# 3DMPE: 3D Multi-Perspective Embedding

arXiv: https://arxiv.org/abs/2607.04898 · HTML: https://mlsanity.com/paper/2607.04898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 55 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 30 of 31)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Stereo Matching by Training a Convolutional Neural Network to Compare Image Patches](https://mlsanity.com/paper/1510.05970/) (2015)
- [Convolutional neural network architecture for geometric matching](https://mlsanity.com/paper/1703.05593/) (2017)
- [Learning Efficient Point Cloud Generation for Dense 3D Object Reconstruction](https://mlsanity.com/paper/1706.07036/) (2017)
- [Unsupervised Learning of Shape and Pose with Differentiable Point Clouds](https://mlsanity.com/paper/1810.09381/) (2018)
- [Image-based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era](https://mlsanity.com/paper/1906.06543/) (2019)
- [Adaptive Gradient Descent without Descent](https://mlsanity.com/paper/1910.09529/) (2019)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [3D-LMNet: Latent Embedding Matching for Accurate and Diverse 3D Point Cloud Reconstruction from a Single Image](https://mlsanity.com/paper/1807.07796/) (2018)
- [Dense 3D Point Cloud Reconstruction Using a Deep Pyramid Network](https://mlsanity.com/paper/1901.08906/) (2019)
- [Single Image 3D Hand Reconstruction with Mesh Convolutions](https://mlsanity.com/paper/1905.01326/) (2019)
- [Pix2Surf: Learning Parametric 3D Surface Models of Objects from Images](https://mlsanity.com/paper/2008.07760/) (2020)
- [Multiview Aggregation for Learning Category-Specific Shape Reconstruction](https://mlsanity.com/paper/1907.01085/) (2019)
- [A Real World Dataset for Multi-view 3D Reconstruction](https://mlsanity.com/paper/2203.11397/) (2022)
- [Local and Global Point Cloud Reconstruction for 3D Hand Pose Estimation](https://mlsanity.com/paper/2112.06389/) (2021)
- [Multi-Perspective, Simultaneous Embedding](https://mlsanity.com/paper/1909.06485/) (2019)
- [A Simple and Scalable Shape Representation for 3D Reconstruction](https://mlsanity.com/paper/2005.04623/) (2020)
- [Probabilistic Reconstruction Networks for 3D Shape Inference from a Single Image](https://mlsanity.com/paper/1908.07475/) (2019)

## Abstract (arXiv)

We study 3D point cloud reconstruction from multiple partially observed 2D projections. Given two or more projections of an unknown 3D point cloud, together with cross-view point correspondences and visibility information, our goal is to recover a consistent 3D configuration when different views contain different subsets of points. We propose 3D Multi-Perspective Embedding (3DMPE), an optimization-based, training-free method that reconstructs the 3D point cloud and, in the variable-projection setting, jointly estimates the projection maps. 3DMPE extends Multi-Perspective Simultaneous Embedding to accommodate missing points and incomplete pairwise distance information across views. We consider both fixed-projection and variable-projection settings. Unlike learning-based reconstruction methods that infer shape from raw images and often depend on training data, 3DMPE operates on geometric observations with established correspondences and does not require category-specific training. Experiments on ShapeNet and Pix3D evaluate reconstruction quality using Chamfer Distance, Earth Mover Distance, and RMSE-Optimize-Align (ROA), and examine the effects of initialization, the number of views, point visibility, and several noise regimes, including noisy distances and erroneous correspondences. The results demonstrate that 3DMPE can effectively reconstruct point clouds from partial multi-view geometric observations.