In this paper, we study Nyström subsampling for vector-valued regression in vector-valued reproducing kernel Hilbert spaces. Standard kernel methods often suffer from prohibitive computational costs due to the construction and inversion of large kernel matrices, which limits their scalability to large datasets. To overcome this bottleneck, we propose an efficient operator learning algorithm based on Nyström subsampling that accommodates functional outputs. Under general source conditions characterized by index functions-extending beyond the classical Hölder-type and operator-monotone frameworks-we establish minimax-optimal convergence rates for the proposed estimator. As an application of the proposed framework, we consider function denoising problems. Unlike classical denoising methods, which are typically tailored to specific signal representations or noise models, our approach formulates denoising within a general operator learning framework. Numerical experiments on signal denoising, real-time audio denoising, image denoising, inverse Radon transform reconstruction, and energy-efficiency prediction confirm that the proposed method achieves performance comparable to full kernel methods while substantially reducing computational cost.

We present VGGT-SLAM, a dense RGBSLAM system constructed by incrementally and globally aligning submaps created from the feed-forward scene reconstruction approach VGGT using only uncalibrated monocular cameras. While related works align submaps using similarity transforms (i.e., translation, rotation, and scale), we show that such approaches are inadequate in the case of uncalibrated cameras. In particular, we revisit the idea of reconstruction ambiguity, where given a set of uncalibrated cameras with no assumption on the camera motion or scene structure, the scene can only be reconstructed up to a 15-degreesof-freedom projective transformation of the true geometry. This inspires us to recover a consistent scene reconstruction across submaps by optimizing over the SL(4) manifold, thus estimating 15-degrees-of-freedom homography transforms between sequential submaps while accounting for potential loop closure constraints. As verified by extensive experiments, we demonstrate that VGGTSLAM achieves improved map quality using long video sequences that are infeasible for VGGT due to its high GPU requirements.

Free-mo ticularly ving without object reliable reconstruction pose or depth from cues monocular and under video arbitrary remains object challenging, motion.

We introduce PARTCRAFTER, the first structured 3D generative model that jointly synthesizes multiple semantically meaningful and geometrically distinct 3D meshes from a single RGB image. Unlike existing methods that either produce monolithic 3D shapes or follow two-stage pipelines, i.e. first segmenting an image and then reconstructing each segment, PARTCRAFTER adopts a unified, compositional generation architecture that does not rely on pre-segmented inputs.

Event-based structured light (SL) systems have attracted increasing attention for their potential in high-performance 3D measurement. Despite the inherent HDR capability of event cameras, reflective and absorptive surfaces still cause event clutter and absence, which produce overexposed and underexposed regions that degrade the reconstruction quality. In this work, we present the first HDR 3D measurement framework specifically designed for event-based SL systems. First, we introduce a multi-contrast HDR coding strategy that facilitates imaging of areas with different reflectance. Second, to alleviate inter-frame interference caused by overexposed and underexposed areas, we propose a universal confidence-driven stereo matching strategy. Specifically, we estimate a confidence map as the fusion weight for features via an energy-guided confidence estimation.

However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured nature of Gaussians, supervision based solely on image rendering loss often leads to inaccurate geometry and inconsistent multi-view alignment. In this work, we propose a novel method that enhances the geometric representation of 3DGaussians through view alignment (VA). Specifically, we incorporate edge-aware image cues into the rendering loss to improve surface boundary delineation. To enforce geometric consistency across views, we introduce a visibility-aware photometric alignment loss that models occlusions and encourages accurate spatial relationships among Gaussians. To further mitigate ambiguities caused by lighting variations, we incorporate normal-based constraints to refine the spatial orientation of Gaussians and improve local surface estimation. Additionally, we leverage deep image feature embeddings to enforce cross-view consistency, enhancing the robustness of the learned geometry under varying viewpoints and illumination. Extensive experiments on standard benchmarks demonstrate that our method achieves stateof-the-art performance in both surface reconstruction and novel view synthesis. The source code is available at https://github.com/LeoQLi/VA-GS.

Beyond novel view synthesis,tit shows great potential for multi-view surface reconstruction. Existing amethods employ optimization-based reconstruction pipelines that achieve precise and complete surface extractions.

Indoor environments are the primary setting where humans spend most of their daily lives. Yet, computationally creating digital twins of these 3D spaces from captured images remains challenging. Factors such as the difficulty of accurate camera pose estimation from indoor images [28, 11, 1] and structural distortions in the resulting 3D reconstructions [22, 12, 21] hinder the development of robust, accurate, and user-friendly solutions for replicating indoor scenes in the digital world. As indoor scenes are typically rich in planar structures such as floors, ceilings, and walls, as well as planar furniture like tables and cabinets, planar primitives are well-suited representations for the accurate 3D reconstruction of indoor scenes. As a result, there has been significant interest among the research community in planar 3D reconstruction in recent years. Planar reconstruction approaches include feedforward solutions in monocular [40, 16, 27, 24, 18, 42] and two-view [11, 1, 28] settings, and per-scene optimization approaches [29, 38, 3, 9] that leverage posed multi-view inputs with the assistance of the feedforward models were studied. However, these approaches face two key limitations: Annotation dependence for feedforward methods: Learning feedforward models [36, 24, 28] typically requires accurate plane masks and 3D plane annotations from monocular or binocular inputs.

Deep neural networks achieve state-of-the-art results for accelerated MRI reconstruction. Most research on deep learning based imaging focuses on improving neural network architectures trained and evaluated on fixed and homogeneous training and evaluation data. In this work, we investigate data curation strategies for improving MRI reconstruction. We assemble a large dataset of raw k-space data from 18 public sources consisting of 1.1M images and construct a diverse evaluation set comprising 48 test sets, capturing variations in anatomy, contrast, number of coils, and other key factors. We propose and study different data filtering strategies to enhance performance of current state-of-the-art neural networks for accelerated MRI reconstruction. Our experiments show that filtering the training data leads to consistent, albeit modest, performance gains. These performance gains are robust across different training set sizes and accelerations, and we find that filtering is particularly beneficial when the proportion of in-distribution data in the unfiltered training set is low.

Unsigned Distance Fields (UDFs) are a natural implicit representation for open surfaces but, unlike Signed Distance Fields (SDFs), are challenging to triangulate into explicit meshes. This is especially true at high resolutions where neural UDFs exhibit higher noise levels, which makes it hard to capture fine details. Most current techniques perform within single voxels without reference to their neighborhood, resulting in missing surface and holes where the UDF is ambiguous or noisy. We show that this can be remedied by performing several passes and by reasoning on previously extracted surface elements to incorporate neighborhood information. Our key contribution is an iterative neural network that does this and progressively improves surface recovery within each voxel by spatially propagating information from increasingly distant neighbors. Unlike single-pass methods, our approach integrates newly detected surfaces, distance values, and gradients across multiple iterations, effectively correcting errors and stabilizing extraction in challenging regions. Experiments on diverse 3D models demonstrate that our method produces significantly more accurate and complete meshes than existing approaches, particularly for complex geometries, enabling UDF surface extraction at higher resolutions where traditional methods fail.