Area-Preserving Parameterization with Tutte Regularization

Jingyao Ke , Bin Xu , Zhouwang Yang

Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 727 -740.

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Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 727 -740. DOI: 10.1007/s40304-021-00271-6
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Area-Preserving Parameterization with Tutte Regularization

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Abstract

Area-preserving parameterization is now widely applied, such as for remeshing and medical image processing. We propose an efficient and stable approach to compute area-preserving parameterization on simply connected open surfaces. From an initial parameterization, we construct an objective function of energy. This consists of an area distortion measure and a new regularization, termed as the Tutte regularization, combined into an optimization problem with sliding boundary constraints. The original area-preserving problem is decomposed into a series of subproblems to linearize the boundary constraints. We design an iteration framework based on the augmented Lagrange method to solve each linear constrained subproblem. Our method generates a high-quality parameterization with area-preserving on facets. The experimental results demonstrate the efficacy of the designed framework and the Tutte regularization for achieving a fine parameterization.

Keywords

Surface parameterization / Area-preserving parameterization / Tutte embedding / Simply connected open surfaces

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Jingyao Ke, Bin Xu, Zhouwang Yang. Area-Preserving Parameterization with Tutte Regularization. Communications in Mathematics and Statistics, 2023, 11(4): 727-740 DOI:10.1007/s40304-021-00271-6

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