3DMPE: 3D Multi-Perspective Embedding
2026-07-06 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionComputational Geometry
AI summaryⓘ
The authors propose a method called 3D Multi-Perspective Embedding (3DMPE) to rebuild 3D point clouds from multiple 2D views that only show parts of the object. Unlike AI methods that need training data, their approach uses geometric information and known matching points across views to reconstruct the full 3D shape without training. They test their method on datasets and measure how close the reconstructed shapes are to the originals, even when some points are missing or there is noise. Their results show that 3DMPE can successfully recover 3D shapes from partial observations in different conditions.
3D point cloud2D projectionspoint correspondencesvisibilityMulti-Perspective Simultaneous EmbeddingChamfer DistanceEarth Mover DistanceShapeNetPix3Dtraining-free reconstruction
Authors
Vahan Huroyan, Md Rahat-uz-Zaman, Stephen Kobourov
Abstract
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.