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山东大学学报 (工学版) ›› 2018, Vol. 48 ›› Issue (5): 9-15, 37.doi: 10.6040/j.issn.1672-3961.0.2018.245

• 机器学习与数据挖掘 • 上一篇    下一篇

基于Delaunay三角化的二维无约束优化EMD方法

胡建平1,2(),李鑫1,谢琪1,3,*(),李玲1,张道畅1   

  1. 1. 东北电力大学理学院, 吉林 吉林 132012
    2. 北京航空航天大学虚拟现实技术与系统国家重点实验室, 北京 100191
    3. 吉林大学数学学院, 吉林 长春 130012
  • 收稿日期:2018-06-07 出版日期:2018-10-01 发布日期:2018-06-07
  • 通讯作者: 谢琪 E-mail:neduhjp307@163.com;xieqi_19820302@126.com
  • 作者简介:胡建平(1981—),男,四川广安人,教授,博士,主要研究方向为计算机图形学与图像处理等. Email: neduhjp307@163.com
  • 基金资助:
    国家自然科学基金资助项目(61672149);吉林省科技发展计划基金资助项目(20170520052JH);吉林省教育厅十三五科学技术研究基金资助项目(吉教科合字[2016]第97号);北京航空航天大学虚拟现实技术与系统国家重点实验室开放基金资助项目(BUAA-VR-16KF-23)

An unconstrained optimization EMD approach in 2D based on Delaunay triangulation

Jianping HU1,2(),Xin LI1,Qi XIE1,3,*(),Ling LI1,Daochang ZHANG1   

  1. 1. College of Science, Northeast Electric Power University, Jilin 132012, Jilin, China
    2. State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing 100191, China
    3. School of Mathematical Science, Jilin University, Changchun 130012, Jilin, China
  • Received:2018-06-07 Online:2018-10-01 Published:2018-06-07
  • Contact: Qi XIE E-mail:neduhjp307@163.com;xieqi_19820302@126.com
  • Supported by:
    国家自然科学基金资助项目(61672149);吉林省科技发展计划基金资助项目(20170520052JH);吉林省教育厅十三五科学技术研究基金资助项目(吉教科合字[2016]第97号);北京航空航天大学虚拟现实技术与系统国家重点实验室开放基金资助项目(BUAA-VR-16KF-23)

摘要:

提出一种改进的基于Delaunay三角化的二维无约束优化经验模态分解(empirical mode decomposition, EMD)方法,对二维图像极值点重新定义,利用对定义的极值点进行Delaunay三角化构建无约束的优化模型对图像进行迭代分解,能够将原始图像自适应分解为尺度从细到粗的内蕴模态图像分量和一个余量。试验结果表明:本研究提出的方法较原始的二维无约束优化EMD方法具有更强的细节获取能力,能够更好地体现原始图像的不同尺度特征。

关键词: 经验模态分解, 无约束优化, Delaunay三角化, 内蕴模态图像, 多尺度特征

Abstract:

An improved unconstrained optimization empirical mode decomposition (EMD) approach in two-dimensional (2D) based on Delaunay triangulation was presented. It firstly redefined the extremum of 2D images, and then constructed an optimization model to decompose the input image iteratively based on the Delaunay triangulation of the image extrema. The proposed approach could adaptively decompose the input image into several intrinsic mode images with fine-coarse scales and a residue. Experiment results demonstrated the proposed method had more powerful capabilities in capturing the multi-scale details and image features than the original 2D unconstrained optimization EMD approach.

Key words: empirical mode decomposition, unconstrained optimization, Delaunay triangulation, intrinsic mode image, multi-scale feature

中图分类号: 

  • TP391

图1

约束点选择方式比较"

图2

不同极值参数选取方式分解比较 注:第一行t=0.6,第二行t=1.0,第三行按式(12)选取"

图3

本研究方法中采用最近点建模(第一行)和Delaunay三角化(第二行)分解比较"

图4

构造图像分解比较"

图5

Woman图像分解比较 注:从上到下分别为IEMD方法[10]、UOA-EMD方法[22]、本研究方法"

图6

MRI图像分解比较 注:从上到下分别为IEMD方法[10]、UOA-EMD方法[22]、本研究方法"

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