Signed Distance Functions

We propose a feed-forward method for dense Signed Distance Field (SDF) regression from unstructured image collections in less than three seconds, without camera calibration or post-hoc fusion. Our key insight is that the intermediate feature space of pretrained multi-view feed-forward geometry transformers already encodes a powerful joint world representation; yet, existing pipelines discard it, routing features through per-view prediction heads before assembling 3D geometry post-hoc, which discards valuable completeness information and accumulates inaccuracies. We instead perform 3D extraction directly from geometry transformer features via learned volumetric extraction: voxelized canonical embeddings that progressively absorb multi-view geometry information through interleaved cross- and self-attention into a structured volumetric latent grid. A simple convolutional decoder then maps this grid to a dense SDF. We additionally propose a scalable, validity-aware supervision scheme directly using SDFs derived from depth maps or 3D assets, tackling practical issues like non-watertight meshes. Our approach yields complete and well-defined distance values across sparse- and dense-view settings and demonstrates geometrically plausible completions. Code and further material can be found at https://lorafib.github.io/fus3d.

Effective robot autonomy requires motion generation that is safe, feasible, and reactive. Current methods are fragmented: fast planners output physically unexecutable trajectories, reactive controllers struggle with high-fidelity perception, and existing solvers fail on high-DoF systems. We present cuRoboV2, a unified framework with three key innovations: (1) B-spline trajectory optimization that enforces smoothness and torque limits; (2) a GPU-native TSDF/ESDF perception pipeline that generates dense signed distance fields covering the full workspace, unlike existing methods that only provide distances within sparsely allocated blocks, up to 10x faster and in 8x less memory than the state-of-the-art at manipulation scale, with up to 99% collision recall; and (3) scalable GPU-native whole-body computation, namely topology-aware kinematics, differentiable inverse dynamics, and map-reduce self-collision, that achieves up to 61x speedup while also extending to high-DoF humanoids (where previous GPU implementations fail). On benchmarks, cuRoboV2 achieves 99.7% success under 3kg payload (where baselines achieve only 72--77%), 99.6% collision-free IK on a 48-DoF humanoid (where prior methods fail entirely), and 89.5% retargeting constraint satisfaction (vs. 61% for PyRoki); these collision-free motions yield locomotion policies with 21% lower tracking error than PyRoki and 12x lower cross-seed variance than GMR. A ground-up codebase redesign for discoverability enabled LLM coding assistants to author up to 73% of new modules, including hand-optimized CUDA kernels, demonstrating that well-structured robotics code can unlock productive human-LLM collaboration. Together, these advances provide a unified, dynamics-aware motion generation stack that scales from single-arm manipulators to full humanoids. Code is available at https://github.com/NVlabs/curobo.

Neural implicit surface reconstruction with signed distance function has made significant progress, but recovering fine details such as thin structures and complex geometries remains challenging due to unreliable or noisy geometric priors. Existing approaches rely on implicit uncertainty that arises during optimization to filter these priors, which is indirect and inefficient, and masking supervision in high-uncertainty regions further leads to under-constrained optimization. To address these issues, we propose GPU-SDF, a neural implicit framework for indoor surface reconstruction that leverages geometric prior uncertainty and complementary constraints. We introduce a self-supervised module that explicitly estimates prior uncertainty without auxiliary networks. Based on this estimation, we design an uncertainty-guided loss that modulates prior influence rather than discarding it, thereby retaining weak but informative cues. To address regions with high prior uncertainty, GPU-SDF further incorporates two complementary constraints: an edge distance field that strengthens boundary supervision and a multi-view consistency regularization that enforces geometric coherence. Extensive experiments confirm that GPU-SDF improves the reconstruction of fine details and serves as a plug-and-play enhancement for existing frameworks. Source code will be available at https://github.com/IRMVLab/GPU-SDF

Ensuring safe robot operation in cluttered and dynamic environments remains a fundamental challenge. While control barrier functions (CBFs) provide an effective framework for real-time safety filtering, their performance critically depends on the underlying geometric representation, which is often simplified, leading to either overly conservative behavior or insufficient collision coverage. Superquadrics (SQs) offer an expressive way to model complex shapes using a few primitives and are increasingly used for robot safety. To integrate this representation into CBF, most existing approaches directly use their implicit functions as barrier candidates. However, we identify a critical but overlooked issue in this practice: the gradients of the implicit SQ function can become severely ill-conditioned, potentially rendering the optimization infeasible and undermining reliable safety filtering. To address this issue, we formulate an SQ-based safety filter that uses signed distance functions (SDFs) as barrier candidates. Since analytical SDFs are unavailable for general SQs, we compute the distance using the efficient Gilbert-Johnson-Keerthi algorithm and derive its gradient in closed form. Extensive simulation and real-world experiments demonstrate consistent collision-free manipulation in cluttered scenes, showing robustness to challenging geometries, sensing noise, and dynamic disturbances, while improving task efficiency in teleoperation tasks. These results highlight a pathway toward safety filters that remain precise and reliable under the geometric complexity of real-world environments.

