The DOI matches its Crossref record; 47 of the 47 references it cites were found in a registry or an index.
RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images
Abstract
This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. We reduce this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of l1-norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques. We verify the efficacy of the proposed robust alignment algorithm with extensive experiments on both controlled and uncontrolled real data, demonstrating higher accuracy and efficiency than existing methods over a wide range of realistic misalignments and corruptions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Robust Real-Time Face Detection
Viola, P., & Jones, M. J. (2004) · International Journal of Computer Vision · doi:10.1023/b:visi.0000013087.49260.fb · Cited by 14,097
Robust Face Recognition via Sparse Representation
Wright, J., Yang, A. Y., Ganesh, A., Sastry, S. S., & Ma, Y. (2009) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.79 · Cited by 9,388
Self-citationRobust principal component analysis?
Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011) · Journal of the ACM · doi:10.1145/1970392.1970395 · Cited by 6,921
Self-citationA Singular Value Thresholding Algorithm for Matrix Completion
Cai, J.-F., Candès, E. J., & Shen, Z. (2010) · SIAM Journal on Optimization · doi:10.1137/080738970 · Cited by 5,809
Labeled Faces in the Wild: A Database forStudying Face Recognition in Unconstrained Environments
Huang, G. B., Mattar, M., Berg, T. L., & Miller, E. G. (2008) · HAL · Cited by 4,445
A survey of image registration techniques
Brown, L. G. (1992) · ACM Computing Surveys · doi:10.1145/146370.146374 · Cited by 4,057
Halko, N., Martinsson, P. G., & Tropp, J. A. (2011) · SIAM Review · doi:10.1137/090771806 · Cited by 4,002
A survey of medical image registration
Maintz, J. B. A., & Viergever, M. A. (1998) · Medical Image Analysis · doi:10.1016/s1361-8415(01)80026-8 · Cited by 3,327
Lucas-Kanade 20 Years On: A Unifying Framework
Baker, S., & Matthews, I. (2004) · International Journal of Computer Vision · doi:10.1023/b:visi.0000011205.11775.fd · Cited by 3,155
Mutual-information-based registration of medical images: a survey
Pluim, J. P. W., Maintz, J. B. A., & Viergever, M. A. (2003) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2003.815867 · Cited by 2,890
Eckstein, J., & Bertsekas, D. P. (1992) · Mathematical Programming · doi:10.1007/bf01581204 · Cited by 2,791
A dual algorithm for the solution of nonlinear variational problems via finite element approximation
Gabay, D., & Mercier, B. (1976) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(76)90003-1 · Cited by 2,514
Kuybeda, O., Frank, G. A., Bartesaghi, A., Borgnia, M., Subramaniam, S., & Sapiro, G. (2013) · Journal of Structural Biology · doi:10.1016/j.jsb.2012.10.010 · Cited by 2,162
Gross, R., Matthews, I., Cohn, J., Kanade, T., & Baker, S. (2010) · Image and Vision Computing · doi:10.1016/j.imavis.2009.08.002 · Cited by 1,621
Lambertian reflectance and linear subspaces
Basri, R., & Jacobs, D. W. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1177153 · Cited by 1,576
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
Lin, Z., Chen, M., & Ma, Y. (2010) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · doi:10.48550/arxiv.1009.5055 · Cited by 1,176
Self-citationGlowinski, R., & Marroco, A. (1975) · Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique · doi:10.1051/m2an/197509r200411 · Cited by 1,105
Toh, K.-C., & Yun, S. (2009) · National University of Singapore · Cited by 923
Ma, Y., Soatto, S., Košecká, J., & Sastry, S. S. (2004) · Interdisciplinary Applied Mathematics · doi:10.1007/978-0-387-21779-6 · Cited by 893
Self-citationRank-Sparsity Incoherence for Matrix Decomposition
Chandrasekaran, V., Sanghavi, S., Parrilo, P. A., & Willsky, A. S. (2011) · SIAM Journal on Optimization · doi:10.1137/090761793 · Cited by 686
Templates for convex cone problems with applications to sparse signal recovery
Becker, S. R., Candès, E. J., & Grant, M. C. (2011) · Mathematical Programming Computation · doi:10.1007/s12532-011-0029-5 · Cited by 608
A Framework for Robust Subspace Learning
De la Torre, F., & Black, M. J. (2003) · International Journal of Computer Vision · doi:10.1023/a:1023709501986 · Cited by 604
Fazel, M., Hindi, H., & Boyd, S. P. (2004) · Proceedings of the 2003 American Control Conference, 2003. · doi:10.1109/acc.2003.1243393 · Cited by 574
Robust video denoising using low rank matrix completion
Ji, H., Liu, C., Shen, Z., & Xu, Y. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539849 · Cited by 483
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
Tao, M., & Yuan, X. (2011) · SIAM Journal on Optimization · doi:10.1137/100781894 · Cited by 453
Randomized Algorithms for Matrices and Data
MAHONEY, M. (2012) · Chapman & Hall/CRC Data Mining and Knowledge Discovery Series · doi:10.1201/b11822-37 · Cited by 409
