Geometric Priors

Feed-forward 3D reconstruction provides an efficient paradigm for scene modeling from image sequences. Scaling these models to large monocular scenarios are constrained by excessive GPU memory footprint, degraded local geometry, and long-term trajectory drift. Existing chunk-based optimization strategies provide limited geometric constraints and fail to maintain global consistency over extended trajectories. We present a unified framework for stable and scalable feed-forward 3D reconstruction from long monocular sequences. Our approach builds on coarse-to-fine trajectory alignment augmented by lightweight geometric prior injection. Distilling monocular geometric cues into the feed-forward backbone via LoRA adaptation improves depth accuracy on fine structures while preserving inference efficiency. We introduce a hybrid-weight sparse ray-field optimization that leverages high-frequency geometric features to guide local point-cloud refinement and enforce consistent inter-frame ray constraints. Unlike prior chunk-based methods, this establishes strong cross-frame geometric coupling while maintaining scalability. Finally, an efficient trajectory stitching strategy with joint ray-error optimization explicitly reduces accumulated drift. Extensive experiments show that our approach achieves competitive trajectory accuracy compared with representative SLAM systems, while maintaining globally consistent 3D reconstruction in large-scale scenarios.

Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.

Large-scale pre-training has transformed representation learning in 2D vision, yet its transferability to 3D single object tracking (SOT) remains insufficiently understood. Directly fine-tuning self-supervised 3D encoders, such as masked autoencoders (MAE), often leads to sub-optimal adaptation because the reconstruction objective is not fully aligned with the spatial-temporal matching requirements of tracking. In this paper, we observe that this difficulty can be interpreted as a layer-wise transfer mismatch: shallow layers tend to preserve transferable geometric cues, while deeper layers become increasingly specialized to the reconstruction pretext task and are less suitable for downstream tracking. Based on this observation, we propose MAETrack, a lightweight adaptation framework for transferring pre-training MAE representations to 3D SOT. MAETrack includes Layer-Selective Initialization (LSI), which initializes only the shallow stages of the tracking backbone from pre-trained weights while re-initializing deeper stages, and Geometric Residual Gating (GRG), which reinforces structurally salient regions in the search BEV features before template-search fusion through residual spatial modulation. Extensive experiments on standard 3D SOT benchmarks show that MAETrack consistently improves upon vanilla fine-tuning baselines with limited computational overhead. More broadly, our results suggest that effective transfer from 3D reconstruction pre-training to 3D tracking is not merely a matter of partial fine-tuning, but depends on a tracking-oriented transfer principle that preserves shallow geometry while adapting deeper representations to the downstream objective.

High-fidelity vehicle assets are essential for controllable traffic scene generation, particularly for synthesizing rare and safety-critical long-tail scenarios. However, reconstructing a reusable vehicle representation from in-the-wild onboard images remains challenging for two reasons. First, image-to-3D generation methods generally produce models without reliable metric scale. Second, onboard cameras usually observe only one side of a target vehicle, making conventional multi-view reconstruction incomplete on unobserved regions. To solve these problems, we propose a feed-forward vehicle asset reconstruction method, which leverages two complementary priors to reconstruct 3D Gaussian representations for vehicles using sparse one-sided observations. To achieve metric-scale reconstruction, a visual foundation model is first utilized to serve as a visual prior for Gaussian initialization. The Gaussian attributes are then estimated by a learnable encoder-decoder module. A symmetry-aware cloning strategy is presented to complete the unobserved side directly in Gaussian space, which exploits the bilateral structure of vehicles as a geometric prior. Experiments on the public dataset demonstrate that the proposed method significantly outperforms existing approaches in both vehicle asset completeness and geometric accuracy.

We present a self-supervised approach, Self-MVGTE, for estimating 3D gaze targets from multiple camera views. Unlike existing methods that independently estimate 2D gaze targets per camera view, Self-MVGTE predicts gaze targets directly in 3D space for the first time. Moreover, it does not require any ground-truth annotations from the target scene and uses only the multi-view input images from a calibrated camera setup, pseudo 2D gaze target labels from a monocular gaze target estimation model, and 3D gaze vectors from a monocular 3D gaze estimation model. A key challenge is that these pseudo labels are inherently noisy and multi-view inconsistent. To address this, we propose a probabilistic ray marching framework, which models the uncertainty of these pseudo labels and exploits 3D gaze vectors as geometric priors. Specifically, these gaze vectors are first integrated into the monocular gaze target estimation model to improve its generalization to unseen scenes, producing higher-quality pseudo labels. Then, for 3D gaze target estimation, we construct a 3D gaze cone by casting a bundle of rays from the eye position around the gaze vector to strictly constrain the solution space. Within this cone, we propose a depth-guided feature sampling strategy using off-the-shelf DINOv2 and Depth-Anything-3 models, and estimate a spatial likelihood distribution of the gaze target. Finally, we convert the pseudo gaze target labels into a target distribution and softly optimize the network. Extensive experiments on the MVGT dataset show that Self-MVGTE achieves state-of-the-art performance, surpassing existing fully-supervised baselines.

We introduce a self-supervised framework for learning joint visuospatial representations from RGB-D observations. While modern vision foundation models are trained almost exclusively on RGB images, many embodied systems have access to explicit depth sensing, which provides geometric information that monocular inputs cannot recover. Our method integrates depth-derived geometric priors with a visual backbone through inter-patch and intra-patch fusion, enabling the model to encode both appearance and spatial structure efficiently. The resulting representation shows promising improvements on 3D awareness while preserving semantic transfer: it outperforms prior methods of comparable scale on multiple 3D geometry benchmarks, and remains competitive when probed for standard RGB-D semantic segmentation tasks.

Generative models like Diffusion Models and Flow Matching have demonstrated remarkable capabilities in synthesizing high-fidelity driving videos, but are severely constrained by high inference latency due to the requirement of extensive sampling steps. We argue that this inefficiency stems from the prevailing reliance on a standard Gaussian source distribution, where consecutive frames are initialized as independent Gaussian noise. This paradigm disregards the rich spatiotemporal correlations inherent in driving videos, compelling the model to regenerate deterministic scene structures existing in previous frames from noise, which is both computationally redundant and prone to geometric inconsistency. To address this problem, we propose GeoFlow, a novel framework designed to achieve efficient driving video generation by harnessing explicit geometric priors. Instead of sampling from standard Gaussian noise, we leverage multi-view geometry and spatially-adaptive noise injection to construct a Geometry-Aligned Prior (GAP) distribution as starting point. This initialization bridges the gap between source distribution and data distribution, yielding a significantly straighter and shorter sampling trajectory. Extensive experiments demonstrate that GeoFlow can achieve remarkable efficiency of both training and inference: merely several hours of fine-tuning on baseline models can significantly boost few-step generation quality, while fully converged training drastically reduces number of inference steps required for state-of-the-art video generation.

