Image Registration using the Rigid Group
Abstract
![](/public/site/graph.png)
Image registration is the process of approximate matching of the source image to the target so that they resemble each other. In this study, two-dimensional image registration is presented using the rigid group. This group is a finite dimensional group (four-dimensional in this case) under composition. The dimensions of the rigid group are scaling, rotation, and translations along the axes. In this paper, an algorithm for the construction of rigid transformation is presented using the discretized objective function. This objective function is based on SSD (sum of the squares of the distances between the pixels intensities) and calculates the discrepancy between the images. The coarse search and the gradient descent approaches have been used for the optimization. The proposed algorithm is implemented on variety of images. The numerical examples illustrate the ability of the proposed algorithm.
Downloads
References
Thompson DW. On growth and form. Cambridge university press; 1942.
Tufail MY. Image registration under conformal diffeomorphisms [doctoral dissertation]. Massey university, Palmerston north, New Zealand; 2017.
Beg MF, Miller MI, Trouvé A, Younes L. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int J Comput Vis. 2005;61(2):139–57. https://doi.org/10.1023/b:visi.0000043755.93987.aa
Cao Y, Miller MI, Winslow RL, Younes L. Large deformation diffeomorphic metric mapping of vector fields. IEEE Transac Med Imag. 2005;24(9):1216–30. https://doi.org/10.1109/tmi.2005.853923
Glaunès J, Qiu A, Miller MI, Younes L. Large deformation diffeomorphic metric curve mapping. Int J Comput Vis. 2008;80(3):317–36. https://doi.org/10.1007/s11263-008-0141-9
Grenander U, Miller MI. Computational anatomy: An emerging discipline. Quart Appl Math. 1998;56(4):617–94. https://doi.org/10.1090/qam/1668732
Joshi SC, Miller MI. Landmark matching via large deformation diffeomorphisms. IEEE Transac Image Proc. 2000;9(8):1357–1370. https://doi.org/10.1109/83.855431
Brown LG. A survey of image registration techniques. ACM Comput Surv. 1992;24(4):325–376. https://doi.org/10.1145/146370.146374
Marsland S, McLachlan RI, Tufail MY. Conformal image registration based on constrained optimization. NZIAM J. 2020;62(3):235–55. https://doi.org/10.1017/s144618112000022x
Smith SM, Jenkinson M, Woolrich MW, et al. Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage. 2004;23:S208-S219. https://doi.org/10.1016/j.neuroimage.2004.07.051
Ullah W, Siddique I, Zulqarnain RM, Alam MM, Ahmad I, Raza UA. Classification of arrhythmia in heartbeat detection using deep learning. Comput Intell Neurosci. 2021;2021:e2195922. https://doi.org/10.1155/2021/2195922
Asif M, Mairaj S, Saeed Z, Ashraf MU, Jambi K, Zulqarnain RM. A novel image encryption technique based on mobius transformation. Comput Intell Neurosci. 2021;2021:e1912859. https://doi.org/10.1155/2021/1912859
Dayan F, Javaid M, Zulqarnain M, Ali MT, Ahmad B. Computing banhatti Indices of hexagonal, honeycomb and derived networks. American J Math Comput Model. 2018;3(2):38–45. https://doi.org/10.11648/j.ajmcm.20180302.11
Grzeszczuk R. An Approach to classifying data with highly localized unmarked features using neural networks. Comput Sci. 2019;20:329–42. https://doi.org/10.7494/csci.2019.20.3.3343
Gupta A. Current research opportunities for image processing and computer vision. Computer Science. 2019;20(4):387–410. https://doi.org/10.7494/csci.2019.20.4.3163
Dabbour AA, Habib R, Saii M. Object pose estimation in monocular image using modified FDCM. Comput Sci. 2020;21(1):97–112. https://doi.org/10.7494/csci.2020.21.1.3426
Chen K. Introduction to variational image-processing models and applications, 2013;90(1):1–8. https://doi.org/10.1080/00207160.2012.757073
Frasczek R, Cyganek B, Wiatr K. Parallelized algorithms for finding similar images and object recognition. Comput Sci. 2013;14(1):113–127. https://doi.org/10.7494/csci.2013.14.1.113
Zitova B, Flusser J. Image registration methods: a survey. Image Vis Comput. 2003;21(11):977–1000. https://doi.org/10.1016/s0262-8856(03)00137-9
Glasbey CA, Mardia KV. A review of image-warping methods. J Appl Statis. 1998;25(2):155–171. https://doi.org/10.1080/02664769823151
Kryjak T, Komorkiewicz M, Gorgon M. Real-time moving object detection for video surveillance system in FPGA. Paper presented at: Conference on Design & Architectures for Signal & Image Processing; November 2–4, 2011; Tampere, Finland. https://doi.org/10.1109/dasip.2011.6136881
Bartoli G. Image registration techniques: A comprehensive survey. Visual Information Processing and Protection Group; 2007. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=b6d9d5785a425a86097956c508908228106863ac
Goshtasby AA. Image registration: Principles, tools and methods. Springer; 2012.
