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Multimodal image registration by elastic matching of edge sketches via optimal control
1. | Otto-Hahn-Str. 15, D-30880 Laatzen, Germany |
2. | University of Leipzig, Department of Mathematics, P. O. B. 10 09 20, D-04009 Leipzig |
References:
[1] |
A. Angelov, Multimodale Bildregistrierung durch elastisches Matching von Kantenskizzen,, Diploma thesis, (2011). Google Scholar |
[2] |
B. Bourdin, Image segmentation with a finite element method,, M2AN Mathematical Modelling and Numerical Analysis, 33 (1999), 229.
doi: 10.1051/m2an:1999114. |
[3] |
C. Brune, H. Maurer and M. Wagner, Detection of intensity and motion edges within optical flow via multidimensional control,, SIAM J. Imaging Sci., 2 (2009), 1190.
doi: 10.1137/080725064. |
[4] |
M. Burger, J. Modersitzki and L. Ruthotto, A hyperelastic regularization energy for image registration,, SIAM J. Sci. Comput., 35 (2013).
doi: 10.1137/110835955. |
[5] |
C. Clason, B. Jin and K. Kunisch, A semismooth Newton method for $L^1$ data fitting with automatic choice of regularization parameters and noise calibration,, SIAM J. Imaging Sci., 3 (2010), 199.
doi: 10.1137/090758003. |
[6] |
B. Dacorogna, Direct Methods in the Calculus of Variations,, Second edition, (2008).
|
[7] |
M. Droske and M. Rumpf, A variational approach to nonrigid morphological image registration,, SIAM J. Appl. Math., 64 (2004), 668.
doi: 10.1137/S0036139902419528. |
[8] |
M. Droske and M. Rumpf, Multiscale joint segmentation and registration of image morphology,, IEEE Trans. Pattern Recognition Machine Intelligence, 29 (2007), 2181. Google Scholar |
[9] |
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions,, Studies in Advanced Mathematics, (1992).
|
[10] |
B. Fischer and J. Modersitzki, Curvature based image registration,, J. Math. Imaging Vision, 18 (2003), 81.
doi: 10.1023/A:1021897212261. |
[11] |
R. Fourer, D. M. Gay and B. W. Kernighan, AMPL. A Modeling Language for Mathematical Programming,, Second edition, (2003). Google Scholar |
[12] |
L. Franek, M. Franek, H. Maurer and M. Wagner, A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data,, Opt. Control Appl. Meth., 33 (2012), 276.
doi: 10.1002/oca.996. |
[13] |
L. A. Gallardo and M. A. Meju, Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data,, Geophysical Research Letters, 30 (2003).
doi: 10.1029/2003GL017370. |
[14] |
H. Goering, H.-G. Roos and L. Tobiska, Finite-Element-Methode,, Third edition, (1993).
|
[15] |
E. Haber and J. Modersitzki, Intensity gradient based registration and fusion of multi-modal images,, Methods of Information in Medicine, 46 (2007), 292. Google Scholar |
[16] |
J. Han, B. Berkels, M. Rumpf, J. Hornegger, M. Droske, M. Fried, J. Scorzin and C. Schaller, A variational framework for joint image registration, denoising and edge detection,, in Bildverarbeitung für die Medizin 2006 (eds. H. Handels, (2006), 246. Google Scholar |
[17] |
S. Henn and K. Witsch, Iterative multigrid regularization techniques for image matching,, SIAM J. Sci. Comput., 23 (2001), 1077.
|
[18] |
G. Hermosillo, C. Chefd'hotel and O. Faugeras, Variational methods for multimodal image matching,, Int. J. Computer Vision, 50 (2002), 329. Google Scholar |
[19] |
M. Hintermüller and S. L. Keeling, Image registration and segmentation based on energy minimization,, in Handbook of Optimization in Medicine (eds. P. M. Pardalos and H. E. Romeijn) Springer, (2009), 213.
|
[20] |
B. Jansen, Interior Point Techniques in Optimization,, Kluwer, (1997).
|
[21] |
C. Laird and A. Wächter, Introduction to IPOPT: A Tutorial for Downloading, Installing, and Using IPOPT,, Revision No. 1830. Available from: , (1830). Google Scholar |
[22] |
J. Min, M. Powell and K. W. Bowyer, Automated performance evaluation of range image segmentation algorithms,, IEEE Trans. Systems, 34 (2004), 263. Google Scholar |
[23] |
J. Modersitzki, Numerical Methods for Image Registration,, Oxford University Press, (2004).
|
[24] |
J. Modersitzki, FAIR. Flexible Algorithms for Image Registration,, SIAM, (2009).
|
[25] |
R. W. Ogden, Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue,, in Biomechanics of Soft Tissue in Cardiovascular Systems (eds. G. A. Holzapfel and R. W. Ogden), (2003), 65. Google Scholar |
[26] |
K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Applications,, Springer, (2000). Google Scholar |
[27] |
H. Richter, Wahrscheinlichkeitstheorie,, Second edition, (1966).
|
[28] |
O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier and F. Lenzen, Variational Methods in Imaging,, Springer, (2009).
|
[29] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,, Math. Program. Ser. A, 106 (2006), 25.
|
[30] |
M. Wagner, Elastic image registration in presence of polyconvex constraints,, Karl-Franzens-Universität Graz, (2010), 2010. Google Scholar |
[31] |
M. Wagner, A direct method for the solution of an optimal control problem arising from image registration,, Numerical Algebra, 2 (2012), 487.
