# SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration

arXiv: https://arxiv.org/abs/2405.20188 · HTML: https://mlsanity.com/paper/2405.20188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 91 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 40)

- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [BANMo: Building Animatable 3D Neural Models from Many Casual Videos](https://mlsanity.com/paper/2112.12761/) (2021)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020)
- [Efficient Learning on Point Clouds with Basis Point Sets](https://mlsanity.com/paper/1908.09186/) (2019)
- [DoubleFusion: Real-time Capture of Human Performances with Inner Body Shapes from a Single Depth Sensor](https://mlsanity.com/paper/1804.06023/) (2018)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [DeepDeform: Learning Non-rigid RGB-D Reconstruction with Semi-supervised Data](https://mlsanity.com/paper/1912.04302/) (2019)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Neural Surface Reconstruction of Dynamic Scenes with Monocular RGB-D Camera](https://mlsanity.com/paper/2206.15258/) (2022)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Learned Vertex Descent: A New Direction for 3D Human Model Fitting](https://mlsanity.com/paper/2205.06254/) (2022)
- [Dynamic Point Fields](https://mlsanity.com/paper/2304.02626/) (2023)
- [Robust 3D Self-portraits in Seconds](https://mlsanity.com/paper/2004.02460/) (2020)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Dense Human Body Correspondences Using Convolutional Networks](https://mlsanity.com/paper/1511.05904/) (2015)
- [FlyCap: Markerless Motion Capture Using Multiple Autonomous Flying Cameras](https://mlsanity.com/paper/1610.09534/) (2016)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Recurrent Multi-view Alignment Network for Unsupervised Surface Registration](https://mlsanity.com/paper/2011.12104/) (2020)

## Built on by (most cited first, 1 of 1)

- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)

## Abstract (arXiv)

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.