Peidong Liu

Global solvers have emerged as a powerful paradigm for 3D vision, offering certifiable solutions to nonconvex geometric optimization problems traditionally addressed by local or heuristic methods. This survey presents the first systematic review of global solvers in geometric vision, unifying the field through a comprehensive taxonomy of three core paradigms: Branch-and-Bound (BnB), Convex Relaxation (CR), and Graduated Non-Convexity (GNC). We present their theoretical foundations, algorithmic designs, and practical enhancements for robustness and scalability, examining how each addresses the fundamental nonconvexity of geometric estimation problems. Our analysis spans ten core vision tasks, from Wahba problem to bundle adjustment, revealing the optimality-robustness-scalability trade-offs that govern solver selection. We identify critical future directions: scaling algorithms while maintaining guarantees, integrating data-driven priors with certifiable optimization, establishing standardized benchmarks, and addressing societal implications for safety-critical deployment. By consolidating theoretical foundations, practical advances, and broader impacts, this survey provides a unified perspective and roadmap toward certifiable, trustworthy perception for real-world applications. A continuously-updated literature summary and companion code tutorials are available at https://github.com/ericzzj1989/Awesome-Global-Solvers-for-3D-Vision.

Recent vision-language-action (VLA) models can generate plausible end-effector motions, yet they often fail in long-horizon, contact-rich tasks because the underlying hand-object interaction (HOI) structure is not explicitly represented. An embodiment-agnostic interaction representation that captures this structure would make manipulation behaviors easier to validate and transfer across robots. We propose FlowHOI, a two-stage flow-matching framework that generates semantically grounded, temporally coherent HOI sequences, comprising hand poses, object poses, and hand-object contact states, conditioned on an egocentric observation, a language instruction, and a 3D Gaussian splatting (3DGS) scene reconstruction. We decouple geometry-centric grasping from semantics-centric manipulation, conditioning the latter on compact 3D scene tokens and employing a motion-text alignment loss to semantically ground the generated interactions in both the physical scene layout and the language instruction. To address the scarcity of high-fidelity HOI supervision, we introduce a reconstruction pipeline that recovers aligned hand-object trajectories and meshes from large-scale egocentric videos, yielding an HOI prior for robust generation. Across the GRAB and HOT3D benchmarks, FlowHOI achieves the highest action recognition accuracy and a 1.7$\times$ higher physics simulation success rate than the strongest diffusion-based baseline, while delivering a 40$\times$ inference speedup. We further demonstrate real-robot execution on four dexterous manipulation tasks, illustrating the feasibility of retargeting generated HOI representations to real-robot execution pipelines.

The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems typically follow a predictor-corrector (PC) structure, but rely on hand-crafted heuristics for step sizes and iteration termination, which are often suboptimal and task-specific. To address this, we unify these problems under a single framework, which enables the design of a general neural solver. Building on this unified view, we propose Neural Predictor-Corrector (NPC), which replaces hand-crafted heuristics with automatically learned policies. NPC formulates policy selection as a sequential decision-making problem and leverages reinforcement learning to automatically discover efficient strategies. To further enhance generalization, we introduce an amortized training mechanism, enabling one-time offline training for a class of problems and efficient online inference on new instances. Experiments on four representative homotopy problems demonstrate that our method generalizes effectively to unseen instances. It consistently outperforms classical and specialized baselines in efficiency while demonstrating superior stability across tasks, highlighting the value of unifying homotopy methods into a single neural framework.

