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<p>3D mesh-based multi-resolution transformation and encoding compression are crucial in 3D reconstruction, with applications spanning medical image processing, 3D scene rendering, and neural radiation fields. Subdivision surfaces, especially Catmull–Clark subdivision, provide powerful geometric representation capabilities for free-form surfaces. However, challenges remain in the efficient editing, rendering, and display of large-scale model datasets. This paper introduces a novel framework for the biorthogonal Catmull–Clark subdivision wavelet (HBSW) based on C-B splines and progressive interpolation. This framework uniformly represents five types of subdivision wavelets, enabling high-precision multi-resolution representation of quadratic surfaces. Specifically, it reduces the mean variance of sphere and ellipsoid models by 15.37 times and 8.55 times, respectively. Meanwhile, HBSW can preserve the sharp geometric features of free-form surfaces with arbitrary topologies, improving the 3D coding compression rate by 7.75% and increasing the PSNR by 1.64%. In addition, this method shortens the wavelet transform time, reducing the model encoding and decoding times by 1.14% and 4.27%, respectively. Experiments show that HBSW outperforms existing methods in terms of 3D coding compression rate, encoding-decoding efficiency, and model transformation quality and is expected to become a powerful tool for various 3D modeling applications. The source code for calculating the orthogonalization coefficients described in this paper is available at <i>https://github.com/guohy2005/orthogonalCoeff-HBSW</i>.</p>

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Enhanced biorthogonal wavelet transform via Catmull–Clark subdivision for efficient 3D modeling

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Huayuan Guo,
  • Weiyang Liu,
  • Ping Hu,
  • MinShi Kang,
  • Hongcheng Tian,
  • Kunlun He

摘要

3D mesh-based multi-resolution transformation and encoding compression are crucial in 3D reconstruction, with applications spanning medical image processing, 3D scene rendering, and neural radiation fields. Subdivision surfaces, especially Catmull–Clark subdivision, provide powerful geometric representation capabilities for free-form surfaces. However, challenges remain in the efficient editing, rendering, and display of large-scale model datasets. This paper introduces a novel framework for the biorthogonal Catmull–Clark subdivision wavelet (HBSW) based on C-B splines and progressive interpolation. This framework uniformly represents five types of subdivision wavelets, enabling high-precision multi-resolution representation of quadratic surfaces. Specifically, it reduces the mean variance of sphere and ellipsoid models by 15.37 times and 8.55 times, respectively. Meanwhile, HBSW can preserve the sharp geometric features of free-form surfaces with arbitrary topologies, improving the 3D coding compression rate by 7.75% and increasing the PSNR by 1.64%. In addition, this method shortens the wavelet transform time, reducing the model encoding and decoding times by 1.14% and 4.27%, respectively. Experiments show that HBSW outperforms existing methods in terms of 3D coding compression rate, encoding-decoding efficiency, and model transformation quality and is expected to become a powerful tool for various 3D modeling applications. The source code for calculating the orthogonalization coefficients described in this paper is available at https://github.com/guohy2005/orthogonalCoeff-HBSW.