基于张量积B样条的几何模型EMD算法及其应用

周财进,陈发来

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6) : 941-953.

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系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6) : 941-953. DOI: 10.12341/jssms13902
论文

基于张量积B样条的几何模型EMD算法及其应用

    周财进,陈发来
作者信息 +

EMD Algorithm of Geometric Models and Its Applications Based on Tensor Product B-Spline

    ZHOU Caijin ,CHEN Falai
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文章历史 +

摘要

经验模态分解(empirical mode decomposition, 简称EMD)算法是一种处理非线性非平稳信号的时频分析方法. 文章针对拓扑同胚于圆盘的开网格模型提出几何模型上的EMD算法, 并应用于网格去噪以及特征编辑. 首先, 借助曲面上离散高斯曲率提取模型的极值点, 随后对模型进行平面参数化, 利用均匀节点的三次张量积B样条计算极大和极小包络曲面, 最后将平均包络曲面离散成网格模型作为分解一次的残差模型, 并将原模型与残差模型的差值向量记为当前分解的偏置向量, 迭代地处理残差模型得到模型各个层次的偏置向量以及最终表示原模型基本形状的残差模型. 通过对偏置向量的处理与重构, 实现算法在网格去噪以及特征编辑的应用. 实验结果表明, 文章算法可以有效地实现网格模型的多尺度分解, 并在网格去噪以及特征编辑方面取得了较好的效果.

Abstract

Empirical mode decomposition (EMD) algorithm is a time-frequency analysis method to process non-linear and non-stationary signals. We proposed an EMD analogous algorithm for three-dimensional surface model which is topologically homeomorphic to a disk and applied the algorithm in mesh denoising and feature editing. First, the extreme points of the model are extracted according to the discrete gaussian curvature. Second, with the help of planar parameterization, the maximum envelope and minimum envelope are calculated by fitting extreme points with an uniform knot cubic product B-spline. Finally, the average envelope is discretized into a mesh model as the residual model of the first decomposition and the difference between original model and residual model is denoted as the current offset vector, we can obtain offset vectors at all levels and the final residual model which represents the overall shape of the original model by iteratively dealing with the residual model. Based on the multi-scale decomposition, mesh denoising and feature editing can be achieved by dealing with these offset vectors and the effectiveness of the proposed method is verified by experiment results.

关键词

经验模态分解(EMD) / 多尺度分解 / 去噪 / 特征编辑.

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周财进 , 陈发来. 基于张量积B样条的几何模型EMD算法及其应用. 系统科学与数学, 2020, 40(6): 941-953. https://doi.org/10.12341/jssms13902
ZHOU Caijin , CHEN Falai. EMD Algorithm of Geometric Models and Its Applications Based on Tensor Product B-Spline. Journal of Systems Science and Mathematical Sciences, 2020, 40(6): 941-953 https://doi.org/10.12341/jssms13902
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