Abstract
The problem of robust alignment of batches of images can be formulated as a low-rank matrix optimization problem, relying on the similarity of well-aligned images. Going further, observing that the images to be aligned are sampled from a union of low-rank subspaces, we propose a new method based on subspace recovery techniques to provide more robust and accurate alignment. The proposed method seeks a set of domain transformations which are applied to the unaligned images so that the resulting images are made as similar as possible. The resulting optimization problem can be linearized as a series of convex optimization problems which can be solved by alternative sparsity pursuit techniques. Compared to existing methods like robust alignment by sparse and low-rank models, the proposed method can more effectively solve the batch image alignment problem, and extract more similar structures from the misaligned images.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Frey, B. J.; Jojic, N. Transformation-invariant clustering using the EM algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 25, No. 1, 1–17, 2003.
Pluim, J. P. W.; Maintz, J. B. A.; Viergever, M. A. Mutual-information-based registration of medical images: A survey. IEEE Transactions on Medical Imaging Vol. 22, No. 8, 986–1004, 2003.
Peng, Y.; Ganesh, A.; Wright, J.; Xu, W.; Ma, Y. RASL: Robust alignment by sparse and lowrank decomposition for linearly correlated images. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 34, No. 11, 2233–2246, 2012.
Candès, E. J.; Li, X.; Ma, Y.; Wright, J. Robust principal component analysis? Journal of the ACM Vol. 58, No. 3, Article No. 11, 2011.
Liu, G.; Lin, Z.; Yan, S.; Sun, J.; Yu, Y.; Ma, Y. Robust recovery of subspace structures by lowrank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 35, No. 1, 171–184, 2013.
Elhamifar, E.; Vidal, R. Sparse subspace clustering. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2790–2797, 2009.
Bian, X.; Krim, H. BI-sparsity pursuit for robust subspace recovery. In: Proceedings of the IEEE International Conference on Image Processing, 3535–3539, 2015.
Rubinstein, R.; Faktor, T.; Elad, M. K-SVD dictionary-learning for the analysis sparse model. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 5405–5408, 2012.
Bian, X.; Krim, H. Robust subspace recovery via bi-sparsity pursuit. arXiv preprint arXiv:1403.8067, 2014.
Elad, M. Sparse and redundant representation modeling—What next? IEEE Signal Processing Letters Vol. 19, No. 12, 922–928, 2012.
Wright, J.; Yang, A. Y.; Ganesh, A.; Sastry, S. S.; Ma, Y. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 31, No. 2, 210–227, 2009.
Candès, E. J.; Romberg, J. K.; Tao, T. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics Vol. 59, No. 8, 1207–1223, 2006.
Donoho, D. L. For most large underdetermined systems of linear equations the minimal l 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics Vol. 59, No. 6, 797–829, 2006.
Ma, Y.; Soatto, S.; Kosecka, J.; Sastry, S. S. An Invitation to 3-D Vision: From Images to Geometric Models, Volume 26. Springer Science & Business Media, 2012.
Baker, S.; Matthews, I. Lucas–Kanade 20 years on: A unifying framework. International Journal of Computer Vision Vol. 56, No. 3, 221–255, 2004.
Vedaldi, A.; Guidi, G.; Soatto, S. Joint data alignment up to (lossy) transformations. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1–8, 2008.
Boyd, S.; Parikh, N.; Chu, E.; Peleato, B.; Eckstein, J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends R in Machine Learning Vol. 3, No. 1, 1–122, 2011.
Liu, G.; Lin, Z.; Yu, Y. Robust subspace segmentation by low-rank representation. In: Proceedings of the 27th International Conference on Machine Learning, 663–670, 2010.
Rockafellar, R. T. Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM Journal on Control Vol. 12, No. 2, 268–285, 1974.
Lin, Z.; Liu, R.; Su, Z. Linearized alternating direction method with adaptive penalty for low-rank representation. In: Proceedings of the Advances in Neural Information Processing Systems 24, 612–620, 2011.
Huang, G. B.; Ramesh, M.; Berg, T.; Learned-Miller, E. Labeled faces in the wild: A database for studying face recognition in unconstrained environments. Technical Report 07-49, University of Massachusetts, Amherst, 2007.
Hore, A.; Ziou, D. Image quality metrics: PSNR vs. SSIM. In: Proceedings of the 20th International Conference on Pattern Recognition, 2366–2369, 2010.
Wang, Z.; Bovik, A. C.; Sheikh, H. R.; Simoncelli, E. P. Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing Vol. 13, No. 4, 600–612, 2004.
LeCun, Y.; Cortes, C.; Burges, C. J. C. The MNIST database of handwritten digits. 2010. Available at http://yann.lecun.com/exdb/mnist.
Acknowledgements
This work was partly supported by the National Natural Science Foundation of China (Grant Nos. 61573150, 61573152, 61370185, 61403085, and 51275094), and Guangzhou Project Nos. 201604016113 and 201604046018.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is published with open access at Springerlink.com
Xianhui Lin received his bachelor degree in automation from South China Agricultural University, Guangzhou, China, in 2014. He is now a master candidate supervised by Prof. Zhu Liang Yu in the College of Automation Science and Engineering, South China University of Technology. His research interests include machine learning and computer vision.
Zhu Liang Yu received his B.S.E.E. and M.S.E.E. degrees, both in electronic engineering, from Nanjing University of Aeronautics and Astronautics, China, in 1995 and 1998, respectively, and his Ph.D. degree from Nanyang Technological University, Singapore, in 2006. He joined the Center for Signal Processing, Nanyang Technological University, in 2000 as a research engineer, then had been a group leader from 2001. In 2008, he joined the College of Automation Science and Engineering, South China University of Technology and was promoted to full professor in 2010. His research interests include signal processing, pattern recognition, machine learning and their applications in communications, biomedical engineering, robotics, etc.
Zhenghui Gu received her Ph.D. degree from Nanyang Technological University in 2003. From 2002 to 2008, she was with the Institute for Infocomm Research, Singapore. She joined the College of Automation Science and Engineering, South China University of Technology, in 2009 as an associate professor. She was promoted to full professor in 2015. Her research interests include signal processing and pattern recognition.
Jun Zhang received his bachelor and master degrees in computer science from Xiangtan University, Xiangtan, China, in 2002 and 2005, respectively, and his doctor degree in pattern recognition and intelligent systems from South China University of Technology, China, in 2012. He was a postdoctoral research fellow in electronic engineering with the University of South California, Los Angeles, USA, from 2015 to 2016. He is currently an associate professor with the School of Information Engineering, Guangdong University of Technology, Guangzhou, China, where he has been the head of the Electrical Engineering Department since March 2016. His current research interests include compressive sensing and biomedical signal processing.
Zhaoquan Cai was born in 1970. He received his bachelor degree from South China University of Technology, Guangzhou, and master degree from Huazhong University of Science and Technology, Wuhan, China. He is now a professor in the School of Computer Science, Huizhou University, and also a member of CCF. His research interests include computer networks, intelligent computing, and databases.
Rights and permissions
Open Access The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Other papers from this open access journal are available free of charge from http://www.springer.com/journal/41095. To submit a manuscript, please go to https://www.editorialmanager.com/cvmj.
About this article
Cite this article
Lin, X., Yu, Z.L., Gu, Z. et al. Batch image alignment via subspace recovery based on alternative sparsity pursuit. Comp. Visual Media 3, 295–304 (2017). https://doi.org/10.1007/s41095-017-0080-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41095-017-0080-x