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This paper introduces a new approach for generating globally consistent normals for point clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) field generated by a point cloud with globally consistent normals is a solution to a PDE with jump boundary conditions and possesses harmonic properties, and the Dirichlet energy of the GWN field can be defined as an integral over the boundary surface, we formulate a boundary energy derived from the Dirichlet energy of the GWN. Taking as input a point cloud with randomly oriented normals, we optimize this energy to restore the global harmonicity of the GWN field, thereby recovering the globally consistent normals. Experiments show that our method outperforms state-of-the-art approaches, exhibiting enhanced robustness to noise, outliers, complex topologies, and thin structures. Our code can be found at \url{https://github.com/liuweizhou319/BIM}., Comment: accepted in siggraph2024

This paper presents a new method, Diffusing Winding Gradients (DWG), for reconstructing watertight 3D surfaces from unoriented point clouds. Our method exploits the alignment between the gradients of the generalized winding number (GWN) field and globally consistent normals to orient points effectively. Starting with an unoriented point cloud, DWG initially assigns a random normal to each point. It computes the corresponding GWN field and extract a level set whose iso-value is the average GWN values across all input points. The gradients of this level set are then utilized to update the point normals. This cycle of recomputing the GWN field and updating point normals is repeated until the GWN level sets stabilize and their gradients cease to change. Unlike conventional methods, our method does not rely on solving linear systems or optimizing objective functions, which simplifies its implementation and enhances its suitability for efficient parallel execution. Experimental results demonstrate that our method significantly outperforms existing methods in terms of runtime performance. For large-scale models with 10 to 20 million points, our CUDA implementation on an NVIDIA GTX 4090 GPU achieves speeds 30-120 times faster than iPSR, the leading sequential method, tested on a high-end PC with an Intel i9 CPU. Additionally, by employing a screened variant of GWN, DWG demonstrates enhanced robustness against noise and outliers, and proves effective for models with thin structures and real-world inputs with overlapping and misaligned scans. For source code and more details, visit our project webpage: https://dwgtech.github.io/.

Traditional sign language teaching methods face challenges such as limited feedback and diverse learning scenarios. Although 2D resources lack real-time feedback, classroom teaching is constrained by a scarcity of teacher. Methods based on VR and AR have relatively primitive interaction feedback mechanisms. This study proposes an innovative teaching model that uses real-time monocular vision and mixed reality technology. First, we introduce an improved hand-posture reconstruction method to achieve sign language semantic retention and real-time feedback. Second, a ternary system evaluation algorithm is proposed for a comprehensive assessment, maintaining good consistency with experts in sign language. Furthermore, we use mixed reality technology to construct a scenario-based 3D sign language classroom and explore the user experience of scenario teaching. Overall, this paper presents a novel teaching method that provides an immersive learning experience, advanced posture reconstruction, and precise feedback, achieving positive feedback on user experience and learning effectiveness., Comment: 8 pages, 6 figures