# Flexible-weighted Chamfer Distance: Enhanced Objective Function for Point Cloud Completion

arXiv: https://arxiv.org/abs/2505.14218 · HTML: https://mlsanity.com/paper/2505.14218/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 64 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 44)

- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Multi-Task Deep Neural Networks for Natural Language Understanding](https://mlsanity.com/paper/1901.11504/) (2019)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [PF-Net: Point Fractal Network for 3D Point Cloud Completion](https://mlsanity.com/paper/2003.00410/) (2020)
- [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)
- [Point Cloud Completion by Skip-attention Network with Hierarchical Folding](https://mlsanity.com/paper/2005.03871/) (2020)

## Built on by (most cited first, 2 of 2)

- [PPC-MT: Parallel Point Cloud Completion with Mamba-Transformer Hybrid Architecture](https://mlsanity.com/paper/2603.00870/) (2026)
- [DINE: Distance Is Not Enough -- Learning Global Deformation Priors for Robust Soft-Tissue Point Cloud Registration](https://mlsanity.com/paper/2607.14946/) (2026)

## Abstract (arXiv)

The Chamfer Distance (CD) is a cornerstone objective function for point cloud completion, yet its inherent symmetric weighting mechanism limits the quality of the generated results. By penalizing local detail deviations and global coverage deficiencies equally, standard CD often causes structural defects such as point aggregation and incomplete spatial structures. We introduce the Flexible-weighted Chamfer Distance (FCD), which decouples CD into local precision and global completeness sub-objectives. FCD employs an asymmetric weighting strategy that prioritizes global structural integrity, steering the optimization away from sub-optimal solutions. As a plug-and-play module with negligible overhead, extensive experiments on state-of-the-art networks demonstrate that FCD significantly enhances global distribution metrics while preserving local precision. Specifically, on the ShapeNet55 benchmark using AdaPoinTr, FCD reduces the Density-aware Chamfer Distance (DCD) by approximately 12.4% (from 0.613 to 0.537), effectively mitigating point clustering. Similarly, on the PCN dataset, the proposed method reduces the Earth Mover's Distance (EMD) from 23.79 to 21.40, demonstrating superior global uniformity compared to the standard CD baseline. Furthermore, FCD demonstrates excellent generalization. When applied to diverse tasks and datasets, including real-world scans (KITTI), industrial components (ABC), and point cloud upsampling (PU-GAN), it yields significant quantitative gains and produces visually more uniform and structurally complete point clouds. These results underscore FCD's potential as a versatile objective function for the broader point cloud generation domain.