# GeoCD: A Differential Local Approximation for Geodesic Chamfer Distance

arXiv: https://arxiv.org/abs/2506.23478 · HTML: https://mlsanity.com/paper/2506.23478/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [6-DOF GraspNet: Variational Grasp Generation for Object Manipulation](https://mlsanity.com/paper/1905.10520/) (2019)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [DoubleFusion: Real-time Capture of Human Performances with Inner Body Shapes from a Single Depth Sensor](https://mlsanity.com/paper/1804.06023/) (2018)
- [Point Cloud GAN](https://mlsanity.com/paper/1810.05795/) (2018)
- [AdaPoinTr: Diverse Point Cloud Completion with Adaptive Geometry-Aware Transformers](https://mlsanity.com/paper/2301.04545/) (2023)
- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)
- [Cascaded Refinement Network for Point Cloud Completion with Self-supervision](https://mlsanity.com/paper/2010.08719/) (2020)

## Abstract (arXiv)

Chamfer Distance (CD) is a widely adopted metric in 3D point cloud learning due to its simplicity and efficiency. However, it suffers from a fundamental limitation: it relies solely on Euclidean distances, which often fail to capture the intrinsic geometry of 3D shapes. To address this limitation, we propose GeoCD, a topology-aware and fully differentiable approximation of geodesic distance designed to serve as a metric for 3D point cloud learning. Our experiments show that GeoCD consistently improves reconstruction quality over standard CD across various architectures and datasets. We demonstrate this by fine-tuning several models, initially trained with standard CD, using GeoCD. Remarkably, fine-tuning for a single epoch with GeoCD yields significant gains across multiple evaluation metrics.