ABSTRACT Surface reconstruction from point clouds with open boundaries and incomplete geometry remains challenging for existing implicit learning methods, as signed distance field and occupancy‐based approaches inherently rely on closed‐surface assumptions and often produce false closures or boundary distortions, while existing unsigned distance field (UDF) methods suffer from unstable optimization, discontinuities near boundaries, and difficulties in reliable surface extraction. To address these issues, this paper proposes an asymptotically consistent surface reconstruction framework based on UDFs for non‐watertight point clouds. The method adopts a fully unsupervised learning strategy, in which a continuous UDF is optimized through a gradient‐guided point projection mechanism combined with geometric and gradient consistency constraints, enabling stable distance estimation without requiring ground‐truth distances or normals. A progressive learning strategy based on high‐confidence projected points is further introduced to alleviate early‐stage instability and improve robustness under sparse sampling and complex topology. In addition, an intersection‐detection‐based isosurface extraction scheme is designed to infer pseudo‐sign information from local gradient configurations, allowing reliable mesh generation using the Marching Cubes algorithm. Extensive experiments demonstrate that the proposed method achieves superior reconstruction accuracy and robustness compared with state‐of‐the‐art methods, particularly in preserving open boundaries, thin‐walled structures, and fractured regions without erroneous infilling.

Surface reconstruction from point clouds has attracted considerable attention in the computer vision community. Most deep learning-based methods focus on modeling signed distance functions (SDFs) and unsigned distance functions (UDFs). However, SDFs are limited to watertight models, and UDFs are non-differentiable at the surface boundary, hindering the learning of smooth representations. In this paper, we introduce a novel method, VFIR, which leverages neural implicit functions to learn vector fields (VFs) for 3D shape modeling. We enhance the network's fitting capability by displacing points along the predicted vector directions, aiming to reduce the deviation between the generated point cloud and the original input. To accelerate convergence, we introduce a progressive learning strategy that incrementally incorporates denser point clouds and corresponding normals during training. For isosurface extraction, we define truncated vector fields (TVFs) that focus computation around surfaces and present an optimized three-state marching cubes (OT-MC) algorithm tailored to the vector field representation. Extensive experiments demonstrate that VFIR achieves state-of-the-art performance with high accuracy and robustness across diverse 3D models, exhibiting strong generalization capabilities and thus representing a promising solution for surface reconstruction across various applications.

ABSTRACT Smooth signed distance surface reconstruction remains a popular technique for generating watertight surfaces from discrete point clouds. However, it frequently encounters issues with geometric detail loss when reconstructing complicated models. In this paper, we introduce a novel reconstruction technique for multi‐scale smooth signed distance surfaces based on Gaussian curvature. Initially, the point cloud data is fitted using the moving least squares to calculate the Gaussian curvature. After that, a curvature‐adaptive octree is constructed based on the Gaussian curvature, which can dynamically adjust the local resolution. Geometric information can be captured more effectively, improving the accuracy of surface reconstruction. Finally, implicit functions are adopted to perform global fitting, and the zero‐level set is obtained through the octree isosurface extraction algorithm. In solving the iterative linear system, multi‐thread techniques are implemented for parallel computation to enhance the execution performance of the algorithm. Experimental results demonstrate that the curvature‐adaptive octree based on Gaussian curvature, can effectively capture complex geometric details, and the algorithm accomplishes high‐precision surface reconstruction at different scales. Furthermore, multi‐thread technology enhances local and global computing performance, ensuring the algorithm's effectiveness in processing large‐scale data.

ABSTRACT Accurate normal estimation is a fundamental task in 3D geometry processing, with wide‐ranging applications in computer vision, robotics, and computer graphics. However, existing globally consistent normal estimation (GCNO) methods are often limited by reduced accuracy and high computational cost when applied to complex models. To address these challenges, we propose a fast and robust point cloud normal estimation method guided by curvature information. The proposed method integrates curvature as a geometric prior into a global winding‐number‐based optimization formulation, effectively enhancing normal orientation consistency while preserving sharp geometric features. Furthermore, to improve computational efficiency, we introduce a PCA‐based visibility‐aware initialization strategy. This strategy adaptively adjusts the initial normal directions by leveraging the local geometric distribution of points, thereby enhancing the consistency of initial normal orientations. Experimental results demonstrate that, compared to the state‐of‐the‐art GCNO method, the proposed approach significantly improves both the accuracy and efficiency of normal estimation. This work provides an effective and precise solution for achieving globally consistent normal estimation in point clouds.

Abstract In computed tomography, the simulation of x‐ray projection is very important for developing and evaluating image reconstruction methods. Currently, the computer aided design models have been used for projection simulation. Compared with the stereolithographic model, the Unigraphics NX (UG) model can describe complex objects with multiple materials. However, calculating the intersection of a ray with a UG model can only be performed by an internal function, which greatly decreases the efficiency of the projection simulation. Therefore, we propose a fast method for projection simulation based on multi‐core. In this method, we use the internal function to calculate the intersection points and the corresponding face normal vectors for a ray. By computing the dot product between the direction vector of the ray and the face normal vectors, we can determine the entry and exit point pairs, and further obtain the simulation projection. On this basis, the projection simulation tasks are evenly decomposed to multiple processes. Then, we invoke these processes by multi‐thread in a main process, and realize parallel implementation of the projection simulation. Numerical experiments demonstrate the accuracy and effectiveness of the method, and we can obtain nearly linear speedup of the multi‐core acceleration.

Summary FDK algorithm is a popular analytical reconstruction method for practical cone‐beam CT scanners. Compared with iterative methods, the FDK algorithm is computationally efficient. However, the reconstruction speed remains a limitation for its application when dealing with high resolution images. In this paper, we propose a fast method for parallel implementation of the FDK algorithm by the use of multi‐GPU. First, we optimize the backprojection operation of FDK according to the property of geometric symmetry and the correlation between adjacent slices. Then, we utilize the multi‐thread technology to realize the parallel implementation of the optimized FDK algorithm on multi‐GPU. Finally, we implement the proposed method on a multi‐GPU platform. Numerical experiment shows that the proposed multi‐GPU‐based approach can reconstruct a 512 cubed volume in 1.9 seconds from 360 projections of resolution 512 ×512, which is 511 times faster than a traditional CPU–based approach and 5 times faster than a single GPU–based approach. In addition, the reconstruction results also indicate that the proposed method can maintain the same precision with traditional method.