Image Registration Based on Sum of Square Difference Cost Function

Document Type: Research Paper

Authors

1 Faculty of Electrical Engineering, Shahid Rajaee Teacher Training University, P.O.Box:16785-163, Tehran, Iran.

2 Electronic Department, Shahid Rajaee Teacher Training University

3 SRTTU

10.22061/jecei.2019.5544.235

Abstract

There are numerous applications for image registration (IR). The main purpose of the IR is to find a map between two different situation images. In this way, the main objective is to find this map to reconstruct the target image as optimum as possible. Needless to say, the IR task is an optimization problem. As the optimization method, although the evolutionary ones are sometimes more effective in escaping the local minima, their speed is not emulated the mathematical ones at all. In this paper, we employed a mathematical framework based on the Newton method. This framework is suitable for any efficient cost function. Yet we used the sum of square difference (SSD). We also provided an effective strategy in order to avoid sticking in the local minima. As one of the fundamental drawback of mathematical-based optimization methods, local minima have been managed properly by our new strategy. Scale and rotation – as two variables of the problem- have been treated solely in a different iteration. In other words, in every iteration, one of these variables is actually the only variable of the problem as the other one is considered constant. Simulation results indicate the effectiveness of the proposed model.

Graphical Abstract

Image Registration Based on Sum of Square Difference Cost Function

Keywords

Main Subjects


[1] J. Fan, X. Cao, P.-T. Yap, and D. Shen, “BIRNet: Brain image registration using dual-supervised fully convolutional networks,” Med. Image Anal., vol. 54, pp. 193–206, May 2019. [2] M. Moradi and M. Sadeghi, “Combining and steganography of 3-D face textures,” J. Electr. Comput. Eng. Innov., vol. 5, no. 2, pp. 93–100, 2017. [3] R. Nain and N. Kumar, “Medical image registration by GSA optimized matching algorithm,” Int. J. Curr. Eng. Technol., vol. 6, no. 2, pp. 472–476, 2016. [4] Z. Xu et al., “Rigid motion correction for magnetic resonance fingerprinting with sliding-window reconstruction and image registration,” Magn. Reson. Imaging, vol. 57, pp. 303–312, Apr. 2019. [5] G. C. S. Ruppert et al., “Medical image registration based on watershed transform from greyscale marker and multi-scale parameter search,” Comput. Methods Biomech. Biomed. Eng. Imaging Vis., vol. 5, no. 2, pp. 138–156, Mar. 2017. [6] R. Panda, S. Agrawal, M. Sahoo, and R. Nayak, “A novel evolutionary rigid body docking algorithm for medical image registration,” Swarm Evol. Comput., vol. 33, pp. 108–118, Apr. 2017. [7] B. Haghighi, N. D. Ellingwood, Y. Yin, E. A. Hoffman, and C. L. Lin, “A GPU-based symmetric non-rigid image registration method in human lung,” Med. Biol. Eng. Comput., vol. 56, no. 3, pp. 355–371, Mar. 2018. [8] A. Sotiras, C. Davatzikos, and N. Paragios, “Deformable medical image registration: a survey,” IEEE Trans. Med. Imaging, vol. 32, no. 7, pp. 1153–1190, Jul. 2013. [9] H. Yu et al., “Learning 3D non-rigid deformation based on an unsupervised deep learning for PET/CT image registration,” presented at The Biomedical Applications in Molecular, Structural, and Functional Imaging, California, United States, 2019. [10] A. Valsecchi, S. Damas, and J. Santamaria, “Evolutionary intensity-based medical image registration: a review,” Curr. Med. Imaging Rev., vol. 9, no. 4, pp. 283–297, Jan. 2014. [11] E. Castillo, “Quadratic penalty method for intensity‐based deformable image registration and 4DCT lung motion recovery,” Med. Phys., vol. 46, no. 5, pp. 2194–2203, May 2019. [12] L. Han, H. Dong, J. R. McClelland, L. Han, D. J. Hawkes, and D. C. Barratt, “A hybrid patient-specific biomechanical model based image registration method for the motion estimation of lungs,” Med. Image Anal., vol. 39, pp. 87–100, July 2017. [13] O. Lobachev, C. Ulrich, B. S. Steiniger, V. Wilhelmi, V. Stachniss, and M. Guthe, “Feature-based multi-resolution registration of immunostained serial sections,” Med. Image Anal., vol. 35, pp. 288–302, Jan. 2017. [14] J. Li, Q. Hu, and M. Ai, “Robust feature matching for remote sensing image registration based on LQ-estimator,” IEEE Geosci. Remote Sens. Lett., vol. 13, no. 12, pp. 1989–1993, Dec. 2016. [15] S. Klein, J. P. W. Pluim, M. Staring, and M. A. Viergever, “Adaptive