Efficient and Robust Camera-independent Multiview 3D Geometric Reconstruction from Noisy Monocular Depth Estimation and Multiple Point Matching
Authors: Marius Leordeanu
Organizations: Institute of Mathematics of the Romanian Academy, Calea Grivitei 21, Bucharest · POLITEHNICA Bucharest, Splaiul Independent,ei 313, Bucharest
We present an efficient and robust method for 3D geometric reconstruction that is based solely on the camera-independent linear relationships among a given set of points, which are stable over time and robustly estimated using multiple point matches. We essentially learn, from correspondences between points across several frames, a linear geometric auto-regression matrix W, which establishes how a point in 3D can be expressed as a linear combination of all the others. This matrix is constant and does not depend on the world coordinate system or the camera pose---it is an intrinsic property of the point set. We also show that the principal eigenvectors of W, which all have eigenvalue 1, provide a homogeneous representation of the 3D point configuration. The first version of our method takes advantage of noisy monocular depth maps in order to obtain, from multiple frames, a robust geometric auto-regression matrix W of linear relationships between the 3D points. Thus, we build on recent advances in deep learning, which now provide monocular depth estimation models that are fast but very often noisy. Our approach handles noise through robust linear estimation over several frames. The second version of our method does not need monocular depth estimation maps. It applies in cases of weak-perspective projection, when the linear combinations between the 3D points can be robustly estimated from their 2D projections in the image. Note that the camera projection matrix is never used in our derivations. Consequently, our method does not recover camera pose, but only 3D structure. This is a key difference between our method and the related literature on 3D geometric reconstruction.
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.
Botao Ye, Marc Pollefeys, Ming-Hsuan Yang +1
Google DeepMind · ETH Zurich · Work done as an intern at Google DeepMind.
Camera pose estimation is a key step in 3D reconstruction and view-synthesis pipelines. We present a deep, global Structure-from-Motion framework based on learned view-graph aggregation. Our method employs a permutation-equivariant, edge-conditioned graph neural network that takes noisy pairwise relative poses as input and outputs globally consistent camera extrinsics. The network is trained without ground-truth supervision, relying solely on a relative-pose consistency objective. This is followed by 3D point triangulation and robust bundle adjustment. Our approach is efficient, scalable to more than a thousand images, and robust to graph density. We evaluate our method on MegaDepth, 1DSfM, Strecha, and BlendedMVS. These experiments demonstrate that our method achieves superior rotation and translation accuracy compared to deep track-centric methods while registering more images across many scenes, and competitive results compared to state-of-the-art classical pipelines, while being much faster.
State-of-the-art single-image 3D reconstruction methods often rely on complex hybrid architectures and loss functions, or compress geometry into latent spaces in order to leverage pre-trained latent diffusion models. In this work, we show that such architectural overhead and intricate loss formulations are unnecessary. We introduce a minimalist pixel-space Diffusion Transformer, built on a plain ViT, that operates directly on raw 3D point map patches and is conditioned on image tokens from a pre-trained DINOv3. Unlike existing latent diffusion approaches, we train our diffusion backbone entirely from scratch, eliminating the need for point map tokenizers. Despite its simplicity, our approach surpasses complex latent-based diffusion models while remaining significantly simpler than hybrid alternatives. Notably, it produces sharper geometric structure and is more robust in highly ambiguous regions, such as transparent objects.
Haofei Xu, Rundi Wu, Philipp Henzler +7
Google · ETH Zurich · University of Tübingen, Tübingen AI Center +3