Gross, R., Matthews, I., Cohn, J., Kanade, T., & Baker, S. (2008) · 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition · doi:10.1109/afgr.2008.4813399 · Cited by 373
Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming
He, B., Tao, M., & Yuan, X. (2012) · SIAM Journal on Optimization · doi:10.1137/110822347 · Cited by 360
Unsupervised Joint Alignment of Complex Images
Huang, G. B., Jain, V., & Learned-Miller, E. (2007) · 2007 IEEE 11th International Conference on Computer Vision · doi:10.1109/iccv.2007.4408858 · Cited by 339
Lanczos Bidiagonalization With Partial Reorthogonalization
Larsen, R. M. (1998) · DAIMI Report Series · doi:10.7146/dpb.v27i537.7070 · Cited by 304
Data driven image models through continuous joint alignment
Learned-Miller, E. G. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.34 · Cited by 290
TILT: Transform Invariant Low-Rank Textures
Zhang, Z., Ganesh, A., Liang, X., & Ma, Y. (2012) · International Journal of Computer Vision · doi:10.1007/s11263-012-0515-x · Cited by 277
Self-citationRASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images
Peng, Y., Ganesh, A., Wright, J., Xu, W., & Ma, Y. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5540138 · Cited by 242
Self-citationRandomized algorithms for matrices and dataPreprint
Mahoney, M. W. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1104.5557 · Cited by 234
Fast algorithms for recovering a corrupted low-rank matrix
Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., & Ma, Y. (2009) · 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) · doi:10.1109/camsap.2009.5413299 · Cited by 211
Self-citationTransformation-invariant clustering using the EM algorithm
Frey, B. J., & Jojic, N. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1159942 · Cited by 205
Wagner, A., Wright, J., Ganesh, A., Zhou, Z., & Ma, Y. (2009) · 2009 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2009.5206654 · Cited by 183
Self-citationA proximal method for composite minimization
Lewis, A. S., & Wright, S. J. (2016) · Mathematical Programming · doi:10.1007/s10107-015-0943-9 · Cited by 167
Image Manifolds which are Isometric to Euclidean Space
Donoho, D. L., & Grimes, C. (2005) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-005-4965-4 · Cited by 127
Camera calibration with lens distortion from low-rank textures
Zhang, Z., Matsushita, Y., & Ma, Y. (2011) · doi:10.1109/cvpr.2011.5995548 · Cited by 105
Self-citationTILT: Transform Invariant Low-Rank Textures
Zhang, Z., Liang, X., Ganesh, A., & Ma, Y. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-19318-7_25 · Cited by 100
Self-citationRandomized Algorithms for Matrices and Data
Mahoney, M. W. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601985071 · Cited by 98
Least squares congealing for unsupervised alignment of images
Cox, M., Sridharan, S., Lucey, S., & Cohn, J. F. (2008) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2008.4587573 · Cited by 84
Transformed component analysis: joint estimation of spatial transformations and image components
Frey, B. J., & Jojić, N. (1999) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.1999.790415 · Cited by 78
Robust parameterized component analysis: theory and applications to 2D facial appearance models
la Torre, F. D., & Black, M. J. (2003) · Computer Vision and Image Understanding · doi:10.1016/s1077-3142(03)00076-6 · Cited by 56
Holistic 3D reconstruction of urban structures from low-rank textures
Mobahi, H., Zhou, Z., Yang, A. Y., & Ma, Y. (2011) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw.2011.6130297 · Cited by 38
Self-citationJoint data alignment up to (lossy) transformations
Vedaldi, A., Guidi, G., & Soatto, S. (2008) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2008.4587781 · Cited by 38
Cited by
Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization
Hu, Y., Zhang, D., Ye, J., Li, X., & He, X. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.271 · Cited by 829
Otazo, R., Candès, E., & Sodickson, D. K. (2015) · Magnetic Resonance in Medicine · doi:10.1002/mrm.25240 · Cited by 697
Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach
Dong, W., Shi, G., & Li, X. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2221729 · Cited by 655
Rank Minimization for Snapshot Compressive Imaging
Liu, Y., Yuan, X., Suo, J., Brady, D. J., & Dai, Q. (2019) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2873587 · Cited by 466
Parallel Multi-Block ADMM with o(1 / k) Convergence
Deng, W., Lai, M.-J., Peng, Z., & Yin, W. (2017) · Journal of Scientific Computing · doi:10.1007/s10915-016-0318-2 · Cited by 455
Metadata
- Authors
- Peng, Y., Ganesh, A., Wright, J., Xu, W., & Ma, Y.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2012-11
- Volume
- 34
- Issue
- 11
- Pages
- 2233-2246
- ISSN
- 0162-8828 (ISSN-L)
- 2160-9292
- OpenAlex
- W1974042113
- Cited by
- 817
- References
- 47
- FWCI
- 84.19
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
