L-Tangent Norm: A Low Computational Cost Criterion for Choosing Regularization Weights and its Use for Range Surface Reconstruction

Florent Brunet, Adrien Bartoli, Rémy Malgouyres, Nassir Navab

3D Data Processing, Visualization and Transmission, Atlanta, June 2008

We are interested in fitting a surface model such as a tensor-product spline to range image data. This is commonly done by finding control points which minimize a compound cost including the goodness of fit and a regularizer, balanced by a regularization parameter. Many approaches choose this parameter as the minimizer of, for example, the cross-validation score or the L-curve criterion. Most of these criteria are expensive to compute and difficult to minimize. We propose a novel criterion, the L-tangent norm, which overcomes these drawbacks. It gives sensible results with a much lower computational cost. This new criterion has been successfully tested with synthetic and real range image data.

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