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):
http://www.mathworks.com/matlabcentral/fileexchange/41250

The theory behind this toolbox is described in the papers:
[1] Harker, M., O’Leary, P., Regularized Reconstruction of a Surface from its Measured Gradient Field, (preprint available at arxiv.org)
[2] Harker, M., O’Leary, P., Direct regularized surface reconstruction from gradients for Industrial Photometric Stereo, Computers in Industry, In Press, 2013.
http://dx.doi.org/10.1016/j.compind.2013.03.013

See also:
[3] 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.
http://dx.doi.org/10.1109/CVPR.2008.4587414
[4] 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.
http://dx.doi.org/10.1109/CVPR.2011.5995427