. - First posted on arXiv 18 Jan 2024. ## Builds on (most cited first, 30 of 34) - [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016) - [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017) - [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019) - [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018) - [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015) - [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022) - [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020) - [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016) - [Text2Mesh: Text-Driven Neural Stylization for Meshes](https://mlsanity.com/paper/2112.03221/) (2021) - [CLIP-Mesh: Generating textured meshes from text using pretrained image-text models](https://mlsanity.com/paper/2203.13333/) (2022) - [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020) - [Point-M2AE: Multi-scale Masked Autoencoders for Hierarchical Point Cloud Pre-training](https://mlsanity.com/paper/2205.14401/) (2022) - [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020) - [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021) - [Unsupervised Point Cloud Pre-Training via Occlusion Completion](https://mlsanity.com/paper/2010.01089/) (2020) - [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020) - [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021) - [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020) - [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022) - [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021) - [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023) - [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021) - [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022) - [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021) - [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021) - [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022) - [GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation](https://mlsanity.com/paper/2211.16762/) (2022) - [SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow](https://mlsanity.com/paper/2211.14020/) (2022) - [DPDist : Comparing Point Clouds Using Deep Point Cloud Distance](https://mlsanity.com/paper/2004.11784/) (2020) - [Recurrent Multi-view Alignment Network for Unsupervised Surface Registration](https://mlsanity.com/paper/2011.12104/) (2020) ## Built on by (most cited first, 5 of 5) - [RBFIM: Perceptual Quality Assessment for Compressed Point Clouds Using Radial Basis Function Interpolation](https://mlsanity.com/paper/2503.14154/) (2025) - [SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration](https://mlsanity.com/paper/2405.20188/) (2024) - [HuGDiffusion: Generalizable Single-Image Human Rendering via 3D Gaussian Diffusion](https://mlsanity.com/paper/2501.15008/) (2025) - [PVNet: Point-Voxel Interaction LiDAR Scene Upsampling Via Diffusion Models](https://mlsanity.com/paper/2508.17050/) (2025) - [Objective Quality Assessment of Point Clouds Using Multi-scale Implicit Structural Similarity](https://mlsanity.com/paper/2601.01200/) (2026) ## Abstract (arXiv) 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.