Authors: Vahan Huroyan, Md Rahat-uz-Zaman, Stephen Kobourov
Organizations: Saint Louis University, St. Louis MO 63103, USA · University of Utah · Technical University of Munich
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.
Recovering metric 3D geometry from monocular images is a fundamental computer vision task, yet current methods remain heavily fragmented by fixed camera model assumptions and inflexible input schemes. We present OmniPoint, a unified framework designed to generalize metric reconstruction across diverse imaging sensors, including pinhole, fisheye, and equirectangular projections, while accommodating varying geometric priors. To overcome projection rigidity, OmniPoint abandons conventional planar depth regression. It instead adopts a decoupled ray and distance representation alongside a decoupled training objective, explicitly separating the camera projection model from the scene structure. To address the severe scarcity of training data for alternative cameras, we introduce a bidirectional augmentation strategy that explicitly bridges labeled perspective data and unlabeled omnidirectional domains in 3D space. Furthermore, to seamlessly integrate optional inputs like camera intrinsics or sparse depth without destabilizing the network through feature distribution shifts, we propose a robust information injection mechanism. This mechanism utilizes learnable input state embeddings to resolve architectural ambiguity and applies vectorized Gaussian smoothing to densify irregular measurements. Extensive experiments demonstrate that OmniPoint achieves state-of-the-art zero-shot performance across multiple benchmarks, establishing a robust new standard for unified monocular 3D reconstruction.
Qualitative results and an illustration of our core idea. Top left: reconstruction results on benchmark images. Top right: reconstruction results on real-world images. Bottom: illustration of reconstruction-guided noise initialization and modulation. Given multiple input images, we predict a point cloud in canonical space, deterministically inject the predicted geometry into the diffusion process through noise inversion, and modulate the resulting noise to preserve the generative flexibility required to complete unobserved regions and refine visible geometry.
View-based point cloud completion aims to recover a complete 3D shape from a partial point cloud, guided by a single-view image. However, existing approaches often suffer from limited performance due to weak modality alignment and limited self-geometry enhancement. To overcome these challenges, we propose a unified geometry-aware framework that integrates efficient modality alignment and adaptive geometry enhancement, mainly to address cross-modal geometric inconsistency of view-guided point cloud completion. Specifically, we propose a geometry-aware modality alignment by integrating a shared self-attention Transformer and cross-modality reconstruction supervision, which aims to bring features of the image and point cloud close to each other in a shared latent space describing the 3D object. To enhance the perception of global shape and local geometric details, we propose an adaptive geometry-aware self-attention module, which simultaneously considers local geometry-aware attention computation and the spatially-variant feature fusion. In addition, we apply a geometry-perceptive anchor refinement module to reorganize the anchor points (representing a local region of the shape) under appropriate supervision, further boosting the completion performance of our method. Extensive experiments on both synthetic and real-world datasets demonstrate that our method achieves superior performance over existing approaches. Our code will be available at https://github.com/weizequan/MAGE.