3D Gaussian splatting (3DGS) has emerged as a widely-used tool for novel view synthesis, offering real-time rendering in a sparse representation. However, the method's reliance on structure-from-motion initialization and photometric optimization can lead to suboptimal geometric reconstruction, particularly for objects with high specularity. In this work, we investigate the integration of geometric priors, in the form of predicted normal and depth maps, into the 3DGS framework to improve the reconstruction quality. We analyze the effect of incorporating these priors into GS-based methods and our evaluation reveals that multi-view predictions, as they are done by the recent visual geometry grounded transformer (VGGT), outperform single-view alternatives. A major factor is the existence of a confidence map for the estimations, which comes as a by-product of multi-view models and which can significantly improve the effectiveness of priors by weighting each prediction appropriately. Extensive experiments on standard benchmarks show consistent improvement in reconstruction quality and significant gains in complex scenes including specular objects.

Video Virtual Try-On (VVT) synthesizes a video of a person wearing a target garment while preserving identity, motion, and scene dynamics. Dominant approaches cast VVT as mask-conditioned video inpainting and rely on separate modules for human parsing, pose estimation, and garment warping. This multi-stage design complicates deployment and, more critically, allows errors in explicit geometric priors to propagate irreversibly into the generated video. We present UniVVT, a unified end-to-end framework that reframes VVT as semantically conditioned video generation, eliminating mask, pose, and warping modules at inference. At its core, a scene-task perceiver built on a Multimodal Large Language Model jointly encodes the source video, target garment, and task instruction into compact, task-aware latent tokens, implicitly capturing what to transfer and where and how to transfer it. A lightweight semantic bridge then aligns these tokens with the conditioning space of a diffusion-based video generator, enabling coherent garment transfer. To robustly couple the heterogeneous components, we devise a three-stage progressive training strategy comprising semantic alignment, joint task adaptation, and flexible-resolution refinement. Extensive experiments demonstrate that UniVVT achieves state-of-the-art performance across multiple benchmarks, validating implicit semantic guidance as a simple and effective alternative to fragile geometric preprocessing for end-to-end virtual try-on.

Codebook-based blind face restoration (BFR) often suffers from ambiguous conditioning features and a fragile prediction mechanism under severe degradation. To address these challenges, we propose GeoMAR, a framework designed to unleash geometrically aligned features with masked autoregressive (MAR) refinement for robust face restoration. For feature conditioning, we introduce a dual-input extraction pipeline to extract component-based geometric descriptions with explicit, spatially faithful anchors. These textual priors are integrated with low-quality (LQ) features via an Aligned Geometric Priors Injector, which employs a KV-Q exchange strategy to generate geometrically aligned features. For prediction mechanism, we reformulate the one-step mapping into a multi-step MAR process. This coarse-to-fine generation progressively refines complex facial regions based on increasingly reliable context. Experiments on one synthetic and three real-world benchmarks demonstrate that GeoMAR achieves highly competitive perceptual quality and coherent visual structures compared with existing methods. The code is available at https://github.com/BRL-SYSU/GeoMAR.git.

Inferring complete 3D geometry and semantics from onboard images remains challenging because occlusions and restricted fields of view leave large scene regions underconstrained. Although satellite imagery provides wide-area context, appearance cues alone offer limited structural guidance and may be unreliable because of spatial or temporal discrepancies. We present GeoScene, a geospatially guided framework that jointly uses satellite imagery and structured OpenStreetMap cues as soft priors for 3D semantic scene completion. GeoScene learns complementary voxel-wise reliability weights for onboard observations and geospatial guidance, and uses them to control feature refinement in observed and unobserved regions. This design preserves local visual evidence while exploiting large-scale road and building structure beyond onboard visibility. Experiments on SemanticKITTI and SSCBench-KITTI-360 demonstrate that GeoScene consistently improves both geometric and semantic completion under the geospatial-prior-assisted setting, with the most pronounced benefits for large-scale static and geospatially structured classes.

Synthetic aperture radar (SAR) image generation can mitigate data scarcity, but controllablegeneration under sparse observation angles remains difficult. Recent SAR generative studies im-prove texture realism, yet explicit geometry-aware control is still limited. This paper studiesthe focused and verifiable setting of intermediate-azimuth completion: 3D-model-derived geo-metric priors guide a diffusion model to synthesize the views missing from sparse-angle trainingdata. GeoDiff-SAR constructs a lightweight multi-bounce ray-tracing prior, encodes the result-ing point cloud, and fuses it with text conditioning while adapting Stable Diffusion 3.5 Mediumthrough low-rank adaptation. On a real four-category aircraft dataset, GeoDiff-SAR reaches anSSIM of 0.812 and azimuth consistency of 0.940, compared with 0.738 and 0.782 for the text-conditioned SD3.5 Medium baseline. The same sparse-angle protocol on five MSTAR vehicleclasses yields an SSIM of 0.878 and azimuth consistency of 0.917. These results support theconclusion that a lightweight 3D geometric prior improves viewpoint adherence for controllableSAR generation; it is intended as generation guidance rather than high-fidelity electromagneticreconstruction.

Topological maps are key outputs of autonomous driving perception systems, delivering essential road information for path planning. They identify instances such as centerlines and traffic signs, along with their connectivity relationships. Due to the lack of explicit markings for centerlines in real-world environments, the detection of centerline instances remains a significant challenge. To tackle this problem, we propose HGeo-TopoMap, which leverages an explicit prior map and implicit spatial relations to hierarchically boost topological mapping. First, a geometric adaptive learning module is designed for the road structure map obtained via inverse perspective mapping. This module discretely encodes semantic and spatial features from the map, followed by a prior-mask attention mechanism that selectively focuses on informative regions. Then, a geometric consistency learning module is devised, which leverages the geometric properties and spatial relationships of centerlines. Built on the geometry-aware decoder, it enforces spatial consistency by aligning features of centerline instances with identical geometric orientations. The proposed method is evaluated on the OpenLane-V2 dataset across the centerline, lane segment, and robustness benchmarks. Beyond substantial improvements in topological mapping accuracy, the proposed method offers the benefit of enhanced robustness, consistently outperforming baselines under both standard and challenging conditions. The source code and model weights will be made publicly available at https://github.com/lynn-yu/HGeo-TopoMap.

