Multi-View Geometry

Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained accuracy due to the absence of explicit multi-view constraints. We introduce the Geometry-Grounded Point Transformer (GGPT), a framework that augments feed-forward reconstruction with reliable sparse geometric guidance. We first propose an improved Structure-from-Motion pipeline based on dense feature matching and lightweight geometric optimisation to efficiently estimate accurate camera poses and partial 3D point clouds from sparse input views. Building on this foundation, we propose a geometry-guided 3D point transformer that refines dense point maps under explicit partial-geometry supervision using an optimised guidance encoding. Extensive experiments demonstrate that our method provides a principled mechanism for integrating geometric priors with dense feed-forward predictions, producing reconstructions that are both geometrically consistent and spatially complete, recovering fine structures and filling gaps in textureless areas. Trained solely on ScanNet++ with VGGT predictions, GGPT generalises across architectures and datasets, substantially outperforming state-of-the-art feed-forward 3D reconstruction models in both in-domain and out-of-domain settings.

Feature extraction, matching, structure from motion (SfM), and novel view synthesis (NVS) have traditionally been treated as separate problems with independent optimization objectives. We present GloSplat, a framework that performs joint pose-appearance optimization during 3D Gaussian Splatting training. Unlike prior joint optimization methods (BARF, NeRF--, 3RGS) that rely purely on photometric gradients for pose refinement, GloSplat preserves explicit SfM feature tracks as first-class entities throughout training: track 3D points are maintained as separate optimizable parameters from Gaussian primitives, providing persistent geometric anchors via a reprojection loss that operates alongside photometric supervision. This architectural choice prevents early-stage pose drift while enabling fine-grained refinement -- a capability absent in photometric-only approaches. We introduce two pipeline variants: (1) GloSplat-F, a COLMAP-free variant using retrieval-based pair selection for efficient reconstruction, and (2) GloSplat-A, an exhaustive matching variant for maximum quality. Both employ global SfM initialization followed by joint photometric-geometric optimization during 3DGS training. Experiments demonstrate that GloSplat-F achieves state-of-the-art among COLMAP-free methods while GloSplat-A surpasses all COLMAP-based baselines.

Affine transformations have been recently used for stereo vision. They can be exploited in various computer vision application, e.g., when estimating surface normals, homographies, fundamental and essential matrices. Even full 3D reconstruction can be obtained by using affine correspondences. First, this paper overviews the fundamental statements for affine transformations and epipolar geometry. Then it is investigated how the transformation accuracy influences the quality of the 3D reconstruction. Besides, we propose novel techniques for estimating the local affine transformation from corresponding image directions; moreover, the fundamental matrix, related to the processed image pair, can also be exploited. Both synthetic and real quantitative evaluations are implemented based on the accuracy of the reconstructed surface normals. For the latter one, a special object, containing three perpendicular planes with chessboard patterns, is constructed. The quantitative evaluations are based on the accuracy of the reconstructed surface normals and it is concluded that the estimation accuracy is around a few degrees for realistic test cases. Special stereo poses and plane orientations are also evaluated in detail.

In operating rooms (OR), world-scale multi-view 3D tracking supports downstream applications such as surgeon behavior recognition, where physically meaningful quantities such as distances and motion statistics must be measured in meters. However, real clinical deployments rarely satisfy the geometric prerequisites for stable multi-view fusion and tracking: camera calibration and RGB-D registration are always unreliable, leading to cross-view geometric inconsistency that produces "ghosting" during fusion and degrades 3D trajectories in a shared OR coordinate frame. To address this, we introduce Geometry OR Tracker, a two-stage pipeline that first rectifies imprecise calibration into a scaleconsistent and geometrically consistent camera setup with a single global scale via a Multi-view Metric Geometry Rectification module, and then performs Occlusion-Robust 3D Point Tracking directly in the unified OR world frame. On the MM-OR benchmark, improved geometric consistency translates into tracking gains: our rectification front-end reduces cross-view depth disagreement by more than 30$\times$ compared to raw calibration. Ablation studies further demonstrate the relationship between calibration quality and tracking accuracy, showing that improved geometric consistency yields stronger world-frame tracking.

We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Bråtelund and Rydell. Our result improves upon previously discovered sets of algebraic constraints in the geometric computer vision literature, which are all incomplete (as they do not generate the vanishing ideal) and sometimes make restrictive assumptions about how a matrix triple should be scaled. Our discussion touches more broadly on generalized compatibility varieties, whose multihomogeneous vanishing ideals are much less well understood. One of our key new discoveries is a simple set of quartic constraints vanishing on compatible fundamental matrix triples. These quartics are also significant in the setting of essential matrices: together with some previously known constraints, we show that they locally cut out the variety of compatible essential matrix triples.

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover $n$ cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,~4,~4,~4) independent of $n$. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Recent state-of-the-art visual trackers produce high quality and long-term-stable segmentation masks. We propose to leverage these strengths for planar object tracking, in which the goal is to estimate a precise 8-degrees-of-freedom homography pose, a geometric representation not estimated by segmentation trackers. We present SAM-H - a planar object tracker that estimates homographies from segmentation mask contours via a training-free pipeline. When SAM-H is applied to masks from SAM 2, it sets a new state-of-the-art performance on the challenging PlanarTrack benchmark by a large margin, +18.4pp on the p@5 metric. We further show that segmentation-based and correspondence-based homography estimation are complementary, and propose WOFTSAM, which out-performs all prior methods on both PlanarTrack and POT-210. We also provide precise re-annotations of PlanarTrack initial poses, enabling more accurate benchmarking in the high-precision p@5 metric. The code and the re-annotations are available at https://github.com/serycjon/WOFTSAM

This paper provides a consistent and extensive evaluation of state-of-the-art filtering and refinement methods on common image matching pipelines. Unlike previous comparisons, the designed benchmark also takes into account the more general, real, and practical cases where camera intrinsics are unavailable. Moreover, a novel and effective strategy combining non-deep traditional computer vision approaches based on planar constraints and cross correlation is presented. Experimental analysis provides several insights for current application design and future research directions. In particular, the choice of a proper evaluation protocol discloses the effective differences within the compared solutions which otherwise would tend to flatten. Moreover, the proposed classical algorithmic approach is competitive with recent deep methods. Besides providing robust baseline using traditional computer vision for the evaluation of deep-based methods, this knowledge is useful to improve and better understand the deep image matching architectures. On one hand, geometry-based filtering is effective in presence of outliers without degrading already robust deep pipelines; on the other hand cross-correlation refinement is valid in the case of corner-like keypoints and allows to not directly discard inaccurate matches by default in deep pipelines but to retain and refine them for achieving a better coverage of the scene.