publication . Article . Preprint . 2017

indirect image registration with large diffeomorphic deformations

Chen, Chong; Öktem, Ozan;
Open Access
  • Published: 13 Jun 2017 Journal: SIAM Journal on Imaging Sciences, volume 11, pages 575-617 (eissn: 1936-4954, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
Abstract
The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper ...
Subjects
arXiv: Computer Science::Computer Vision and Pattern Recognition
free text keywords: Applied Mathematics, General Mathematics, Large deformation diffeomorphic metric mapping, Vector field, Noisy data, Artificial intelligence, business.industry, business, Diffeomorphism, Regularization (mathematics), Computer vision, Shape theory, Image registration, Iterative reconstruction, Mathematics, Mathematics - Numerical Analysis, Computer Science - Computer Vision and Pattern Recognition, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Optimization and Control, 65F22, 65R32, 65R30, 65D18, 94A12, 94A08, 92C55, 54C56, 57N25, 47A52
34 references, page 1 of 3

[2] A. I. Awad and M. Hassaballah, eds., Image Feature Detectors and Descriptors: Foundations and Applications, vol. 630 of Studies in Computational Intelligence, Springer-Verlag, 2016.

[3] M. Bauer, S. Joshi, and K. Modin, Di eomorphic density matching by optimal information transport, SIAM Journal on Imaging Sciences, 8 (2015), pp. 1718{1751.

[4] A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaees in Probability and Statisties, Springer-Verlag, 2004.

[5] E. Bladt, D. M. Pelt, S. Bals, and K. J. Batenburg, Electron tomography based on highly limited data using a neural network reconstruction technique, Ultramicroscopy, 158 (2015), pp. 81{88. [OpenAIRE]

[6] F. Bonin-Font, A. Ortiz, and G. Oliver, Visual navigation for mobile robots: A survey, Journal of Intelligent and Robotic Systems, 53 (2008), pp. 263{296.

[7] M. Bruveris and D. D. Holm, Geometry of image registration: The di eomorphism group and momentum maps, in Geometry, Mechanics, and Dynamics: The Legacy of Jerry Marsden, C. D. E., D. D. Holm, G. Patrick, and T. Ratiu, eds., vol. 73 of Fields Institute Communications, Springer-Verlag, 2015, pp. 19{56.

[8] M. Burger and S. Osher, A guide to the TV zoo, in Level Set and PDE Based Reconstruction Methods in Imaging, M. Burger and S. Osher, eds., vol. 2090 of Lecture Notes in Mathematics, Springer-Verlag, 2013, pp. 1{70.

[9] A. Chambolle and T. Pock, A rst-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40 (2011), pp. 120{145.

[10] G. E. Christensen, R. D. Rabbitt, and M. I. Miller, Deformable template model using large deformation kinematics, IEEE Transactions on Image Processing, 5 (1996), pp. 1435{1447.

[11] T. D'Arcy, On Growth and Form, Cambridge University Press, New York, 1945.

[12] S. Dawn, V. Saxena, and B. Sharma, Remote sensing image registration techniques: A survey, in Image and Signal Processing. Proceedings of the 4th International Conference, ICISP 2010, TroisRivieres, QC, Canada, June 30-July 2, 2010, A. Elmoataz, O. Lezoray, F. Nouboud, D. Mammass, and J. Meunier, eds., vol. 6134 of Lecture Notes in Computer Science, 2010, pp. 103{112.

[13] C. Demant, B. Streicher-Abel, and C. Garnica, Industrial Image Processing: Visual Quality Control in Manufacturing, Springer-Verlag, 2013.

[14] M. Grasmair, Generalized Bregman distances and convergence rates for non-convex regularization methods, Inverse Problems, 26 (2010), p. 115014. [OpenAIRE]

[15] U. Grenander and M. Miller, Pattern Theory. From Representation to Inference, Oxford University Press, 2007.

[16] Y. Hong, S. Joshi, M. Sanchez, M. Styner, and M. Niethammer, Metamorphic geodesic regression, in Medical Image Computing and Computer-Assisted Intervention { MICCAI 2012 15th International Conference, Nice, France, October 1-5, 2012, Proceedings, Part II, N. Ayache, P. Delingette, H. Golland, and K. Mori, eds., vol. 7512 of Lecture Notes in Computer Science, Springer-Verlag, 2012, pp. 197{205.

