基于拟共形映射的特征点匹配

Chun-xue WANG; 刘利刚

doi:10.1631/FITEE.1500411

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基于拟共形映射的特征点匹配

常规文章 | Updated：2022-05-19

- 基于拟共形映射的特征点匹配
- Feature matching using quasi-conformal maps
- 信息与电子工程前沿（英文） 2017年18卷第5期页码：644-657
- Affiliations：
  
  School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
- Author bio：
  
  E-mail:lgliu@ustc.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61672482 and 11626253) and the One Hundred Talent Project of the Chinese Academy of Sciences
- DOI：10.1631/FITEE.1500411
  中图分类号： TP391
- 收稿：2015-11-26，
  
  录用：2016-3-24，
  
  纸质出版：2017-05
- Accepted：
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Chun-xue WANG, 刘利刚. 基于拟共形映射的特征点匹配[J]. 信息与电子工程前沿（英文）, 2017,18(5):644-657.

Chun-xue WANG, Li-gang LIU. Feature matching using quasi-conformal maps[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(5): 644-657.
Chun-xue WANG, 刘利刚. 基于拟共形映射的特征点匹配[J]. 信息与电子工程前沿（英文）, 2017,18(5):644-657. DOI： 10.1631/FITEE.1500411.

Chun-xue WANG, Li-gang LIU. Feature matching using quasi-conformal maps[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(5): 644-657. DOI： 10.1631/FITEE.1500411.

摘要

本文提出一种在两幅图像之间寻找保持几何关系一致的特征点对应的自动方法。虽然传统的SIFT（Scale-invariant feature transform）方法能得到一些对应点，但是其中有些对应点是无效的，我们的目标就是去除其中的无效对应点，使得剩下的对应点能够保持在拟共形映射下的几何关系。我们将问题描述为集成Beltrami系数项的拟共形映射的带约束优化问题，是通过交替求解线性系统和线性约束的凸二次规划来求解的。我们的方法非常简单而且对噪声点不敏感，优于一些已有的方法。

Abstract

We present a fully automatic method for finding geometrically consistent correspondences while discarding outliers from the candidate point matches in two images. Given a set of candidate matches provided by scale-invariant feature transform (SIFT) descriptors

which may contain many outliers

our goal is to select a subset of these matches retaining much more geometric information constructed by a mapping searched in the space of all diffeomorphisms. This problem can be formulated as a constrained optimization involving both the Beltrami coefficient (BC) term and quasi-conformal map

and solved by an efficient iterative algorithm based on the variable splitting method. In each iteration

we solve two subproblems

namely a linear system and linearly constrained convex quadratic programming. Our algorithm is simple and robust to outliers. We show that our algorithm enables producing more correct correspondences experimentally compared with state-of-the-art approaches.

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