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Volume 8 Issue 5
May  2021

IEEE/CAA Journal of Automatica Sinica

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Chengcai Leng, Hai Zhang, Guorong Cai, Zhen Chen and Anup Basu, "Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1025-1037, May 2021. doi: 10.1109/JAS.2021.1003979
Citation: Chengcai Leng, Hai Zhang, Guorong Cai, Zhen Chen and Anup Basu, "Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1025-1037, May 2021. doi: 10.1109/JAS.2021.1003979

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

doi: 10.1109/JAS.2021.1003979
Funds:  This work was supported by the National Natural Science Foundation of China (61702251, 41971424, 61701191, U1605254), the Natural Science Basic Research Plan in Shaanxi Province of China (2018JM6030), the Key Technical Project of Fujian Province (2017H6015), the Science and Technology Project of Xiamen (3502Z20183032), the Doctor Scientific Research Starting Foundation of Northwest University (338050050), Youth Academic Talent Support Program of Northwest University (360051900151), and the Natural Sciences and Engineering Research Council of Canada, Canada
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  • This paper presents a novel medical image registration algorithm named total variation constrained graph-regularization for non-negative matrix factorization (TV-GNMF). The method utilizes non-negative matrix factorization by total variation constraint and graph regularization. The main contributions of our work are the following. First, total variation is incorporated into NMF to control the diffusion speed. The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information. Second, we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power. Third, the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given. Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

     