Extracting an explicit surface that exactly matches the zero-level set of a neural signed distance function (SDF) remains challenging. Sampling-based isosurfacing methods such as Marching Cubes introduce discretization error. In contrast, continuous piecewise affine (CPWA) analytic approaches typically require plain ReLU MLPs, which limits the ability to learn high-frequency SDFs in practice. We present TetraSDF, an analytic isosurface extraction framework for SDFs that retains the expressiveness of grid-based encoders while enabling exact zero-level set extraction, by representing the SDF with a ReLU MLP composed with a multi-resolution tetrahedral positional encoder. Our positional encoder's barycentric interpolation preserves a global CPWA structure, allowing us to track ReLU linear regions within an encoder-induced polyhedral complex. We further introduce a fixed analytic input preconditioner derived from the encoder's metric to reduce directional bias, thereby stabilizing training. Across multiple benchmarks, TetraSDF matches or surpasses existing grid-based encoders in SDF reconstruction accuracy, while faithfully recovering the network's zero-level set as a triangle mesh.

Reconstructing signed distance functions (SDFs) from point cloud data benefits many robot autonomy capabilities, including localization, mapping, motion planning, and control. Methods that support online and large-scale SDF reconstruction often rely on discrete volumetric data structures, which affects the continuity and differentiability of the SDF estimates. Neural network methods have demonstrated high-fidelity differentiable SDF reconstruction but they tend to be less efficient, experience catastrophic forgetting and memory limitations in large environments, and are often restricted to truncated SDF. This work proposes OREN, a hybrid method that combines an explicit prior from octree interpolation with an implicit residual from neural network regression. Our method achieves non-truncated (Euclidean) SDF reconstruction with computational and memory efficiency comparable to volumetric methods and differentiability and accuracy comparable to neural network methods. Extensive experiments demonstrate that OREN outperforms the state of the art in terms of accuracy and efficiency, providing a scalable solution for downstream tasks in robotics and computer vision.

Accurate segmentation of vascular networks from sparse CT scan slices remains a significant challenge in medical imaging, particularly due to the thin, branching nature of vessels and the inherent sparsity between imaging planes. Existing deep learning approaches, based on binary voxel classification, often struggle with structural continuity and geometric fidelity. To address this challenge, we present VesselSDF, a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction. Our method reformulates vessel segmentation as a continuous SDF regression problem, where each point in the volume is represented by its signed distance to the nearest vessel surface. This continuous representation inherently captures the smooth, tubular geometry of blood vessels and their branching patterns. We obtain accurate vessel reconstructions while eliminating common SDF artifacts such as floating segments, thanks to our adaptive Gaussian regularizer which ensures smoothness in regions far from vessel surfaces while producing precise geometry near the surface boundaries. Our experimental results demonstrate that VesselSDF significantly outperforms existing methods and preserves vessel geometry and connectivity, enabling more reliable vascular analysis in clinical settings.

High-fidelity surface reconstruction from multi-view images is a core problem in 3D computer vision. While neural implicit surfaces like SDFs offer smooth geometry, they are often bottlenecked by the computational intensity of volume rendering. Conversely, 3D Gaussian Splatting (3DGS) provides rapid training but lacks geometry continuity, often leading to fragmented surfaces. This paper presents a novel framework that integrates Signed Distance Fields directly into the splatting pipeline. By leveraging the continuous nature of SDFs to regularize Gaussian primitives, our method effectively fills geometric holes and suppresses noise inherent in sparse point clouds. Unlike hybrid approaches that rely on heavy volumetric sampling, our approach utilizes the efficiency of splatting to achieve faster convergence. Extensive evaluations demonstrate that our method produces high-quality surfaces with significantly fewer primitives, offering a more compact and efficient representation for both indoor and outdoor environments.