stochastic gradient descent optimisation for image registration,” Int. J. Comput. Vis., vol. 81, no. 3, pp. 227–239, Mar. 2009. [16] Y. Wu, W. Ma, Q. Miao, and S. Wang, “Multimodal continuous ant colony optimization for multisensor remote sensing image registration with local search,” Swarm and Evolutionary Computation, vol. 47, pp. 89-95, June 2019. [17] H. Ismkhan, “Effective heuristics for ant colony optimization to handle large-scale problems,” Swarm Evol. Comput., vol. 32, pp. 140–149, Feb. 2017. [18] F. Ayatollahi, S. B. Shokouhi, and A. Ayatollahi, “A new hybrid particle swarm optimization for multimodal brain image registration,” J. Biomed. Sci. Eng., vol. 05, no. 04, pp. 153–161, 2012. [19] Behravan, SH. Zahiri, SM. Razavi, "Clustering a Big Mobility Dataset Using an Automatic Swarm Intelligence-Based Clustering Method," J. Electr. Comput. Eng. Innov., vol. 6, no. 2, pp. 243-261, 2019. [20] S. Elhag, A. Fernández, A. Bawakid, S. Alshomrani, and F. Herrera, “On the combination of genetic fuzzy systems and pairwise learning for improving detection rates on Intrusion Detection Systems,” Expert Syst. Appl., vol. 42, no. 1, pp. 193–202, Jan. 2015. [21] A. Mang and G. Biros, “A semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registration,” SIAM J. Sci. Comput., vol. 39, no. 6, pp. B1064–B1101, Jan. 2017. [22] S. Ying, D. Li, B. Xiao, Y. Peng, S. Du, and M. Xu, “Nonlinear image registration with bidirectional metric and reciprocal regularization,” PLoS One, vol. 12, no. 2, pp. 1–19, 2017. [23] K. Chen, G. N. Grapiglia, J. Yuan, and D. Zhang, “Improved optimization methods for image registration problems,” Numer. Algorithms, vol. 80, no. 2, pp. 305–336, Feb. 2019. [24] E. Ferrante and N. Paragios, “Slice-to-volume medical image registration: A survey,” Med. Image Anal., vol. 39, pp. 101–123, Jul. 2017. [25] S. Klein, M. Staring, and J. P. W. Pluim, “Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines,” IEEE Trans. Image Process., vol. 16, no. 12, pp. 2879–2890, Dec. 2007. [26] S. Etemadi, M. Saadatmand-Tarzjan, M. Shamirzaei, and J. Khosravi, “An efficient 3D gradient-based algorithm for medical image registration using correlation-coefficient maximization,” in Proc. 4th International Conference on Computer and Knowledge Engineering (ICCKE), pp. 663–668, 2014. [27] J. Le Moigne, W. J. Campbell, and R. F. Cromp, “An automated parallel image registration technique based on the correlation of wavelet features,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 8, pp. 1849–1864, Aug. 2002. [28] K. Yang, A. Pan, Y. Yang, S. Zhang, S. Ong, and H. Tang, “Remote sensing image registration using multiple image features,” Remote Sens., vol. 9, no. 6, p. 581, Jun. 2017. [29] Y. Qiao, B. P. F. Lelieveldt, and M. Staring, “An efficient preconditioner for stochastic gradient descent optimization of image registration,” IEEE Trans. Med. Imaging, vol. 9, pp. 10–19, 2019. [30] J. Zhang, G. Chen, and Z. Jia, “An image stitching algorithm based on histogram matching and sift algorithm,” Int. J. Pattern Recognit. Artif. Intell., vol. 31, no. 04, pp. 1754006-2–14, Apr. 2017. [31] H. Jagadish and J. Prakash, “Adaptive Markov random field model for area based image registration and change detection,” Int. J. Appl. or Innov. Eng. Manag., vol. 6, no. 4, pp. 50–58, 2017. [32] Y. Li, C. Chen, Fei Yang, and J. Huang, “Deep sparse representation for robust image registration,” in Proc. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4894–4901, 2015. [33] F. Maes, D. Vandermeulen, and P. Suetens, “Comparative evaluation of multiresolution optimization strategies for multimodality image registration by maximization of mutual information,” Med. Image Anal., vol. 3, no. 4, pp. 373–386, Dec. 1999. [34] E. Vural and P. Frossard, “Analysis of descent-based image registration,” SIAM J. Imaging Sci., vol. 6, no. 4, pp. 2310–2349, Jan. 2013. [35] Y. Qiao, B. van Lew, B. P. F. Lelieveldt, and M. Staring, “Fast automatic step size estimation for gradient descent optimization of image registration,” IEEE Trans. Med. Imaging, vol. 35, no. 2, pp. 391–403, Feb. 2016. [36] M. Unser and P. Thevenaz, “Optimization of mutual information for multiresolution image registration,” IEEE Trans. Image Process., vol. 9, no. 12, pp. 2083–2099, 2000. [37] J. Dong, K. Lu, J. Xue, S. Dai, R. Zhai, and W. Pan, “Accelerated nonrigid image registration using improved Levenberg–Marquardt method,” Inf. Sci. (Ny)., vol. 423, pp. 66–79, Jan. 2018.