Recovering scene-consistent 4D crowd motion from monocular video in large-scale scenes remains challenging due to severe depth ambiguity and complex scene geometry. Existing monocular crowd reconstruction methods typically rely on single-plane assumptions, leading to unreliable metric scale and spatial drift under complex terrain. We propose Crowd4D, the first scene-aware 4D crowd reconstruction framework that jointly optimizes the crowd and scene from a monocular RGB video in large-scale scenes. Crowd4D explicitly incorporates scene geometry and ensures consistency across image and scene spaces via a multi-stage optimization strategy. A key bottleneck of this task lies in accurate human-scene alignment, particularly in scale and position. However, human and scene reconstructions are typically decoupled. To address this, we introduce the Human-Scene Interaction Proxy, abbreviated as HSIP, as an intermediate representation derived from Scene Interaction Point Clouds and a Scene Interaction Surface, abbreviated as SIPC and SIS. These representations encode explicit scene-aware geometric priors and redefine the optimization space for large-scale monocular 4D crowd reconstruction. To further improve temporal stability under occlusions, we introduce Crowd Structural Coherence Regularization, abbreviated as CSCR, which leverages HSIP-based spatial priors to impose soft temporal consistency on pairwise relative displacements and directions within local crowd neighborhoods. Extensive experiments demonstrate that Crowd4D consistently outperforms existing state-of-the-art methods and enables robust monocular 4D crowd reconstruction in complex, large-scale real-world scenes.

Monocular depth foundation models have demonstrated remarkable generalization capabilities across diverse environments. However, they continue to struggle with metric depth estimation in diverse environments. This limitation stems from the inherent scale ambiguity of single-view inference, leading to misaligned scale predictions even when the relative geometry is accurate. Conversely, recent multi-view foundation models leverage cross-view cues to learn robust scene-level geometry and consistent scale. Yet, these benefits typically vanish during single-image inference, as the absence of explicit geometric constraints causes performance to degrade. To bridge this gap, we propose a novel framework that transfers the scale-aware geometric priors of multi-view models into monocular depth foundation models. Specifically, we introduce an Epipolar Distillation (EpiDistill), an approach utilizing Rectified Stereo Tokens, which enables the single-view prediction model to retain epipolar attention patterns and maintain geometric consistency without requiring multi-view inputs at inference. Experimental results demonstrate that our method significantly improves zero-shot metric depth estimation, particularly on challenging datasets like ETH3D and DIODE where scale alignment is critical. Furthermore, our approach is model-agnostic, consistently boosting the performance of state-of-the-art ViT-based models, including UniDepthV2 and DepthPro.

We present AeroMap3D, a monocular 6-DoF UAV localization system that anchors onboard imagery to visual, geometric, and semantic map priors for GNSS-denied navigation. AeroMap3D addresses two fundamental challenges in map-referenced aerial localization: the cross-view discrepancy between UAV imagery and satellite maps, and the structural inconsistency between bare-earth digital elevation models (DEMs) and urban scenes. First, we introduce a lightweight adapter that enables a dense matcher pretrained on internet-scale generic data to perform reliable UAV-to-map registration without finetuning. By estimating the scale ratio and yaw offset between the UAV image and map tile, the adapter removes the dominant geometric misalignment induced by altitude, camera field of view, and heading before dense correspondence estimation. Second, AeroMap3D lifts 2D UAV-map correspondences onto DEM terrain while using OpenStreetMap annotations to reject semantically unreliable matches before RANSAC-PnP pose estimation, thereby reducing errors caused by unmodeled building heights and off-nadir structures. Delayed map-based pose measurements are further fused with relative-motion priors using a delayed-state EKF for continuous trajectory estimation. Without UAV-Terra3D retraining or tuning, AeroMap3D localizes all trajectories across eight Austin sites within 50 m and achieves 5.88 m mean 3D error over 55 km of flight.

4D spatio-temporal reasoning, jointly modeling 3D spatial structure and temporal evolution, is essential for understanding dynamic worlds and enabling embodied interaction. While current Multimodal Large Language Models (MLLMs) show strong capabilities in static scene understanding and coarse-grained 4D tasks, they still have notable limitations in continuous dynamic scene perception, especially in tracking dynamic object evidence for coherent 4D spatio-temporal reasoning. This shortcoming stems mainly from relying on sparse frame-level observations, fragmenting continuous dynamic cues and leaving models unable to disentangle genuine object dynamics from camera-induced apparent motion. Inspired by humans tracking dynamic cues while compensating for viewpoint changes, we propose DynTrace, a training-free framework for 4D spatio-temporal reasoning with two complementary components. Dynamic Trajectory Visualization (DTV) reprojects world-coordinate trajectories onto the image plane, providing geometry-informed visual priors that disentangle genuine object dynamics from camera-induced apparent motion. Meanwhile, the Dynamic Trace Token (DT-Token), organized into a Dynamic Trace Graph (DTG), tracks object-level dynamic cues, trace evolution, and key moments, maintaining continuous dynamic object evidence for coherent 4D reasoning. Together, these two components equip MLLMs with continuously tracked dynamic object evidence, grounded in geometry-informed visual priors and structured spatio-temporal traces. DynTrace consistently improves open-source MLLMs, achieving state-of-the-art results on Dyn-Bench, VLM4D, and DSI-Bench, validating the importance of tracking dynamic object evidence for robust 4D spatio-temporal reasoning.

Current visual generation models are capable of producing high-quality content, yet they lack a coherent perception of the spatial structure. Existing generative novel view synthesis methods typically introduce explicit geometry priors, which enforce spatial consistency but inherently restrict generalization in large view changes. In contrast, recent interactive generative methods favor implicit scene modeling, offering greater flexibility at the cost of precise camera control and geometry consistency. In this paper, we propose MetaView, a diffusion-based monocular novel view synthesis framework that enables rendering under large view changes from a single image. Our key insight is to combine implicit geometry modeling with minimal yet essential explicit 3D cues: we incorporate implicit geometry priors from a feed-forward geometry perception network to regularize structure without imposing restrictive reconstruction pipelines, while leveraging metric depth to anchor the generation to a metric scale. This design allows MetaView to achieve both geometry consistency and precise controllability. Extensive experiments demonstrate that, under challenging monocular large viewpoint changes, MetaView significantly outperforms existing methods and exhibits superior generalization. Our code is publicly available at https://github.com/KlingAIResearch/MetaView.

SLAM methods based on 3D Gaussian Splatting (3DGS) have demonstrated impressive tracking and mapping performance, but typically require additional geometric information from external depth sensors. Meanwhile, recent SLAM systems that leverage geometric priors from pre-trained feed-forward models enable real-time dense reconstruction, yet often discard original RGB information during optimization, thus degrading overall reconstruction quality. We present GeoGS-SLAM, an online monocular dense reconstruction system that combines the 3DGS-based map representation with learned geometric priors. Given uncalibrated RGB input, we first employ a feed-forward visual geometry model to predict camera and scene priors. The Gaussian scene map is then expanded by directly sampling Gaussian primitives from both RGB input and geometric priors. Camera poses and the scene map are jointly optimized through a coarse-to-fine strategy that minimizes both photometric and geometric losses. To ensure global consistency, we further incorporate online loop closure detection and pose graph optimization. Extensive experiments across indoor and outdoor benchmarks demonstrate that GeoGS-SLAM achieves superior rendering quality and tracking accuracy compared to state-of-the-art methods while maintaining online real-time performance. Project page: https://rlgao.github.io/geogs_slam.

Vision-centric autonomous driving requires accurate metric geometry and ego-motion estimation from synchronized multi-camera observations. Recent visual geometry models show strong performance in pose estimation, depth prediction, and 3D reconstruction, but are not tailored to rigid multi-camera driving systems. They often encode camera poses as entangled representations, in which time-varying ego-motion and static camera-rig geometry are jointly modeled, limiting the utilization of vehicle-side geometric priors. We propose Trajectory-Rig Decoupled Metric Geometry Learning (TRIG), a geometry perception framework for autonomous driving. TRIG factorizes camera poses into ego-trajectory and camera-rig components, enabling separate modeling of ego-motion and static multi-camera topology. We introduce decoupled pose encoding and supervision, which separately constrain trajectory evolution and rig geometry for metric-consistent learning. Moreover, sparse Temporal--Spatial attention separates cross-camera interaction from temporal aggregation, reducing global attention cost while preserving geometric reasoning. Experiments on five autonomous driving benchmarks show that TRIG achieves state-of-the-art performance in pose estimation, metric depth prediction, and 3D reconstruction.

World Action Models (WAMs) have shown strong potential for robotic manipulation by jointly modeling visual future dynamics and executable action sequences. However, existing video-action co-training methods primarily optimize appearance-oriented video latents, which may insufficiently capture the temporally evolving geometry required for precise manipulation. We propose MECo-WAM, a Multi-Expert Co-Training World Action Model that injects action-relevant 4D geometric priors into video-action representations while preserving the original lightweight inference graph. During training, MECo-WAM combines video and action experts with a lightweight 4D expert supervised by relational targets from a frozen VGGT encoder. Asymmetric expert visibility prevents non-causal shortcuts from auxiliary geometry to action generation. To transfer geometric knowledge into the deployed video-action pathway, we introduce decayed 4D read-mask attention, which provides restricted current-frame geometric guidance early in training and progressively removes this dependency. We further propose action-aware temporal geometric distillation, which aligns within-frame geometric relations and their temporal evolution while emphasizing visual regions most relevant to robot actions. At deployment, all auxiliary 4D components are removed. Experiments on LIBERO (98.2%), RoboTwin 2.0 (92.6%), and challenging real-world manipulation tasks show that MECo-WAM improves manipulation performance without increasing inference cost.

4D scene synthesis from monocular videos has made significant progress in recent years. However, existing methods are typically constrained by view interpolation. As a result, they struggle to infer unseen regions beyond the observed views. In this paper, we reformulate the task as 4D scene synthesis with unseen regions, which extends beyond traditional interpolation settings. Camera-conditioned video generation enables unseen region synthesis by guiding generation along specified cameras. However, these methods lack explicit 3D priors and are optimized with random camera trajectories. This design leads to severe inconsistencies under large trajectory deviations. To address this limitation, we build a unified training and inference framework with panoramic trajectory guidance. While this design improves cross-view consistency, the panoramic representation alone fails to model dynamic content effectively. Object motion in panoramic space introduces scale and shape distortions. To address this, we propose PanoGaussian, a unified Panoramic-Gaussian representation that distills the panoramic representation into an explicit dynamic Gaussian representation to capture dynamic physical priors of the 4D scene. Experiments demonstrate that PanoGaussian achieves consistent 4D scene synthesis even under large viewpoint variations.

Table Structure Recognition (TSR) aims to recover the row and column layout of tables from document images, a key step in document understanding pipelines. Accurate TSR depends on precise boundary localization: small errors in row or column boundaries can propagate into incorrect cell assignments and structural inconsistencies. Yet detection-based approaches treat table elements as generic objects, ignoring a fundamental property of table layout: rows and columns play structurally distinct roles and their boundaries carry unequal importance. We propose an Edge-constrained Fine-grained Localization loss (EFL) that formalizes this structural asymmetry by encoding table-specific geometric priors into the training objective: row-like elements are supervised with emphasis on their horizontal boundaries, while column-like elements prioritize vertical boundaries. Implemented within a real-time detector with distribution-based boundary refinement (D-FINE), EFL operates during training only and guides boundary refinement toward structurally meaningful adjustments with no change to the inference pipeline. The proposed approach, ConRTF, is also data-efficient, maintaining robust accuracy with as few as 2k--3k annotated tables. Experiments on PubTables-1M and two private datasets show consistent improvements over the optimized baseline and several real-time detectors including RT-DETRv2 and YOLOv10-11, with gains of up to +1.6 GriTS points at equal inference speed.

Most end-to-end autonomous driving methods rely solely on instantaneous sensor observations, limiting them to reactive behavior without the anticipatory foresight human drivers employ through prior experience. We introduce geospatial visual priors, street-level visual context anchored to the intended driving route, providing visual-spatial foresight independent of real-time sensors. We propose a memory augmentation module featuring a dual-memory architecture and an adaptive memory gate, which can be easily integrated into existing end-to-end approaches. This design pairs a contextual memory for retrieved priors with a persistent fallback memory, and dynamically regulates the influence of memories based on current state compatibility. Evaluated on the NAVSIM-v2 benchmark, our approach consistently improves performance across diverse end-to-end baselines. Furthermore, because these priors are independent of onboard sensors, our method inherently improves robustness against sensor corruption, while the dual-memory design ensures safe fallback when the retrieved priors themselves become unreliable. Our project page is available at https://ori-mrg.github.io/PriorEye.

