2006, 3(2): 389-418. doi: 10.3934/mbe.2006.3.389

Multiscale Image Registration

1. 

Department of Mathematics, Stanford University, Stanford, CA 94305-2125, United States

2. 

Department of Radiation Oncology, Stanford University, Stanford, CA 94305-5947, United States, United States

Received  December 2005 Revised  January 2006 Published  February 2006

A multiscale image registration technique is presented for the registration of medical images that contain significant levels of noise. An overview of the medical image registration problem is presented, and various registration techniques are discussed. Experiments using mean squares, normalized correlation, and mutual information optimal linear registration are presented that determine the noise levels at which registration using these techniques fails. Further experiments in which classical denoising algorithms are applied prior to registration are presented, and it is shown that registration fails in this case for significantly high levels of noise, as well. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese [20] is presented, and accurate registration of noisy images is achieved by obtaining a hierarchical multiscale decomposition of the images and registering the resulting components. This approach enables successful registration of images that contain noise levels well beyond the level at which ordinary optimal linear registration fails. Image registration experiments demonstrate the accuracy and efficiency of the multiscale registration technique, and for all noise levels, the multiscale technique is as accurate as or more accurate than ordinary registration techniques.
Citation: Dana Paquin, Doron Levy, Eduard Schreibmann, Lei Xing. Multiscale Image Registration. Mathematical Biosciences & Engineering, 2006, 3 (2) : 389-418. doi: 10.3934/mbe.2006.3.389
[1]

Dana Paquin, Doron Levy, Lei Xing. Hybrid multiscale landmark and deformable image registration. Mathematical Biosciences & Engineering, 2007, 4 (4) : 711-737. doi: 10.3934/mbe.2007.4.711

[2]

Zhao Yi, Justin W. L. Wan. An inviscid model for nonrigid image registration. Inverse Problems and Imaging, 2011, 5 (1) : 263-284. doi: 10.3934/ipi.2011.5.263

[3]

Dana Paquin, Doron Levy, Lei Xing. Multiscale deformable registration of noisy medical images. Mathematical Biosciences & Engineering, 2008, 5 (1) : 125-144. doi: 10.3934/mbe.2008.5.125

[4]

Yuan-Nan Young, Doron Levy. Registration-Based Morphing of Active Contours for Segmentation of CT Scans. Mathematical Biosciences & Engineering, 2005, 2 (1) : 79-96. doi: 10.3934/mbe.2005.2.79

[5]

Christiane Pöschl, Jan Modersitzki, Otmar Scherzer. A variational setting for volume constrained image registration. Inverse Problems and Imaging, 2010, 4 (3) : 505-522. doi: 10.3934/ipi.2010.4.505

[6]

Wenxiang Cong, Ge Wang, Qingsong Yang, Jia Li, Jiang Hsieh, Rongjie Lai. CT image reconstruction on a low dimensional manifold. Inverse Problems and Imaging, 2019, 13 (3) : 449-460. doi: 10.3934/ipi.2019022

[7]

José M. Amigó, Beata Graff, Grzegorz Graff, Roberto Monetti, Katarzyna Tessmer. Detecting coupling directions with transcript mutual information: A comparative study. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4079-4097. doi: 10.3934/dcdsb.2019051

[8]

Luca Bertelli, Frédéric Gibou. Fast two dimensional to three dimensional registration of fluoroscopy and CT-scans using Octrees on segmentation maps. Mathematical Biosciences & Engineering, 2012, 9 (3) : 527-537. doi: 10.3934/mbe.2012.9.527

[9]

Marcus Wagner. A direct method for the solution of an optimal control problem arising from image registration. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 487-510. doi: 10.3934/naco.2012.2.487

[10]

Angel Angelov, Marcus Wagner. Multimodal image registration by elastic matching of edge sketches via optimal control. Journal of Industrial and Management Optimization, 2014, 10 (2) : 567-590. doi: 10.3934/jimo.2014.10.567

[11]

Yangang Chen, Justin W. L. Wan. Numerical method for image registration model based on optimal mass transport. Inverse Problems and Imaging, 2018, 12 (2) : 401-432. doi: 10.3934/ipi.2018018

[12]

Ho Law, Gary P. T. Choi, Ka Chun Lam, Lok Ming Lui. Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022010

[13]

Rudolf Ahlswede. The final form of Tao's inequality relating conditional expectation and conditional mutual information. Advances in Mathematics of Communications, 2007, 1 (2) : 239-242. doi: 10.3934/amc.2007.1.239

[14]

Kateřina Škardová, Tomáš Oberhuber, Jaroslav Tintěra, Radomír Chabiniok. Signed-distance function based non-rigid registration of image series with varying image intensity. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1145-1160. doi: 10.3934/dcdss.2020386

[15]

Eitan Tadmor, Prashant Athavale. Multiscale image representation using novel integro-differential equations. Inverse Problems and Imaging, 2009, 3 (4) : 693-710. doi: 10.3934/ipi.2009.3.693

[16]

Huan Han. A variational model with fractional-order regularization term arising in registration of diffusion tensor image. Inverse Problems and Imaging, 2018, 12 (6) : 1263-1291. doi: 10.3934/ipi.2018053

[17]

Yunmei Chen, Jiangli Shi, Murali Rao, Jin-Seop Lee. Deformable multi-modal image registration by maximizing Rényi's statistical dependence measure. Inverse Problems and Imaging, 2015, 9 (1) : 79-103. doi: 10.3934/ipi.2015.9.79

[18]

Mohamed Alahyane, Abdelilah Hakim, Amine Laghrib, Said Raghay. Fluid image registration using a finite volume scheme of the incompressible Navier Stokes equation. Inverse Problems and Imaging, 2018, 12 (5) : 1055-1081. doi: 10.3934/ipi.2018044

[19]

Xiaojun Zheng, Zhongdan Huan, Jun Liu. On the solvability of a semilinear higher-order elliptic problem for the vector field method in image registration. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022068

[20]

Thomas Y. Hou, Dong Liang. Multiscale analysis for convection dominated transport equations. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 281-298. doi: 10.3934/dcds.2009.23.281

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (12)

[Back to Top]