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Regularized quadratic penalty methods for shape from shading. (English) Zbl 06802150
Summary: Shape from shading (SFS) denotes the problem of reconstructing a 3D surface, starting from a single shaded image which represents the surface itself. Minimization techniques are commonly used for solving the SFS problem, where the objective function is a weighted combination of the brightness error, plus one or more terms aiming to obtain a valid solution. We present a regularized quadratic penalty method where quadratic penalization is used to adaptively adjust the smoothing weights, and regularization improves the robustness and reliability of the procedure. A nonmonotone Barzilai-Borwein method is employed to efficiently solve the arising subproblems. Numerical results are provided showing the reliability of the proposed approach.
MSC:
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
65K05 Numerical mathematical programming methods
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