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  • [1]
    D. D. Yu, F. Yang, C. Y. Yang, C. C. Leng, J. Cao, Y. N. Wang, and J. Tian, “Fast rotation-free feature-based image registration using improved N-SIFT and GMM-based parallel optimization,” IEEE Trans. Biomed. Eng., vol. 63, no. 8, pp. 1653–1664, Aug. 2016. doi: 10.1109/TBME.2015.2465855
    [2]
    A. A. Goshtasby, 2D and 3D Image Registration: For Medical, Remote Sensing, and Industrial Applications. Hoboken, USA: John Wiley & Sons, Inc., 2005.
    [3]
    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. doi: 10.1109/TMI.2013.2265603
    [4]
    C. C. Leng, J. J. Xiao, M. Li, and H. P. Zhang, “Robust adaptive principal component analysis based on intergraph matrix for medical image registration,” Comput. Intell. Neurosci., vol. 2015, Article No. 829528, Apr. 2015.
    [5]
    M. G. Gong, S. M. Zhao, L. C. Jiao, D. Y. Tian, and S. Wang, “A novel coarse-to-fine scheme for automatic image registration based on SIFT and mutual information,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 7, pp. 4328–4338, Jul. 2014. doi: 10.1109/TGRS.2013.2281391
    [6]
    J. Woo, M. Stone, and J. L. Prince, “Multimodal registration via mutual information incorporating geometric and spatial context,” IEEE Trans. Image Process., vol. 24, no. 2, pp. 757–769, Feb. 2015. doi: 10.1109/TIP.2014.2387019
    [7]
    D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vision, vol. 60, no. 2, pp. 91–110, Nov. 2004. doi: 10.1023/B:VISI.0000029664.99615.94
    [8]
    B. Rister, M. A. Horowitz, and D. L. Rubin, “Volumetric image registration from invariant keypoints,” IEEE Trans. Image Process., vol. 26, no. 10, pp. 4900–4910, Oct. 2017. doi: 10.1109/TIP.2017.2722689
    [9]
    F. R. K. Chung, Spectral Graph Theory. Providence, USA: American Mathematical Society, 1997.
    [10]
    A. K. Bhandari, A. Ghosh, and I. V. Kumar, “A local contrast fusion based 3D Otsu algorithm for multilevel image segmentation,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 200–213, Jan. 2020. doi: 10.1109/JAS.2019.1911843
    [11]
    L. He, N. Ray, Y. S. Guan, and H. Zhang, “Fast large-scale spectral clustering via explicit feature mapping,” IEEE Trans. Cybern., vol. 49, no. 3, pp. 1058–1071, Mar. 2019. doi: 10.1109/TCYB.2018.2794998
    [12]
    C. C. Leng, W. Xu, I. Cheng, and A. Basu, “Graph matching based on stochastic perturbation,” IEEE Trans. Image Process., vol. 24, no. 12, pp. 4862–4875, Dec. 2015. doi: 10.1109/TIP.2015.2469153
    [13]
    J. Tang, L. Shao, X. L. Li, and K. Lu, “A local structural descriptor for image matching via normalized graph Laplacian embedding,” IEEE Trans. Cybern., vol. 46, no. 2, pp. 410–420, Feb. 2016. doi: 10.1109/TCYB.2015.2402751
    [14]
    X. Yang and Z. Y. Liu, “Adaptive graph matching,” IEEE Trans. Cybern., vol. 48, no. 5, pp. 1432–1445, May 2018. doi: 10.1109/TCYB.2017.2697968
    [15]
    J. C. Yan, C. S. Li, Y. Li, and G. T. Cao, “Adaptive discrete hypergraph matching,” IEEE Trans. Cybern., vol. 48, no. 2, pp. 765–779, Feb. 2018. doi: 10.1109/TCYB.2017.2655538
    [16]
    J. Y. Ma, J. Zhao, J. W. Tian, A. L. Yuille, and Z. W. Tu, “Robust point matching via vector field consensus,” IEEE Trans. Image Process., vol. 23, no. 4, pp. 1706–1721, Apr. 2014. doi: 10.1109/TIP.2014.2307478
    [17]
    J. Chen, J. Y. Ma, C. C. Yang, L. Ma, and S. Zheng, “Non-rigid point set registration via coherent spatial mapping,” Signal Process., vol. 106, pp. 62–72, Jan. 2015. doi: 10.1016/j.sigpro.2014.07.004
    [18]
    J. Y. Ma, J. Zhao, and A. L. Yuille, “Non-rigid point set registration by preserving global and local structures,” IEEE Trans. Image Process., vol. 25, no. 1, pp. 53–64, Jan. 2016. doi: 10.1109/TIP.2015.2467217
    [19]
    J. Y. Ma, J. J. Jiang, H. B. Zhou, J. Zhao, and X. J. Guo, “Guided locality preserving feature matching for remote sensing image registration,” IEEE Trans. Geosci. Remote Sens., vol. 56, no. 8, pp. 4435–4447, Aug. 2018. doi: 10.1109/TGRS.2018.2820040
    [20]
    J. Y. Ma, J. Zhao, J. J. Jiang, H. B. Zhou, and X. J. Guo, “Locality preserving matching,” Int. J. Comput. Vision, vol. 127, no. 5, pp. 512–531, May. 2019. doi: 10.1007/s11263-018-1117-z
    [21]
    H. C. Chen, X. Zhang, S. Y. Du, Z. Z. Wu, and N. N. Zheng, “A correntropy-based affine iterative closest point algorithm for robust point set registration,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 981–991, Jul. 2019. doi: 10.1109/JAS.2019.1911579
    [22]
    L. Xu and I. King, “A PCA approach for fast retrieval of structural patterns in attributed graphs,” IEEE Trans. Syst.,Man,Cybern.,Part B:Cybern., vol. 31, no. 5, pp. 812–817, Oct. 2001. doi: 10.1109/3477.956043
    [23]
    T. Caelli and S. Kosinov, “An eigenspace projection clustering method for inexact graph matching,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 4, pp. 515–519, Apr. 2004. doi: 10.1109/TPAMI.2004.1265866
    [24]
    M. Xu, H. Chen, and P. K. Varshney, “Dimensionality reduction for registration of high-dimensional data sets,” IEEE Trans. Image Process., vol. 22, no. 8, pp. 3041–3049, Aug. 2013. doi: 10.1109/TIP.2013.2253480