34 references, page 1 of 3
Related research
Abstract
The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper ...
Subjects
arXiv: Computer Science::Computer Vision and Pattern Recognition
free text keywords: Applied Mathematics, General Mathematics, Large deformation diffeomorphic metric mapping, Vector field, Noisy data, Artificial intelligence, business.industry, business, Diffeomorphism, Regularization (mathematics), Computer vision, Shape theory, Image registration, Iterative reconstruction, Mathematics, Mathematics - Numerical Analysis, Computer Science - Computer Vision and Pattern Recognition, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Optimization and Control, 65F22, 65R32, 65R30, 65D18, 94A12, 94A08, 92C55, 54C56, 57N25, 47A52
34 references, page 1 of 3

[2] A. I. Awad and M. Hassaballah, eds., Image Feature Detectors and Descriptors: Foundations and Applications, vol. 630 of Studies in Computational Intelligence, Springer-Verlag, 2016.

[3] M. Bauer, S. Joshi, and K. Modin, Di eomorphic density matching by optimal information transport, SIAM Journal on Imaging Sciences, 8 (2015), pp. 1718{1751.

[4] A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaees in Probability and Statisties, Springer-Verlag, 2004.

[5] E. Bladt, D. M. Pelt, S. Bals, and K. J. Batenburg, Electron tomography based on highly limited data using a neural network reconstruction technique, Ultramicroscopy, 158 (2015), pp. 81{88. [OpenAIRE]

[6] F. Bonin-Font, A. Ortiz, and G. Oliver, Visual navigation for mobile robots: A survey, Journal of Intelligent and Robotic Systems, 53 (2008), pp. 263{296.

[7] M. Bruveris and D. D. Holm, Geometry of image registration: The di eomorphism group and momentum maps, in Geometry, Mechanics, and Dynamics: The Legacy of Jerry Marsden, C. D. E., D. D. Holm, G. Patrick, and T. Ratiu, eds., vol. 73 of Fields Institute Communications, Springer-Verlag, 2015, pp. 19{56.

[8] M. Burger and S. Osher, A guide to the TV zoo, in Level Set and PDE Based Reconstruction Methods in Imaging, M. Burger and S. Osher, eds., vol. 2090 of Lecture Notes in Mathematics, Springer-Verlag, 2013, pp. 1{70.

[9] A. Chambolle and T. Pock, A rst-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40 (2011), pp. 120{145.

[10] G. E. Christensen, R. D. Rabbitt, and M. I. Miller, Deformable template model using large deformation kinematics, IEEE Transactions on Image Processing, 5 (1996), pp. 1435{1447.

[11] T. D'Arcy, On Growth and Form, Cambridge University Press, New York, 1945.

[12] S. Dawn, V. Saxena, and B. Sharma, Remote sensing image registration techniques: A survey, in Image and Signal Processing. Proceedings of the 4th International Conference, ICISP 2010, TroisRivieres, QC, Canada, June 30-July 2, 2010, A. Elmoataz, O. Lezoray, F. Nouboud, D. Mammass, and J. Meunier, eds., vol. 6134 of Lecture Notes in Computer Science, 2010, pp. 103{112.

[13] C. Demant, B. Streicher-Abel, and C. Garnica, Industrial Image Processing: Visual Quality Control in Manufacturing, Springer-Verlag, 2013.

[14] M. Grasmair, Generalized Bregman distances and convergence rates for non-convex regularization methods, Inverse Problems, 26 (2010), p. 115014. [OpenAIRE]

[15] U. Grenander and M. Miller, Pattern Theory. From Representation to Inference, Oxford University Press, 2007.

[16] Y. Hong, S. Joshi, M. Sanchez, M. Styner, and M. Niethammer, Metamorphic geodesic regression, in Medical Image Computing and Computer-Assisted Intervention { MICCAI 2012 15th International Conference, Nice, France, October 1-5, 2012, Proceedings, Part II, N. Ayache, P. Delingette, H. Golland, and K. Mori, eds., vol. 7512 of Lecture Notes in Computer Science, Springer-Verlag, 2012, pp. 197{205.

34 references, page 1 of 3
Related research
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publication . Article . Preprint . 2017

indirect image registration with large diffeomorphic deformations

Chen, Chong; Öktem, Ozan;