Emerging 3D scene representations, such as Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS), have demonstrated their effectiveness in Simultaneous Localization and Mapping (SLAM) for photo-realistic rendering, particularly when using high-quality video sequences as input. However, existing methods struggle with motion-blurred frames, which are common in real-world scenarios like low-light or long-exposure conditions. This often results in a significant reduction in both camera localization accuracy and map reconstruction quality. To address this challenge, we propose a dense visual SLAM pipeline (i.e., MBA-SLAM) to handle severe motion-blurred inputs. Our approach integrates an efficient motion blur-aware tracker with either neural radiance fields or Gaussian Splatting based mapper. By accurately modeling the physical image formation process of motion-blurred images, our method simultaneously learns 3D scene representation and estimates the cameras’ local trajectory during exposure time, enabling proactive compensation for motion blur caused by camera movement. In our experiments, we demonstrate that MBA-SLAM surpasses previous state-of-the-art methods in both camera localization and map reconstruction, showcasing superior performance across a range of datasets, including synthetic and real datasets featuring sharp images as well as those affected by motion blur, highlighting the versatility and robustness of our approach.

Existing micro aerial vehicle (MAV) detection methods mainly rely on the target's appearance features in RGB images, whose diversity makes it difficult to achieve generalized MAV detection. We notice that different types of MAVs share the same distinctive features in event streams due to their high-speed rotating propellers, which are hard to see in RGB images. This letter studies how to detect different types of MAVs from an event camera by fully exploiting the features of propellers in the original event stream. The proposed method consists of three modules to extract the salient and spatio-temporal features of the propellers while filtering out noise from background objects and camera motion. Since there are no existing event-based MAV datasets, we introduce a novel MAV dataset for the community. This is the first event-based MAV dataset comprising multiple scenarios and different types of MAVs. Without training, our method significantly outperforms state-of-the-art methods and can deal with challenging scenarios, achieving a precision rate of 83.0% (+30.3%) and a recall rate of 81.5% (+36.4%) on the proposed testing dataset.

We present VicaSplat, a novel framework for joint 3D Gaussians reconstruction and camera pose estimation from a sequence of unposed video frames, which is a critical yet underexplored task in real-world 3D applications. The core of our method lies in a novel transformer-based network architecture. In particular, our model starts with an image encoder that maps each image to a list of visual tokens. All visual tokens are concatenated with additional inserted learnable camera tokens. The obtained tokens then fully communicate with each other within a tailored transformer decoder. The camera tokens causally aggregate features from visual tokens of different views, and further modulate them frame-wisely to inject view-dependent features. 3D Gaussian splats and camera pose parameters can then be estimated via different prediction heads. Experiments show that VicaSplat surpasses baseline methods for multi-view inputs, and achieves comparable performance to prior two-view approaches. Remarkably, VicaSplat also demonstrates exceptional cross-dataset generalization capability on the ScanNet benchmark, achieving superior performance without any fine-tuning. Project page: https://lizhiqi49.github.io/VicaSplat.

In this paper, we explore the potential of Snapshot Compressive Imaging (SCI) technique for recovering the underlying 3D scene structure from a single temporal compressed image. SCI is a cost-effective method that enables the recording of high-dimensional data, such as hyperspectral or temporal information, into a single image using low-cost 2D imaging sensors. To achieve this, a series of specially designed 2D masks are usually employed, reducing storage and transmission requirements and offering potential privacy protection. Inspired by this, we take one step further to recover the encoded 3D scene information leveraging powerful 3D scene representation capabilities of neural radiance fields (NeRF). Specifically, we propose SCINeRF, in which we formulate the physical imaging process of SCI as part of the training of NeRF, allowing us to exploit its impressive performance in capturing complex scene structures. In addition, we further integrate the popular 3D Gaussian Splatting (3DGS) framework and propose SCISplat to improve 3D scene reconstruction quality and training/rendering speed by explicitly optimizing point clouds into 3D Gaussian representations. To assess the effectiveness of our method, we conduct extensive evaluations using both synthetic data and real data captured by our SCI system. Experimental results demonstrate that our proposed approach surpasses the state-of-the-art methods in terms of image reconstruction and novel view synthesis. Moreover, our method also exhibits the ability to render high frame-rate multi-view consistent images in real time by leveraging SCI and the rendering capabilities of 3DGS. Codes will be available at: https://github.com/WU- CVGL/SCISplat.