北大中文核心期刊
中国科学引文数据库（CSCD）来源期刊
中国科技核心期刊
入选数学领域高质量科技期刊
Scopus
EBSCO 

运筹学学报 ›› 2018, Vol. 22 ›› Issue (1): 109-118.doi: 10.15960/j.cnki.issn.1007-6093.2018.01.009

• 运筹学 • 上一篇    下一篇

基于带约束的隐表示非线性形状配准

郑杨1 胡娟2  王永波2  彭亚新1,*   

  1. 1. 上海大学理学院数学系, 上海 200444; 2. 上海电气集团股份有限公司中央研究院, 上海 200070
  • 收稿日期:2017-01-19 出版日期:2018-03-15 发布日期:2018-03-15
  • 通讯作者: 彭亚新 E-mail: yaxin.peng@shu.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 11771276, 11471208, 11601315), 扬帆计划(No. 16YF1404000), 点云处理算法研究及程序开发, 骨科手术导航算法研究及程序模块开发

Nonlinear shape registration via constrained implicit  representation

ZHENG Yang1  HU Juan2  WANG Yongbo2  PENG  Yaxin1,*   

  1. 1. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, China; 2. Central Research Institute of Shanghai Electric, Shanghai 200070, China
  • Received:2017-01-19 Online:2018-03-15 Published:2018-03-15

PDF

459

摘要：

主要通过对形状进行带约束的隐表示来研究非线性形状配准. 首先, 采用隐函数的零水平集来表示形状, 并结合从整体到局部的策略, 对形状配准问题进行了建模. 其次, 为提高模型精度, 对全局尺度形变和局部非线性形变引入了尺度约束和带状约束. 进一步, 给出了一阶变分, 并应用负梯度流进行数值求解. 最后，多个数据集上与现有经典算法的对比实验表明, 给出的算法具有更优的精度.

关键词: 非线性形状配准, 隐表示, 尺度约束, 带状区域约束

Abstract:

This paper addresses the nonlinear shape registration by using the constrained implicit representation for the shape. First, we adopt the level set of the implicit function to represent the shape and model the shape registration, where a global-to-local strategy is applied. Then, in order to improve the regularity, the scale and the bending constraints are introduced to the global and local parameters respectively. Further, a first order variational model is deduced and solved by the gradient descent method. Finally, the comparison of the proposed algorithm with some state-of-the-art approaches on a variety of data sets validates our better performance.

Key words: nonlinear shape registration, implicit representation, scale constraint, bending constraint