    [25]
    C. C. Leng, H. Zhang, G. R. Cai, I. Cheng, and A. Basu, “Graph regularized Lp smooth non-negative matrix factorization for data representation,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 584–595, Mar. 2019. doi: 10.1109/JAS.2019.1911417
    [26]
    J. B. Tenenbaum, V. de Silva, and J. C. Langford, “A global geometric framework for nonlinear dimensionality reduction,” Science, vol. 290, no. 5500, pp. 2319–2323, Dec. 2000. doi: 10.1126/science.290.5500.2319
    [27]
    S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science, vol. 290, no. 5500, pp. 2323–2326, Dec. 2000. doi: 10.1126/science.290.5500.2323
    [28]
    M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” in Proc. 14th Int. Conf. Neural Information Processing Systems, Cambridge, USA, 2001, pp. 585–591.
    [29]
    D. Cai, X. F. He, and J. W. Han, “Isometric projection,” in Proc. 22nd AAAI Conf. Artificial Intelligence, Vancouver, Canada, 2007, pp. 528–533.
    [30]
    S. P. Liu, Y. T. Xian, H. F. Li, and Z. T. Yu, “Text detection in natural scene images using morphological component analysis and Laplacian dictionary,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 214–222, Jan. 2020.
    [31]
    R. He, T. N. Tan, and L. Wang, “Robust recovery of corrupted low-rank matrix by implicit regularizers,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 36, no. 4, pp. 770–783, Apr. 2014. doi: 10.1109/TPAMI.2013.188
    [32]
    D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature, vol. 401, no. 6755, pp. 788–791, Oct. 1999. doi: 10.1038/44565
    [33]
    W. Xu, X. Liu, and Y. H. Gong, “Document clustering based on non-negative matrix factorization,” in Proc. 26th Annu. Int. ACM SIGIR Conf. Research and Development in Information Retrieval, Toronto, Canada, 2003, pp. 267–273.
    [34]
    F. Shahnaz, M. W. Berry, V. Pauca, and R. J. Plemmons, “Document clustering using nonnegative matrix factorization,” Inf. Process. Manage., vol. 42, no. 2, pp. 373–386, 2006. doi: 10.1016/j.ipm.2004.11.005
    [35]
    H. F. Liu, Z. H. Wu, X. L. Li, D. Cai, and T. S. Huang, “Constrained nonnegative matrix factorization for image representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 34, no. 7, pp. 1299–1311, Jul. 2012. doi: 10.1109/TPAMI.2011.217
    [36]
    D. Wang, X. B. Gao, and X. M. Wang, “Semi-supervised nonnegative matrix factorization via constraint propagation,” IEEE Trans. Cybern., vol. 46, no. 1, pp. 233–244, Jan. 2016. doi: 10.1109/TCYB.2015.2399533
    [37]
    D. Cai, X. F. He, J. W. Han, and T. S. Huang, “Graph regularized nonnegative matrix factorization for data representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 8, pp. 1548–1560, Aug. 2011. doi: 10.1109/TPAMI.2010.231
    [38]
    X. Luo, M. C. Zhou, H. Leung, Y. N. Xia, Q. S. Zhu, Z. H. You, and S. Li, “An incremental-and-static-combined scheme for matrix-factorization- based collaborative filtering,” IEEE Trans. Autom. Sci. Eng., vol. 13, no. 1, pp. 333–343, Jan. 2016. doi: 10.1109/TASE.2014.2348555
    [39]
    X. L. Li, G. S. Cui, and Y. S. Dong, “Graph regularized non-negative low-rank matrix factorization for image clustering,” IEEE Trans. Cybern., vol. 47, no. 11, pp. 3840–3853, Nov. 2017. doi: 10.1109/TCYB.2016.2585355
    [40]
    R. H. Shang, W. B. Wang, R. Stolkin, and L. C. Jiao, “Non-negative spectral learning and sparse regression-based dual-graph regularized feature selection,” IEEE Trans. Cybern., vol. 48, no. 2, pp. 793–806, Feb. 2018. doi: 10.1109/TCYB.2017.2657007
    [41]
    A. Ghaffari and E. Fatemizadeh, “Image registration based on low rank matrix: Rank-regularized SSD,” IEEE Trans. Med. Imaging, vol. 37, no. 1, pp. 138–150, Jan. 2018. doi: 10.1109/TMI.2017.2744663
    [42]
    M. S. Shang, X. Luo, Z. G. Liu, J. Chen, Y. Yuan, and M. C. Zhou, “Randomized latent factor model for high-dimensional and sparse matrices from industrial applications,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 131–141, Jan. 2019. doi: 10.1109/JAS.2018.7511189
    [43]
    X. Luo, Z. G. Liu, S. Li, M. S. Shang, and Z. D. Wang, “A fast non-negative latent factor model based on generalized momentum method,” IEEE Trans. Syst.,Man,Cybern.:Syst., vol. 51, no. 1, pp. 610–620, Jan. 2021. doi: 10.1109/TSMC.2018.2875452
    [44]
    X. Luo, M. C. Zhou, S. Li, L. Hu, and M. S. Shang, “Non-negativity constrained missing data estimation for high-dimensional and sparse matrices from industrial applications,” IEEE Trans. Cybern., vol. 50, no. 5, pp. 1844–1855, May 2020. doi: 10.1109/TCYB.2019.2894283
    [45]
    D. Wu, Q. He, X. Luo, M. S. Shang, Y. He, and G. Y. Wang, “A posterior-neighborhood-regularized latent factor model for highly accurate web service QoS prediction, ” IEEE Trans. Serv. Comput., to be published. DOI: 10.1109/TSC.2019.2961895
    [46]
    X. Luo, Z. D. Wang, and M. S. Shang, “An instance-frequency-weighted regularization scheme for non-negative latent factor analysis on high-dimensional and sparse data,” IEEE Trans. Syst., Man, Cybern.: Syst., to be published. DOI: 10.1109/TSMC.2019.2930525
