As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting (TeT-Splatting), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously.

Reconstructing hand-held objects from a single RGB image is an important and challenging problem. Existing works utilizing Signed Distance Fields (SDF) reveal limitations in comprehensively capturing the complex hand-object interactions, since SDF is only reliable within the proximity of the target, and hence, infeasible to simultaneously encode local hand and object cues. To address this issue, we propose DDF-HO, a novel approach leveraging Directed Distance Field (DDF) as the shape representation. Unlike SDF, DDF maps a ray in 3D space, consisting of an origin and a direction, to corresponding DDF values, including a binary visibility signal determining whether the ray intersects the objects and a distance value measuring the distance from origin to target in the given direction. We randomly sample multiple rays and collect local to global geometric features for them by introducing a novel 2D ray-based feature aggregation scheme and a 3D intersection-aware hand pose embedding, combining 2D-3D features to model hand-object interactions. Extensive experiments on synthetic and real-world datasets demonstrate that DDF-HO consistently outperforms all baseline methods by a large margin, especially under Chamfer Distance, with about 80% leap forward. Codes are available at https://github.com/ZhangCYG/DDFHO.

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces.

Published in IEEE Robotics and Automation Letters, vol. Abstract-- This paper presents a new approach for 6DoF Direct LiDAR-Inertial Odometry (D-LIO) based on the simultaneous mapping of truncated distance fields on CPU. Such continuous representation (in the vicinity of the points) enables working with raw 3D LiDAR data online, avoiding the need of LiDAR feature selection and tracking, simplifying the odometry pipeline and easily generalizing to many scenarios. The method is based on the proposed Fast Truncated Distance Field (Fast-TDF) method as a convenient tool to represent the environment, employing binary masks that encodes the L1 distance. Such representation enables i) solving the LiDAR point-cloud registration as a nonlinear optimization process without the need of selecting/tracking LiDAR features in the input data, ii) simultaneously producing an accurate truncated distance field map of the environment, and iii) updating such map at constant time independently of its size. The approach is tested using open datasets, aerial and ground. It is also benchmarked against other state-of-the-art odometry approaches, demonstrating the same or better level of accuracy with the added value of an online-generated TDF representation of the environment, that can be used for other robotics tasks as planning or collision avoidance. Accurate vehicle localization is a crucial aspect of robotics, directly influencing autonomous navigation, remote exploration, and other advanced applications. V arious techniques are employed to improve localization, combining data from different sensors such as cameras, inertial measurement units (IMUs), LiDAR and radar [1].

Lifting convolution operators to 3D (3DCNNs) seems like a plausible and promising next step.

Li Zhang (lizhangfd@fudan.edu.cn) is the corresponding author. To further increase efficiency, we include a pre-filtering process to remove nearly transparent tetrahedra, reducing the number of tetrahedra necessary for splatting.

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape.

We thank all reviewers for their useful feedback. Reviewers acknowledge that NDFs are "well founded", "simple and general, which promises wider applicability"[ There is no evidence that it should work competitively on all classes together. We find that NDF outperforms all baselines. "Is there a test/train split, and are quantitative statistics provided on the test We follow the suggestion and added training time. We also transferred key information into the main paper.

We find that transparent and opaque surfaces align with the non-negative local minima and the zero iso-surface, respectively, in the learned distance field of NeuS. Traditional iso-surfacing extraction algorithms, such as marching cubes, which rely on fixed iso-values, are ill-suited for such data. We develop a method to extract the transparent and opaque surface simultaneously based on DCUDF.