The variational approach to shape from shading
Computer Vision, Graphics, and Image Processing
A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Computer Vision: Three-Dimensional Data from Images
Computer Vision: Three-Dimensional Data from Images
Reconstructing discontinuous surfaces from a given gradient field using partial integrability
Computer Vision and Image Understanding
Shapelets Correlated with Surface Normals Produce Surfaces
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Optimal Reconstruction of Approximate Planar Surfaces Using Photometric Stereo
IEEE Transactions on Pattern Analysis and Machine Intelligence
A graph-spectral method for surface height recovery
Pattern Recognition
Surface-from-Gradients without Discrete Integrability Enforcement: A Gaussian Kernel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
What is the range of surface reconstructions from a gradient field?
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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This paper addresses the issue of regularization in the surface reconstruction from gradients problem in Industrial Photometric Stereo. Regularization of the solution is a necessary step in an industrial environment, where algorithms must cope with non-Gaussian noise, such as outliers, or non-Lambertian textures such as corrosion. Introducing Tikhonov regularization into the global least squares solution suppresses the influence of outliers in the reconstruction. Viable methods should both minimize a global least squares cost function and also introduce some form of regularization into the solution; state-of-the-art methods to this end are grossly inefficient and are severely limited in the size of surface they can reconstruct. We present a new algorithm which can reconstruct a surface of 1200x1200, (i.e., greater than 1M-pixel) in a few seconds. This is orders of magnitude faster than state-of-the-art methods incorporating regularization, and hence presents the first method viable for regularized reconstructions in practical applications.