Ogiela MR. Methods of the Straightening Transformation and Analysis of Outer Contours of Objects in Medical Image Recognitio. Comput Sci. 1999;1(1):103–112. https://doi.org/10.7494/csci.1999.1.1.3574
Ogiela MR. Fitting of tonal curve and balancing of gray levels in contrast expansion and preliminary imaging of structures in the analysis. Comput Sci. 2000;2:81–92. https://doi.org/10.7494/csci.2000.2.0.3580
Saxena S, Singh RK. A survey of recent and classical image registration methods. Int J Sig Proc Image Process Pattern Recog. 2014;7(4):167–76. https://doi.org/10.14257/ijsip.2014.7.4.16
Younes L. Shapes and diffeomorphisms. Berlin: Springer; 2010. https://doi.org/10.1007/978-3-642-12055-8
Hill DL, Batchelor PG, Holden M, Hawkes DJ. Medical image registration. Phy Med Biol. 2001;46(3):R1. https://doi.org/10.1088/0031-9155/46/3/201
Kotsas P, Dodd T. Rigid registration of medical images using 1D and 2D binary projections. J Dig Imag. 2011;24(5):913–925. https://doi.org/10.1007/s10278-010-9352-z
Goshtasby AA. 2-D and 3-D image registration: for medical, remote sensing, and industrial applications. John Wiley & Sons; 2005.
Knaan D, Joskowicz L. Effective intensity-based 2D/3D rigid registration between fluoroscopic X-ray and CT. Med Image Computi Comput-Assis Interven. 2003;351–358.
Livyatan H, Yaniv Z, Joskowicz L. Gradient-based 2-D/3-D rigid registration of fluoroscopic X-ray to CT. IEEE Transactions on medical imaging. 2003;22(11):1395–406. https://doi.org/10.1109/tmi.2003.819288
Yaniv Z. Rigid registration. Image-Guid Interven. 2008:159–92. https://doi.org/10.1007/978-0-387-73858-1_6
Jenkinson M, Smith S. A global optimisation method for robust affine registration of brain images. Med Image Anal. 2001;5(2):143–56. https://doi.org/10.1016/s1361-8415(01)00036-6
Modersitzki J. FAIR: Flexible algorithms for image registration. Society for Industrial and Applied Mathematics; 2009.
Denton ER, Sonoda LI, Rueckert D, et al. Comparison and evaluation of rigid, affine, and nonrigid registration of breast MR images. J Comput Assist Tomo. 1999;23(5):800–805. https://doi.org/10.1097/00004728-199909000-00031
Abdel-All NH, Abdel-Razek MA, Abdel-Aziz HS, Khalil AA. Geometry of evolving plane curves problem via lie group analysis. Stud Math Sci. 2011;2(1):51–62.
Chong EK, Zak SH. An introduction to optimization. John Wiley & Sons; 2013.
Mirjalili S, Lewis A. The whale optimization algorithm. Adv Eng Soft. 2016;95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Kirmani SK, Jamil RN. Optimization of complex geometry using tenth order partial differential equation. Sci Inq Rev. 2018;2(2):23–31. https://doi.org/10.32350/sir/22/020203
Inc. The MathWorks. Optimization Math Toolbox: https://au.mathworks.com/help/optim/ug/lsqnonlin.html?searchHighlight=lsqnonlin&stid=srchtitle . Natick, Massachusetts, United State, 2020.
Rashid M, Iqbal MA, Noor NA. DFT-mBJ study of electronic and magnetic properties of cubic CeCrO3 compound: an ab-initio investigation. Sci Inq Rev. 2017;1(1):27–36. https://doi.org/10.32350/sir/11/010104
Iqbal MA, Erum N. Opto-Electronic investigation of rubidium based Fluoro-Perovskite for Low Birefringent Lens Materials. Sci Inq Rev. 2017;1(1):37–48. https://doi.org/10.32350/sir/11/010105
Copyright (c) 2023 Muhammad Yousuf Tufail
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.