Learning a 4D scene representation from a single monocular video that supports dynamic novel-view synthesis while maintaining faithful geometry over time remains challenging. Dynamic Gaussian Splatting achieves strong rendering performance through photometric optimization, yet does not explicitly enforce multi-view geometric consistency. In contrast, 3D foundation models recover coherent scene geometry and camera motion, but their point-based outputs are not designed for photorealistic rendering. We propose Ground4D, a geometry-grounded framework built on two stages. First, we perform geometry initialization via 3D foundation models, leveraging VGGT in a training-free manner to reconstruct multi-view-consistent 3D geometry and camera poses from monocular video. The recovered geometry provides a structured and reliable initialization for dynamic Gaussian representations. Second, we conduct geometry-consistency-aware refinement via dynamic Gaussian Splatting, optimizing the representation through differentiable rendering while maintaining multi-view geometric consistency across both observed and synthesized viewpoints. Furthermore, Ground4D inherently models the continuous 4D dynamics of the scene, naturally supporting rendering at arbitrary timestamps. By integrating foundation-level geometric priors into dynamic Gaussian optimization, Ground4D achieves stronger reconstruction fidelity and rendering performance, underscoring the role of geometry-grounded constraints in robust 4D scene modeling.

3D Gaussian Splatting (3DGS) has emerged as a promising technique for novel view synthesis. However, 3DGS requires dense input views to achieve high-quality rendering. In sparse-view scenarios, 3DGS often prones to overfitting, resulting in noticeable artifacts and degraded rendering quality. Previous methods explore to address this issue by introducing additional priors (e.g. depth priors) or integrating regularization techniques (e.g. Dropout). However, these methods are often applied without principled guidance. In particular, prior-based augmentation typically samples novel viewpoints randomly, while Dropout-based regularization randomly removes Gaussians. The compounded randomness introduces uncertainty and instability, limiting the fidelity of novel view synthesis. In this paper, we propose a novel method for sparse-view 3DGS that incorporates Fisher Information to quantitatively guide the utilization of geometric priors and regularization. Specifically, our method comprises two key components: (1) Stereo augmentation with Fisher Information. By leveraging Fisher Information, we actively select most informative supporting views and use depth priors to curate reliable pseudo ground truths, which reduces randomness in augmentation and improves stability and rendering fidelity; (2) Uncertainty-aware regularization. We reduce the instability of Dropout-based regularization by using Fisher Information to quantitatively measure the uncertainty of each 3D Gaussian, and adaptively adjust the removal probability, leading to more stable and effective regularization. With these two components, our method effectively mitigates overfitting and improves the stability of optimization in sparse-view 3DGS, resulting in superior rendering fidelity. Extensive experiments show that our method achieves state-of-the-art performance in sparse-view novel view synthesis benchmarks.

Generalist robot policies must follow user instructions while reasoning about how objects, cameras, and robot actions interact in the 3D physical world. Recent vision-language-action models (VLAs) and video world-action models (WAMs) inherit strong semantic or temporal priors from large-scale foundation models, but they still operate primarily on 2D image frames or 2D-derived latent spaces, leaving implicit the 3D geometry required for contact-rich manipulation. We propose the Geometric Action Model (GAM), a language-conditioned manipulation policy that directly repurposes a pretrained geometric foundation model (GFM) as a shared substrate for perception, temporal prediction, and action decoding. GAM splits the GFM at an intermediate layer: the shallow layers serve as an observation encoder, and a causal future predictor inserted at the split layer forecasts future latent tokens conditioned on language, proprioception, and action history. The predicted future tokens are then routed through the remaining GFM blocks for feature propagation and decoding, allowing a single backbone to produce both future geometry and actions. This design equips the GFM with language-conditioned temporal world modeling through minimal architectural modification while preserving its rich geometric priors. Across a broad suite of simulation and real-robot manipulation benchmarks, GAM is more accurate, more robust, faster, and lighter than current foundation-model-scale baselines.

Precise biomedical image segmentation is crucial for clinical diagnosis. Geometric cues (e.g., boundary, shape, and topology) can improve structural consistency, yet most are task-specific and lack a unified geometric foundation that generalizes across organs and modalities. We are motivated by the observation that several medical segmentation targets can be approximated as globally near-convex shapes. A convex region is one in which any two interior points can be connected by a line segment entirely contained within the region. In practice, medical targets may exhibit small local concavities or boundary irregularities; we refer to such globally convex-like shapes as near-convex. Motivated by this, we derive Hadwiger Shape Priors from Hadwiger's theorem as an interpretable global regularizer using three 2D measures: area A, perimeter P, and Euler characteristic chi, enabling transfer across organs and modalities. However, because medical datasets are shape-heterogeneous, enforcing near-convex priors uniformly can over-regularize non-convex anatomy with significant concavities, washing out concavities and fine details and degrading segmentation accuracy. To address this challenge, we propose Conflict-Aware Objective Balancing (CAOB), which integrates shape priors with segmentation in a gradient-aware manner. For each prior, CAOB removes only the gradient component that conflicts with segmentation while preserving the remaining aligned component, and adaptively regulates objective influences to prevent prior dominance. This enables stable use of shape priors on shape-heterogeneous data without erasing genuine concavities or fine structural details. We call this plug-and-play framework HadBalance.

Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols. Retraining DNN models to address these distribution shifts is often impractical due to the high cost of acquiring and annotating new medical datasets. To address this, we introduce VarDeepPCA, a novel lightweight variational DNN framework designed to restore/refine degraded segmentation maps by leveraging intrinsic geometric priors. Unlike existing approaches that require target-domain data or extensive pre-training, our VarDeepPCA explicitly learns a distribution of valid anatomical geometries using only small in-distribution (ID) datasets. Theoretically, our novel variational learning framework leverages a reinterpretation of the softmax mapping to implicitly perform exact distribution modeling, thereby enabling computationally efficient, sampling-free learning and inference. This also enables VarDeepPCA to provide uncertainty estimates associated with its restored segmentation maps. We empirically validate our framework across 4 distinct clinical applications, using 14 publicly available datasets, involving segmentation of the myocardium, neuroretinal rim, prostate, and fetal head. Comparisons against 15 existing methods demonstrate that VarDeepPCA consistently restores segmentation maps produced by the existing methods on OOD data to (i) significantly improve anatomical plausibility of geometries and clinical utility of the segmentations, and (ii) significantly reduce errors, without needing any more training data than that used by existing methods.

