Regularized Least-Squares Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0
This toolbox is for the reconstruction of a surface from its measured gradient field. It is assumed that the gradient field is corrupted by noise, and thereby the package provides algorithms which compute the least-squares solution to the problem, along with various forms of regularization, including:
1) Spectral Regularization
2) Tikhonov Regularization
3) Constrained Regularization (Dirichlet Boundary Values)
4) Weighted Least-Squares
Examples of these types of regularization and how to use the toolbox are given in the accompanying documentation file: g2sIntro.pdf
This toolbox requires the Discrete Orthogonal Polynomial Toolbox (DOPbox):
The theory behind this toolbox is described in the papers:
 Harker, M., O’Leary, P., Regularized Reconstruction of a Surface from its Measured Gradient Field, (preprint available at arxiv.org)
 Harker, M., O’Leary, P., Direct regularized surface reconstruction from gradients for Industrial Photometric Stereo, Computers in Industry, In Press, 2013.
 Harker, M., O’Leary, P., Least squares surface reconstruction from measured gradient fields, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1-7.
 Harker, M., O’Leary, P., Least squares surface reconstruction from gradients: Direct algebraic methods with spectral, Tikhonov, and constrained regularization, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011, pp. 2529-2536.