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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.

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Acknowledgements

We would like to thank the anonymous reviewers for their comments that greatly improve the manuscript. The work is supported by Anhui Center for Applied Mathematics, the NSF of China (No. 11871447), the special project of strategic leading science and technology of CAS (No.XDC08010100), and the National Key Research and Development Program of MOST of China (No. 2018AAA0101001).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, People’s Republic of China

    Jingyao Ke & Zhouwang Yang

  2. CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences, University of Science and Technology of China, Hefei, People’s Republic of China

    Bin Xu

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  1. Jingyao Ke
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Correspondence to Zhouwang Yang.

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Ke, J., Xu, B. & Yang, Z. Area-Preserving Parameterization with Tutte Regularization. Commun. Math. Stat. 11, 727–740 (2023). https://doi.org/10.1007/s40304-021-00271-6

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  • DOI: https://doi.org/10.1007/s40304-021-00271-6

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