Organizations: Department of Computer Science and Business Systems, Gargi Memorial Institute of Technology, Baruipur, Kolkata, West Bengal 700144, India · Computer and Informatics Group, Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata, West Bengal 700064, India · Engineering Sciences, Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai, Maharashtra 400094, India
Key part of robotics, augmented reality, and digital inspection is dense 3D reconstruction from depth observations. Traditional volumetric fusion techniques, including truncated signed distance functions (TSDF), enable efficient and deterministic geometry reconstruction; however, they depend on heuristic weighting and fail to transparently convey uncertainty in a systematic way. Recent neural implicit methods, on the other hand, get very high fidelity but usually need a lot of GPU power for optimization and aren't very easy to understand for making decisions later on. This work presents BayesFusion-SDF, a CPU-centric probabilistic signed distance fusion framework that conceptualizes geometry as a sparse Gaussian random field with a defined posterior distribution over voxel distances. First, a rough TSDF reconstruction is used to create an adaptive narrow-band domain. Then, depth observations are combined using a heteroscedastic Bayesian formulation that is solved using sparse linear algebra and preconditioned conjugate gradients. Randomized diagonal estimators are a quick way to get an idea of posterior uncertainty. This makes it possible to extract surfaces and plan the next best view while taking into account uncertainty. Tests on a controlled ablation scene and a CO3D object sequence show that the new method is more accurate geometrically than TSDF baselines and gives useful estimates of uncertainty for active sensing. The proposed formulation provides a clear and easy-to-use alternative to GPU-heavy neural reconstruction methods while still being able to be understood in a probabilistic way and acting in a predictable way. GitHub: https://mazumdarsoumya.github.io/BayesFusionSDF
Figures & tables
Aspect
Traditional TSDF Fusion
Neural Implicit Reconstruction
Proposed Probabilistic SDF (BayesFusion)
Representation
Discrete voxel SDF
Continuous neural field
Probabilistic voxel SDF (GRF)
Computation
CPU/GPU, real-time feasible
GPU, training-intensive
CPU-first sparse linear algebra
Uncertainty Estimation
Heuristic weights
Limited / indirect
Explicit posterior variance
Determinism
High
Optimization-dependent
High (solver-based)
Training Requirement
None
Required
None
Scalability
Good with sparse structures
Heavy for large scenes
Sparse hierarchical domain
Table 1: Comparison of representative dense reconstruction paradigms.
Multi-view surface reconstruction is a core problem in computer vision. One prominent line of work represents the surface implicitly as a signed distance field (SDF), optimizing it based on the photometric loss between rendered and observed pixel colors. These approaches typically employ SDF-based volume rendering to obtain a differentiable relaxation of discontinuous visibility along rays, thereby reducing reliance on silhouette supervision. In this paper, we reformulate SDF-based volume rendering as probabilistic surface rendering, where each pixel color is modeled as a mixture distribution induced by the random first ray-surface intersection. To this end, we introduce Stochastic Signed Distance Processes (SSDP), which model the SDF along each ray as a stochastic process, inducing a first-passage-time distribution for each ray. We then derive the first-passage probability for each sampling interval based on Bayesian filtering, together with its practical approximation for parallel rendering. We further show that NeuS, an existing SDF-based volume rendering method, arises as a special case of our formulation. Experiments on the DTU and MobileBrick datasets demonstrate that our method outperforms baselines in both surface reconstruction and uncertainty quantification, supporting the effectiveness of our first-passage formulation. Our code is available at https://github.com/skmhrk1209/SSDP.
Hiroki Sakuma, Masatoshi Okutomi
Department of Systems and Control Engineering Institute of Science Tokyo
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.
Zhirui Dai, Qihao Qian, Tianxing Fan +1
Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093, USA
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.
Laura Fink, Linus Franke, George Kopanas +2
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Inria, Université Côte d’Azur, France · Google DeepMind, UK