|
[32] |
B. Zitová and J. Flusser, Image registration methods: A survey,, Image and Vision Computing, 21 (2003), 977. Google Scholar |
show all references
References:
[1] |
A. Angelov, Multimodale Bildregistrierung durch elastisches Matching von Kantenskizzen,, Diploma thesis, (2011). Google Scholar |
[2] |
B. Bourdin, Image segmentation with a finite element method,, M2AN Mathematical Modelling and Numerical Analysis, 33 (1999), 229.
doi: 10.1051/m2an:1999114. |
[3] |
C. Brune, H. Maurer and M. Wagner, Detection of intensity and motion edges within optical flow via multidimensional control,, SIAM J. Imaging Sci., 2 (2009), 1190.
doi: 10.1137/080725064. |
[4] |
M. Burger, J. Modersitzki and L. Ruthotto, A hyperelastic regularization energy for image registration,, SIAM J. Sci. Comput., 35 (2013).
doi: 10.1137/110835955. |
[5] |
C. Clason, B. Jin and K. Kunisch, A semismooth Newton method for $L^1$ data fitting with automatic choice of regularization parameters and noise calibration,, SIAM J. Imaging Sci., 3 (2010), 199.
doi: 10.1137/090758003. |
[6] |
B. Dacorogna, Direct Methods in the Calculus of Variations,, Second edition, (2008).
|
[7] |
M. Droske and M. Rumpf, A variational approach to nonrigid morphological image registration,, SIAM J. Appl. Math., 64 (2004), 668.
doi: 10.1137/S0036139902419528. |
[8] |
M. Droske and M. Rumpf, Multiscale joint segmentation and registration of image morphology,, IEEE Trans. Pattern Recognition Machine Intelligence, 29 (2007), 2181. Google Scholar |
[9] |
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions,, Studies in Advanced Mathematics, (1992).
|
[10] |
B. Fischer and J. Modersitzki, Curvature based image registration,, J. Math. Imaging Vision, 18 (2003), 81.
doi: 10.1023/A:1021897212261. |
[11] |
R. Fourer, D. M. Gay and B. W. Kernighan, AMPL. A Modeling Language for Mathematical Programming,, Second edition, (2003). Google Scholar |
[12] |
L. Franek, M. Franek, H. Maurer and M. Wagner, A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data,, Opt. Control Appl. Meth., 33 (2012), 276.
doi: 10.1002/oca.996. |
[13] |
L. A. Gallardo and M. A. Meju, Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data,, Geophysical Research Letters, 30 (2003).
doi: 10.1029/2003GL017370. |
[14] |
H. Goering, H.-G. Roos and L. Tobiska, Finite-Element-Methode,, Third edition, (1993).
|
[15] |
E. Haber and J. Modersitzki, Intensity gradient based registration and fusion of multi-modal images,, Methods of Information in Medicine, 46 (2007), 292. Google Scholar |
[16] |
J. Han, B. Berkels, M. Rumpf, J. Hornegger, M. Droske, M. Fried, J. Scorzin and C. Schaller, A variational framework for joint image registration, denoising and edge detection,, in Bildverarbeitung für die Medizin 2006 (eds. H. Handels, (2006), 246. Google Scholar |
[17] |
S. Henn and K. Witsch, Iterative multigrid regularization techniques for image matching,, SIAM J. Sci. Comput., 23 (2001), 1077.
|
[18] |
G. Hermosillo, C. Chefd'hotel and O. Faugeras, Variational methods for multimodal image matching,, Int. J. Computer Vision, 50 (2002), 329. Google Scholar |
[19] |
M. Hintermüller and S. L. Keeling, Image registration and segmentation based on energy minimization,, in Handbook of Optimization in Medicine (eds. P. M. Pardalos and H. E. Romeijn) Springer, (2009), 213.
|
[20] |
B. Jansen, Interior Point Techniques in Optimization,, Kluwer, (1997).
|
[21] |
C. Laird and A. Wächter, Introduction to IPOPT: A Tutorial for Downloading, Installing, and Using IPOPT,, Revision No. 1830. Available from: , (1830). Google Scholar |
[22] |
J. Min, M. Powell and K. W. Bowyer, Automated performance evaluation of range image segmentation algorithms,, IEEE Trans. Systems, 34 (2004), 263. Google Scholar |
[23] |
J. Modersitzki, Numerical Methods for Image Registration,, Oxford University Press, (2004).
|
[24] |
J. Modersitzki, FAIR. Flexible Algorithms for Image Registration,, SIAM, (2009).
|
[25] |
R. W. Ogden, Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue,, in Biomechanics of Soft Tissue in Cardiovascular Systems (eds. G. A. Holzapfel and R. W. Ogden), (2003), 65. Google Scholar |
[26] |
K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Applications,, Springer, (2000). Google Scholar |
[27] |
H. Richter, Wahrscheinlichkeitstheorie,, Second edition, (1966).
|
[28] |
O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier and F. Lenzen, Variational Methods in Imaging,, Springer, (2009).
|
[29] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,, Math. Program. Ser. A, 106 (2006), 25.
|
[30] |
M. Wagner, Elastic image registration in presence of polyconvex constraints,, Karl-Franzens-Universität Graz, (2010), 2010. Google Scholar |
[31] |
M. Wagner, A direct method for the solution of an optimal control problem arising from image registration,, Numerical Algebra, 2 (2012), 487.
|
[32] |
B. Zitová and J. Flusser, Image registration methods: A survey,, Image and Vision Computing, 21 (2003), 977. Google Scholar |
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