Full Text:   <5330>

CLC number: TP391

On-line Access: 2017-05-24

Received: 2015-11-26

Revision Accepted: 2016-03-24

Crosschecked: 2017-04-22

Cited: 0

Clicked: 10676

Citations:  Bibtex RefMan EndNote GB/T7714


Li-gang Liu


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2017 Vol.18 No.5 P.644-657


Feature matching using quasi-conformal maps

Author(s):  Chun-xue Wang, Li-gang Liu

Affiliation(s):  School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Corresponding email(s):   lgliu@ustc.edu.cn

Key Words:  Feature correspondence, Quasi-conformal map, Splitting method

Chun-xue Wang, Li-gang Liu. Feature matching using quasi-conformal maps[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(5): 644-657.

@article{title="Feature matching using quasi-conformal maps",
author="Chun-xue Wang, Li-gang Liu",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Feature matching using quasi-conformal maps
%A Chun-xue Wang
%A Li-gang Liu
%J Frontiers of Information Technology & Electronic Engineering
%V 18
%N 5
%P 644-657
%@ 2095-9184
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500411

T1 - Feature matching using quasi-conformal maps
A1 - Chun-xue Wang
A1 - Li-gang Liu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
IS - 5
SP - 644
EP - 657
%@ 2095-9184
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1500411

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.


概要: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。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Belongie, S., Malik, J., Puzicha, J., 2002. Shape matching and object recognition using shape contexts. IEEE Trans. Patt. Anal. Mach. Intell., 24(4):509-522.

[2]Bers, L., 1977. Quasiconformal mappings, with applications to differential equations, function theory and topology. Bull. Am. Math. Soc., 83(6):1083-1100.

[3]Boyd, S., Parikh, N., Chu, E., et al., 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn., 3(1):1-122.

[4]Chui, H., Rangarajan, A., 2003. A new point matching algorithm for non-rigid registration. Comput. Vis. Image Understand., 89(2-3):114-141.

[5]Daripa, P., 1991. On a numerical method for quasi-conformal grid generation. J. Comput. Phys., 96(1):229-236.

[6]Daripa, P., 1992. A fast algorithm to solve nonhomogeneous Cauchy-Reimann equations in the complex plane. SIAM J. Sci. Stat. Comput., 13(6):1418-1432.

[7]Duchenne, O., Bach, F., Kweon, I.S., et al., 2011. A tensor-based algorithm for high-order graph matching. IEEE Trans. Patt. Anal. Mach. Intell., 33(12):2383-2395.

[8]Fischler, M.A., Bolles, R.C., 1981. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM, 24(6):381-395.

[9]Gardiner, F.P., Lakic, N., 2000. Quasiconformal Teichmüller Theory. American Mathematical Society, Providence, USA.

[10]Gu, X.D., Yau, S.T., 2008. Computational Conformal Geometry. International Press, Somerville, MA, USA.

[11]Heider, P., Pierre-Pierre, A., Li, R., et al., 2011. Local shape descriptors, a survey and evaluation. Eurographics Workshop on 3D Object Retrieval, p.1-8.

[12]Hinton, G.E., Williams, C.K.I., Revow, M.D., 1991. Adaptive elastic models for hand-printed character recognition. 4th Int. Conf. on Neural Information Processing Systems, p.512-519.

[13]Ho, K.T., Lui, L.M., 2016. QCMC: quasi-conformal parameterizations for multiply-connected domains. Adv. Comput. Math., 42(2):279-312.

[14]Jian, B., Vemuri, B.C., Marroquin, J.L., 2005. Robust nonrigid multimodal image registration using local frequency maps. Biennial Int. Conf. on Information Processing in Medical Imaging, p.504-515.

[15]Lam, K.C., Lui, L.M., 2014. Landmark and intensity-based registration with large deformations via quasi-conformal maps. SIAM J. Imag. Sci., 7(4):2364-2392.

[16]Lazebnik, S., Schmid, C., Ponce, J., 2004. Semi-local affine parts for object recognition. British Machine Vision Conf., p.779-788.

[17]Lazebnik, S., Schmid, C., Ponce, J., 2005. A maximum entropy framework for part-based texture and object recognition. ICCV, p.832-838.

[18]Lehto, O., Virtanen, K.I., Lucas, K.W., 1973. Quasiconformal Mappings in the Plane. Springer New York.

[19]Li, Y., Xie, X., Yang, Z., 2015. Alternating direction method of multipliers for solving dictionary learning. Commun. Math. Stat., 3:37-55.

[20]Lipman, Y., Yagev, S., Poranne, R., et al., 2014. Feature matching with bounded distortion. ACM Trans. Graph., 33(3):26.

[21]Lui, L.M., Ng, T.C., 2015. A splitting method for diffeomorphism optimization problem using Beltrami coefficients. J. Sci. Comput., 63(2):573-611.

[22]Lui, L.M., Wong, T.W., Zeng, W., et al., 2012. Optimization of surface registrations using Beltrami holomorphic flow. J. Sci. Comput., 50(3):557-585.

[23]Mastin, C.W., Thompson, J.F., 1984. Quasiconformal mappings and grid generation. SIAM J. Sci. Stat. Comput., 5(2):305-310.

[24]Montagnat, J., Delingette, H., Ayache, N., 2001. A review of deformable surfaces: topology, geometry and deformation. Image Vis. Comput., 19(14):1023-1040.

[25]Nealen, A., Müller, M., Keiser, R., et al., 2006. Physically based deformable models in computer graphics. Comput. Graph. For., 25(4):809-836.

[26]Sasaki, Y., 2007. The Truth of the F-measure. School of Computer Science, University of Manchester.

[27]Taimouri, V., Hua, J., 2014. Deformation similarity measurement in quasi-conformal shape space. Graph. Models, 76(2):57-69.

[28]Tuytelaars, T., Mikolajczyk, K., 2008. Local invariant feature detectors: a survey. Found. Trends Comput. Graph. Vis., 3(3):177-280.

[29]van Kaick, O., Zhang, H., Hamarneh, G., et al., 2011. A survey on shape correspondence. Comput. Graph. Forum, 30(6):1681-1707.

[30]Vedaldi, A., Fulkerson, B., 2010. Vlfeat: an open and portable library of computer vision algorithms. Proc. 18th ACM Int. Conf. on Multimedia, p.1469-1472.

[31]Wang, S., Wang, Y., Jin, M., et al., 2007. Conformal geometry and its applications on 3D shape matching, recognition, and stitching. IEEE Trans. Patt. Anal. Mach. Intell., 29(7):1209-1220.

[32]Weber, O., Myles, A., Zorin, D., 2012. Computing extremal quasiconformal maps. Comput. Graph. For., 31(5):1679-1689.

[33]Wright, S.J., 2015. Coordinate descent algorithms. Math. Program., 151(1):3-34.

[34]Yezzi, A., Mennucci, A., 2005. Conformal metrics and true ”gradient flows” for curves. ICCV, p.913-919.

[35]Zeng, W., Gu, X.D., 2011. Registration for 3D surfaces with large deformations using quasi-conformal curvature flow. CVPR, p.2457-2464.

[36]Zeng, W., Hua, J., Gu, X., 2009. Symmetric conformal mapping for surface matching and registration. Int. J. CAD/CAM, 9(1):103-109.

[37]Zhao, Z., Feng, X., Teng, S., et al., 2012. Multiscale point correspondence using feature distribution and frequency domain alignment. Math. Probl. Eng., 2012:382369.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE