Poisson Surface Reconstruction
đź“ś Abstract
This paper describes a new algorithm for surface reconstruction from oriented points. The method solves for an implicit function whose gradient best matches the input point normals, and produces the zero set of the function as the output surface. The technique computes an approximate indicator function from which the gradient is computed, and a regularized solution is obtained using a multigrid solver on an adaptive octree grid. We observe that the problem setting and solution bear strong resemblance to the problem of determining electrostatic potential from discrete samples of charged particles. To address computational efficiency, the algorithm is organized as a stream-processing pipeline, requiring just a few bits to represent each octree node. The algorithm can handle very large data sets and scales to millions of points provided the input is well-conditioned.
✨ Summary
The paper titled “Poisson Surface Reconstruction” by Michael Kazhdan, Matthew Bolitho, and Hugues Hoppe presents a novel algorithm for reconstructing surfaces from oriented points. The work was initially presented at the Symposium on Geometry Processing in July 2006 and addresses the challenge of surface reconstruction by defining an implicit function whose gradient resembles the input point normals. The researchers apply the Poisson problem, closely related to how electrostatic potentials are determined from discrete samples, allowing effective surface reconstruction through an adaptive octree grid.
The algorithm’s strength lies in its ability to handle large datasets, scaling to millions of points efficiently. It introduces a regularized approach using a multigrid solver, significantly optimizing the solution process and computational requirements by employing a stream-processing pipeline.
Subsequent research has frequently cited this method due to its robust performance in 3D scanning technologies and graphics applications. For example, it significantly impacts how 3D models are generated from real-world scanning data, as evident in successive works that emphasize efficient and accurate modeling (Geometric Modeling in Computer Graphics, High-Quality Surface Reconstruction with Depth Maps). The algorithm’s adaptability to varied applications, such as in mesh generation and computational geometry, further underscores its influence. Notably, it has been integrated into popular software tools used for 3D reconstruction and computer graphics, supporting applications ranging from cultural heritage preservation to animations and gaming.