Shape from gradient fields using kernel Poisson equation

Shape from gradient fields is a traditional issue in image processing and computer vision fields, and is also the final step for many applications. Most methods convert the problem to Poisson equation and project the original data to another space like Fourier and Discrete Cosine Domain. In this paper we propose a kernel method to solve Poisson equation. By converting the traditional Poisson equation to its kernel representation form, the underlying surface can be recovered by least squares. With further considering an even extension of the original gradient field, Gram matrix becomes balanced and the recovered surface will not oscillate at boundary. The special processing of boundary assumes a Neumann boundary condition instead of Dietrich boundary, which is more useful in practical situation. The experimental results validate the superiority of the proposed method over existing ones.