北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (7): 1202-1207.doi: 10.13700/j.bh.1001-5965.2014.0505

• 论文 • 上一篇    下一篇

基于渐非凸渐凹化过程的子图匹配算法

李晶1,2, 刘传凯3, 王勇1,4, 古楠楠5, 石锐2, 李琳2   

  1. 1. 中国酒泉卫星发射中心, 酒泉 732750;
    2. 重庆大学 通信工程学院, 重庆 400044;
    3. 北京航天飞行控制中心, 北京 100094;
    4. 哈尔滨工业大学 航天学院, 哈尔滨 150006;
    5. 首都经济贸易大学 统计学院, 北京 100026
  • 收稿日期:2014-08-11 修回日期:2014-11-20 出版日期:2015-07-20 发布日期:2015-07-30
  • 通讯作者: 刘传凯(1983—),男,山东潍坊人,工程师,chuankai.liu@gmail.com,主要研究方向为空间操作、视觉导航. E-mail:chuankai.liu@gmail.com
  • 作者简介:李晶(1982—),女,山东济宁人,工程师,jing_li@outlook.com
  • 基金资助:
    国家自然科学基金(61305137)

Subgraph matching algorithm based on graduated nonconvexity and concavity procedure

LI Jing1,2, LIU Chuankai3, WANG Yong1,4, GU Nannan5, SHI Rui2, LI Lin2   

  1. 1. Jiuquan Satellite Launch Center, Jiuquan 732750, China;
    2. College of Communication Engineering, Chongqing University, Chongqing 400044, China;
    3. Beijing Aerospace Flight Control Center, Beijing 100094;
    4. School of Astronautics, Harbin Institute of Technology, Harbin 150006, China;
    5. College of Statistics, Capital University of Economics and Business, Beijing 100026, China
  • Received:2014-08-11 Revised:2014-11-20 Online:2015-07-20 Published:2015-07-30

摘要: 如何实现外点存在情况下的鲁棒高效匹配是图匹配领域的关键问题之一.针对此问题,提出将渐非凸渐凹化过程(GNCCP)用于子图匹配,即将外点存在情况下的图匹配问题建模为一个基于相似矩阵的二次组合优化问题,然后通过扩展GNCCP来近似优化,是一种新的采用二阶约束图匹配算法.相较于现有算法,提出的算法优势在于可以泛化目标函数定义方式,有效处理外点存在的情况的图匹配问题,且能同时实现有向图匹配和无向图匹配.人工数据与真实数据上的实验证实了算法的有效性.

关键词: 图匹配, 组合优化, 渐非凸渐凹化过程(GNCCP), 关键点对应, 有向图

Abstract: To achieve robust and efficient matching with outliers is a fundamental problem in the field of graph matching. To tackle this problem, a novel subgraph matching algorithm was proposed, which was based on the recently proposed graduated nonconvexity and concavity procedure (GNCCP). Specifically speaking, the graph matching problem in the existence of outliers was firstly formulated as a quadratic combinatorial optimization problem based on the affinity matrix, which was then optimized by extending the GNCCP. This is a new second-order constraint graph matching algorithm. Compared with the existing algorithms, there are mainly three benefits for the proposed algorithm, which are as follows. Firstly, it has a flexible objective function formulation; secondly, it is effective in graph matching problems with outliers; thirdly, it is applicable on both directed graphs and undirected graphs. Simulations on both synthetic and real world datasets validate the effectiveness of the proposed method.

Key words: graph matching, combinatorial optimization, graduated nonconvexity and concavity procedure (GNCCP), point correspondence, directed graph

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