Tobias Martin, Pushkar Joshi, Miklós Bergou and Nathan Carr Efficient Non-linear Optimization via Multi-scale Gradient Filtering Computer Graphics Forum 32
We present a method for accelerating the convergence of continuous nonlinear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyze this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace-Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized in order to arrive at a solution that is optimal across multiple scales.
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