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.

Vision-based navigation models, particularly foundation models, generate viable trajectories from RGB observations alone. However, even state-of-the-art transformer- and diffusion-based policies struggle to generalize in unfamiliar deployment environments containing unseen obstacles or shifted conditions. The resulting trajectories often remain goal-directed but unsafe. Existing efforts improve safety through external trajectory correction or internal geometric priors, yet the resulting policies are not trained to explicitly represent obstacle boundaries or traversable free-space structure. To address this, we propose a navigation model that incorporates these structures directly into the policy via fine-tuning and is designed to be compatible with diverse RGB-based backbones. Across multiple robot platforms, indoor environments, and static and dynamic obstacle scenarios, our method reduces collision frequency relative to ViNT, NoMaD, and their CARE-augmented variants while maintaining goal-reaching performance.

Traditional UV unwrapping relies on direct optimization of geometric distortion energies and can fail through invalid initialization, local minima, or topological foldovers. We recast fixed-chart UV unwrapping as continuous neural reparameterization: an untrained SIREN maps per-vertex mesh features to UV coordinates, and its weights are optimized for a geometric objective. The practical contribution is a robust chart-solver recipe, combining Laplace--Beltrami spectral inputs, Tutte residual warm-up, a $C^2$ determinant extension, an injectivity barrier, and validity-checked retry/fallback routing, rather than a claim that any single component guarantees validity or that recutting methods should be replaced. NTK--LBO diagnostics show that spectral conditioning changes update geometry, especially at initialization and mid-rank subspaces, but does not by itself predict chart success. On compact pre-cut charts and a 47-chart stratified Thingi10K/xatlas-cut benchmark, the neural solver produces zero flips on all compact charts and 42/47 valid zero-flip stratified solves. BFF and OptCuts comparisons sharpen the scope: recutting can be faster and lower-distortion when allowed, while the neural solver targets supplied-chart validity and validation-first atlas construction. On Amara Spatial generated meshes, the full atlas construction path gives packed-atlas coverage on a 25-asset set and 1000/1000 strict locally valid atlases with zero UV flips in a large-scale Rust atlas run after fallback routing.

Effective visuo-tactile integration is critical for robotic dexterous manipulation, especially when visual observations are unreliable or occluded. However, robustly aligning sparse, heterogeneous tactile measurements with dense visual representations remains a fundamental challenge. Most existing approaches require policies to learn cross-modal correspondences implicitly from limited demonstrations, without leveraging geometric priors. As a result, they are often data-inefficient and generalize poorly when visual observations are degraded. To address this limitation, we propose a framework that explicitly grounds physical contacts in the image domain. Using robot forward kinematics and camera calibration, we project tactile sensor locations directly onto the RGB image plane. We then render force-modulated Gaussian saliency maps to model spatial uncertainty arising from kinematic and calibration errors. By integrating these 2D spatial anchors through a zero-initialized conditioning architecture, our method injects physical contact priors into standard visual backbones while preserving pre-trained visual representations. We evaluate our method on six dexterous manipulation tasks in both simulation and the real world under severe visual occlusions. Real-world experiments show that explicit RGB-S grounding in the image domain improves real-world occluded manipulation success rates by $26.7$ percentage points over the strongest implicit visuo-tactile baseline, suggesting its improved spatial reasoning and robustness to occlusion. Project page: touch-as-saliency.github.io

Vision-Language Models (VLMs) often struggle with robust 3D spatial reasoning. Prevailing methods that rely on fine-tuning with 3D visual question-answering (VQA) datasets may overfit dataset-specific biases, while integrating specialized 3D visual encoders is often inflexible and cumbersome. In this paper, we argue that genuine spatial understanding should emerge from learning fundamental geometric priors, not only from high-level VQA supervision. We propose GASP (Geometric-Aware Spatial Priors), a framework that injects these priors directly into the LLM's transformer layers. GASP employs a small correspondence head, applied as a deep supervision signal across all layers, and is trained with a dual objective leveraging ground-truth geometry from large-scale video scenes: a contrastive loss on ground-truth point correspondences enforces 2D view-invariance, while a depth consistency supervision resolves 3D geometric ambiguities. Our analysis first provides a diagnostic showing that standard VLMs' internal correspondence matching accuracy is very low (often below 5%). We then demonstrate that our training substantially improves this behavior, boosting peak layer-wise correspondence to over 70% and maintaining over 85% temporal robustness while baselines remain below 5%. These internal improvements translate to significant gains on downstream spatial benchmarks including +18.2% on All-Angles Bench and +29.0% on VSI-Bench, all without training on any 3D VQA data. Our findings indicate that learning from fundamental geometric priors is a promising and generalizable pathway towards VLMs with more reliable 3D spatial reasoning.

In point clouds, noise directly perturbs point coordinates that encode both spatial location and geometry, making one-to-one correspondence construction more challenging than in images. Existing methods impose statistical mappings across noisy variants via noise or optimal transport, but suffer from correspondence ambiguity. In this work, we propose Self-Induced Mirror-Point Consistency (SIMPC) to learn deterministic correspondences between points and the underlying surface in an unsupervised manner. For each noisy point, SIMPC generates a mirror-point on the opposite side of the underlying surface, guided by geometric priors during the denoising process. By encouraging consistency between the denoising targets of the original point and its mirror counterpart, SIMPC effectively localizes the position of underlying surface. Extensive experiments on synthetic and real-world datasets demonstrate that SIMPC significantly outperforms state-of-the-art unsupervised methods and surpasses several strong supervised counterparts.

