Surface Reconstruction from 2D Gradient Domain with Fast Poisson Equation Solver

Surface reconstruction from the 2D gradient domain involves a fast Poisson equation solver as its computational core. This technique recovers surface geometry by leveraging gradient information between adjacent pixels, where the gradient field serves as input to reconstruct the underlying surface through Poisson-based integration. The algorithm typically implements discrete gradient operators and solves the resulting Poisson system using efficient numerical methods like multigrid solvers or Fast Fourier Transform (FFT)-based approaches. Key computational steps include constructing the divergence field from input gradients and solving the Poisson equation ∇²z = ∇·G, where G represents the gradient field and z denotes the reconstructed surface height. This methodology finds extensive applications in computer graphics for height field reconstruction, virtual reality environments, and game development for terrain generation. Additionally, it serves medical imaging applications for 3D organ reconstruction and facilitates 3D printing through surface normalization. The implementation often utilizes sparse linear algebra libraries for efficient matrix operations and may incorporate boundary condition handlers for practical scenarios. With its computational efficiency and mathematical robustness, this approach presents broad practical prospects across multiple technical domains.