    [47]
    L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D:Nonlinear Phenom., vol. 60, no. 1-4, pp. 259–268, Nov. 1992. doi: 10.1016/0167-2789(92)90242-F
    [48]
    W. He, H. Y. Zhang, and L. P. Zhang, “Total variation regularized reweighted sparse nonnegative matrix factorization for hyperspectral unmixing,” IEEE Trans. Geosci. Remote Sens., vol. 55, no. 7, pp. 3909–3921, Jul. 2017. doi: 10.1109/TGRS.2017.2683719
    [49]
    L. Tong, B. Qian, J. Yu, and C. B. Xiao, “Spectral and spatial total-variation-regularized multilayer non-negative matrix factorization for hyperspectral unmixing,” J. Appl. Remote Sens., vol. 13, no. 3, Article No. 036510, Sep. 2019.
    [50]
    Y. Yuan, Z. H. Zhang, and Q. Wang, “Improved collaborative non-negative matrix factorization and total variation for hyperspectral unmixing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 13, pp. 998–1010, Mar. 2020. doi: 10.1109/JSTARS.2020.2977399
    [51]
    C. C. Leng, G. R. Cai, D. D. Yu, and Z. Y. Wang, “Adaptive total-variation for non-negative matrix factorization on manifold,” Pattern Recognit. Lett., vol. 98, pp. 68–74, Oct. 2017. doi: 10.1016/j.patrec.2017.08.027
    [52]
    H. L. Zhang, L. M. Tang, Z. Fang, C. C. Xiang, and C. Y. Li, “Nonconvex and nonsmooth total generalized variation model for image restoration,” Signal Process., vol. 143, pp. 69–85, Feb. 2018. doi: 10.1016/j.sigpro.2017.08.021
    [53]
    W. D. Zhao, H. M. Lu, and D. Wang, “Multisensor image fusion and enhancement in spectral total variation domain,” IEEE Trans. Multimed., vol. 20, no. 4, pp. 866–879, Apr. 2018. doi: 10.1109/TMM.2017.2760100
    [54]
    F. X. Yang, F. Ma, Z. L. Ping, and G. X. Xu, “Total variation and signature-based regularizations on coupled nonnegative matrix factorization for data fusion,” IEEE Access, vol. 7, pp. 2695–2706, Nov. 2018.
    [55]
    T. P. Zhang, B. Fang, Y. Y. Tang, G. H. He, and J. Wen, “Topology preserving non-negative matrix factorization for face recognition,” IEEE Trans. Image Process., vol. 17, no. 4, pp. 574–584, Apr. 2008. doi: 10.1109/TIP.2008.918957
    [56]
    H. Q. Yin and H. W. Liu, “Nonnegative matrix factorization with bounded total variational regularization for face recognition,” Pattern Recognit. Lett., vol. 31, no. 16, pp. 2468–2473, Dec. 2010. doi: 10.1016/j.patrec.2010.08.001
    [57]
    C. C. Leng, Z. Chen, G. R. Cai, I. Cheng, Z. H. Xiong, J. Tian, and A. Basu, “Total variation constrained graph regularized NMF for medical image registration,” in Proc. the 12th IEEE Image, Video, and Multidimensional Signal Processing Workshop, Bordeaux, France, 2016, pp. 1–5.
    [58]
    P. Paatero and U. Tapper, “Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values,” Environmetrics, vol. 5, no. 2, pp. 111–126, Jun. 1994. doi: 10.1002/env.3170050203
    [59]
    D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Proc. 13th Int. Conf. Neural Information Processing Systems, Denver, USA, 2000, pp. 556–562.
    [60]
    D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Prob., vol. 19, no. 6, pp. S165–S187, Nov. 2003. doi: 10.1088/0266-5611/19/6/059
    [61]
    A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Roy. Stat. Soc.:Ser. B (Methodol.), vol. 39, no. 1, pp. 1–22, 1977.
    [62]
    D. Cai, X. He, and J. Han, “Document clustering using locality preserving indexing,” IEEE Trans. Knowl. Data Eng., vol. 17, no. 12, pp. 1624–1637, Dec. 2005. doi: 10.1109/TKDE.2005.198
    [63]
    R. Zass and A. Shashua, “Probabilistic graph and hypergraph matching,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition, Anchorage, USA, 2008, pp. 1221–1228.
    [64]
    C. Harris and M. Stephens, “A combined corner and edge detector,” in Proc. 4th Alvey Vision Conf., Manchester, UK, 1988, pp. 147–151.
    [65]
    A. Myronenko and X. B. Song, “Point set registration: Coherent point drift,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 12, pp. 2262–2275, Dec. 2010. doi: 10.1109/TPAMI.2010.46
    [66]
    C. C. Leng, H. Zhang, G. R. Cai, Z. Chen, and A. Basu. “Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration,” [Online]. Available: http://biomedic.doc.ic.ac.uk/brain-development/index.php?n=Main.Datasets, Accessed on: May 26, 2020.

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    Highlights

    • This paper presents a novel image registration algorithm named Total Variation constrained Graph-regularization for Non-negative Matrix Factorization (TV-GNMF).
    • Total variation is incorporated into NMF to denoise in smooth regions and preserve the features or details of data in edge regions.
    • Graph regularization is added into NMF to reveal intrinsic geometry and structure information of data to enhance the discrimination power.
    • The multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.
    • Experimental results show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

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