Generating 4D scenes from a single-view video is inherently ill-posed: a single viewpoint lacks the information needed to recover a complete, dynamic scene with full coverage. Existing methods are typically limited to monocular videos, simple 3D effects, or only small viewpoint perturbations around the original viewpoint, falling short of true 4D generation. Meanwhile, the lack of large-scale datasets capturing full-scope 4D scenes with synchronized multi-view videos further hinders progress in this direction. We propose a novel single-view video-to-4D framework that casts full-scope 4D generation as a multi-view video synthesis followed by optimization-based 4D reconstruction from the generated views. To instantiate this formulation end-to-end, we make three key contributions. First, we introduce Real-MV-4D, a large-scale dataset of synchronized multi-view videos captured in diverse real-world environments to provide the 4D supervision. Second, we train a multi-view video diffusion model driven by a novel fused time(T)-view(V) attention mechanism that directly embeds geometric reprojection priors and explicit camera conditioning into its view-time interactions. Unlike basic feature fusion, this direct binding strictly aligns the generation process with physical 3D priors to produce a dense, synchronized T$\times$V video grid. Third, rather than relying on non-interactive and inconsistent 2D video interpolations, we lift the synthesized multi-view videos into an explicit 4D representation (i.e. 4DGS), regularized by a Flow Matching Distillation loss that exploits the multi-view prior to improve novel-view rendering. Extensive experiments demonstrate that our method outperforms existing approaches in both visual fidelity and geometric consistency, enabling full-scope 4D scene generation from single-view videos.

In 3D scene understanding, deep learning models rely on large models and extensive training to capture basic geometric structures that are present in the 3D data. However, existing methods lack explicit mechanisms to incorporate geometric information, such as learnable primitive shapes, often necessitating large models and more training data which in turn increases cost and can limit generalization. We introduce GIBLy, a lightweight geometric inductive bias layer that integrates learnable geometric priors into 3D segmentation pipelines. GIBLy enhances existing architectures -- whether MLP-based, convolution-based, or transformer-based -- by providing features aligned with simple geometric shapes (and thus human-interpretable) that improve segmentation performance with minimal computational overhead. We validate our approach across multiple 3D semantic segmentation benchmarks, demonstrating consistent performance gains, including up to +11.5% mIoU on TS40K with PTV3, while adding only 58K extra parameters. Our results highlight the benefit of explicitly encoding geometric structure to support accurate and efficient 3D scene understanding, with a lightweight add-on layer

Stereo matching on top-bottom equirectangular images provides an effective framework for full-surround perception, as vertically aligned epipolar lines enable the use of advanced perspective stereo architectures that are largely driven by large-scale datasets and monocular priors. However, the performance of such adaptations is severely limited by the scarcity of omnidirectional stereo datasets and the degradation of perspective monocular priors under spherical distortions. To address these challenges, we propose H-OmniStereo, a zero-shot omnidirectional stereo matching framework. First, we construct high-quality synthetic dataset comprising over 2.8 million top-bottom equirectangular stereo pairs to scale up training. Second, we introduce an equirectangular monocular normal estimator, specifically operating in a heading-aligned coordinate system. Beyond providing distortion-robust and cross-view-consistent geometric priors for establishing reliable correspondences in stereo matching, this design boosts training efficiency and accommodates train-test FoV mismatches. Extensive experiments show that our approach achieves higher accuracy than existing methods on out-of-domain datasets and successfully generalizes to real-world consumer camera setups using a single model. The model and dataset will be released at https://github.com/JIANG-CX/H-OmniStereo.

Drone-view geo-localization aims to match a query drone image, often captured under adverse weather conditions (e.g., rain, snow, fog), against a gallery of geo-tagged satellite images. Weather-induced degradations in the drone view, such as noise, reduced visibility, and partial occlusions, severely exacerbate the intrinsic cross-view domain gap. While prior methods predominantly rely on weather-specific architectures or data augmentations, they have largely overlooked road map data, a readily available modality that provides strong, inherently weather-invariant geometric layout cues (e.g., road networks and building footprints) at negligible additional cost. We introduce GeoFuse, a cross-modal fusion framework that integrates precisely aligned road map tiles with satellite imagery to yield more discriminative and weather-resilient representations. We first augment the existing University-1652 and DenseUAV benchmarks with geo-aligned road maps, supplying structural priors robust to meteorological variations. Building on this, we propose a flexible fusion module that combines satellite and road map features via token-level and channel-level interactions, with a lightweight dynamic gating mechanism that adaptively weights modality contributions per instance. Finally, we employ class-level cross-view contrastive learning to promote robust alignment between weather-degraded drone features and the fused satellite-roadmap representations. Extensive experiments under diverse weather conditions show that GeoFuse consistently outperforms state-of-the-art methods, achieving +3.46% and +23.18% Recall@1 accuracy on the University-1652 and DenseUAV benchmarks, respectively.

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment. To bridge this gap, we conduct an analysis from an optimization perspective and formalize the intrinsic relationship among data symmetry priors, model equivariance, and generalization capability. Specifically, we propose for the first time a quantifiable definition of non strict symmetry at the dataset level (rather than sample level) and use it as a constraint to formulate the restoration inverse problem. We then show that the equivariance for restoration models can be naturally derived from this inverse problems incorporated the proposed symmetry constraints, and that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk. Guided by these insights, we propose a Sample Adaptive Equivariant Network that uses a hypernetwork and transformation learnable equivariant convolutions to dynamically align with each sample's inherent symmetry. Extensive experiments on super resolution, denoising, and deraining validate our theoretical findings and show significant superiority over standard baselines and traditional equivariant models. Our code and supplementary material are available at https://github.com/tanfy929/SA-Conv.

Generative novel view synthesis faces a fundamental dilemma: geometric priors provide spatial alignment but become sparse and inaccurate under view changes, while appearance priors offer visual fidelity but lack geometric correspondence. Existing methods either propagate geometric errors throughout generation or suffer from signal conflicts when fusing both statically. We introduce MoCam, which employs structured denoising dynamics to orchestrate a coordinated progression from geometry to appearance within the diffusion process. MoCam first leverages geometric priors in early stages to anchor coarse structures and tolerate their incompleteness, then switches to appearance priors in later stages to actively correct geometric errors and refine details. This design naturally unifies static and dynamic view synthesis by temporally decoupling geometric alignment and appearance refinement within the diffusion process. Experiments demonstrate that MoCam significantly outperforms prior methods, particularly when point clouds contain severe holes or distortions, achieving robust geometry-appearance disentanglement.

Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by incompatible geometric priors on pre-trained cross-modal features, resulting in suboptimal adaptation performance. We first analyze these methods from a polar decomposition perspective (i.e., radial and angular sub-manifolds). Under this new geometric view, we identify three overlooked limitations in them: 1) Angular dynamics distortion: The radial-angular coupling induces non-uniform speed on the angular sub-manifold, leading to regression training difficulty and extra truncation errors. 2) Radial dynamics neglect: Feature normalization discards modality confidence, failing to distinguish out-of-distribution and in-distribution data, and abandoning crucial radial dynamics. 3) Context-agnostic unconditional flow: Dataset-specific information loss during pre-trained cross-modal feature extraction remains unrecovered. To resolve these issues, we propose warped product flow matching (WP-FM), a unified Riemannian framework that reformulates alignment on a warped product manifold. Within this framework, we derive direct product flow matching (DP-FM) by introducing a constant-warping metric, which yields a decoupled cylindrical manifold (i.e., direct product manifold). DP-FM enables independent radial evolution and constant-speed angular geodesic transport, effectively eliminating angular dynamics distortion while preserving radial consistency. Meanwhile, we incorporate classifier-free guidance by conditioning the flow on the pre-trained VLMs' hidden states to inject missing dataset-specific information. Extensive results across 11 benchmarks have demonstrated that DP-FM achieves a new state-of-the-art for multi-step few-shot adaptation.

Despite the success of Large-Vision Language Models (LVLMs), general optimization objectives (e.g., standard MLE) fail to constrain visual trajectories, leading to language bias and hallucination. To mitigate this, current methods introduce geometric priors from visual experts as additional supervision. However, we observe that such supervision is typically suboptimal: it is biased toward geometric precision and offers limited reasoning utility. To bridge this gap, we propose Perceptual Flow Network (PFlowNet), which eschews rigid alignment with the expert priors and achieves interpretable yet more effective visual reasoning. Specifically, PFlowNet decouples perception from reasoning to establish a self-conditioned generation process. Based on this, it integrates multi-dimensional rewards with vicinal geometric shaping via variational reinforcement learning, thereby facilitating reasoning-oriented perceptual behaviors while preserving visual reliability. PFlowNet delivers a provable performance guarantee and competitive empirical results, particularly setting new SOTA records on V* Bench (90.6%) and MME-RealWorld-lite (67.0%).

3D Gaussian Splatting (3DGS) has been widely adopted for scene reconstruction, where training inherently constitutes a highly coupled and non-convex optimization problem. Recent works commonly incorporate geometric priors, such as LiDAR measurements, either for initialization or as training constraints, with the goal of improving photometric reconstruction quality. However, in large-scale outdoor scenarios, such geometric supervision is often spatially incomplete and uneven, which limits its effectiveness as a reliable prior and can even be detrimental to the final reconstruction. To address this challenge, we model partially observable geometry as a continuous energy field induced by geometric evidence and propose EnerGS. Rather than enforcing geometry as a hard constraint, EnerGS provides a soft geometric guidance for the optimization of Gaussian primitives, allowing geometric information to steer the optimization process without directly restricting the solution space. Extensive experiments on large-scale outdoor scenes demonstrate that, under both sparse multi-view and monocular settings, EnerGS consistently improves photometric quality and geometric stability, while effectively mitigating overfitting during 3DGS training.

Landslide susceptibility prediction is critical for geohazard risk assessment and mitigation. Conventional data-driven paradigm achieves high predictive accuracy but require sufficient conditioning factors and large-scale landslide inventories. However, in practical engineering applications across mountainous and plateau regions, data-scarce conditions are commonly observed, where such data requirements are rarely satisfied, rendering conventional data-driven paradigm inapplicable. To address this issue, we propose a knowledge-data dually driven paradigm for accurate landslide susceptibility prediction under data-scarce conditions. The essential idea behind the proposed novel paradigm is the integration of the geomorphic prior knowledge with scarce landslide data. To validate the proposed paradigm, we first applied it to a data-rich region in central Italy, where a conventional data-driven paradigm trained on the full dataset served as the baseline. By utilizing only 30% of the available landslide data, the proposed paradigm achieved comparable predictive accuracy to the baseline, demonstrating its effectiveness under data-scarce conditions. The paradigm was further evaluated in a genuinely data-scarce environment for application, the Qilian Permafrost Region of the Tibetan Plateau, where it also yielded reliable susceptibility predictions, confirming its applicability under data-scarce conditions.

Indoor robot navigation is often compromised by glass surfaces, which severely corrupt depth sensor measurements. While foundation models like Depth Anything 3 provide excellent geometric priors, they lack an absolute metric scale. We propose a training-free framework that leverages depth foundation models as a structural prior, employing a robust local RANSAC-based alignment to fuse it with raw sensor depth. This naturally avoids contamination from erroneous glass measurements and recovers an accurate metric scale. Furthermore, we introduce \ti{GlassRecon}, a novel RGB-D dataset with geometrically derived ground truth for glass regions. Extensive experiments demonstrate that our approach consistently outperforms state-of-the-art baselines, especially under severe sensor depth corruption. The dataset and related code will be released at https://github.com/jarvisyjw/GlassRecon.

We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction, they are inherently limited in capturing motion ambiguity and lack mechanisms to assess prediction reliability. By leveraging the kernel-based probabilistic nature of GPs, our approach introduces three key capabilities: (i) uncertainty quantification for motion predictions, (ii) motion estimation for unobserved or sparsely sampled regions, and (iii) temporal extrapolation beyond observed training frames. To scale GPs to the large number of Gaussian primitives in 4DGS, we design spatio-temporal kernels that capture the correlation structure of deformation fields and adopt variational Gaussian Processes with inducing points for tractable inference. Our experiments show that GP-4DGS enhances reconstruction quality while providing reliable uncertainty estimates that effectively identify regions of high motion ambiguity. By addressing these challenges, our work takes a meaningful step toward bridging probabilistic modeling and neural graphics.

UAVs play an important role in applications such as autonomous exploration, disaster response, and infrastructure inspection. However, UAV VLN in complex 3D environments remains challenging. A key difficulty is the structural representation mismatch between 2D visual perception and the 3D trajectory decision space, which limits spatial reasoning. To this end, we propose SpatialFly, a geometry-guided spatial representation framework for UAV VLN. Operating on RGB observations without explicit 3D reconstruction, SpatialFly introduces a geometry-guided 2D adaptive representation mechanism. Specifically, the geometric prior injection module injects global structural cues into 2D semantic tokens to provide scene-level geometric guidance. The geometry-aware reparameterization module then uses geometry-conditioned cross-modal attention and gated residual fusion to adaptively reparameterize the visual tokens. Experimental results show that SpatialFly consistently outperforms state-of-the-art UAV VLN baselines across both seen and unseen environments, reducing NE by 4.03m and improving SR by 1.27% over the strongest baseline on the unseen Full split. Additional trajectory-level analysis shows that SpatialFly produces trajectories with better path alignment and smoother, more stable motion.