Image Registration Based on Low Rank Matrix: Rank-Regularized SSD

Similarity measure is a main core of image registration algorithms. Spatially varying intensity distortion is an important challenge, which affects the performance of similarity measures. Correlation among the pixels is the main characteristic of this distortion. Similarity measures such as sum-of-squared-differences (SSD) and mutual information ignore this correlation; hence, perfect registration cannot be achieved in the presence of this distortion. In this paper, we model this correlation with the aid of the low rank matrix theory. Based on this model, we compensate this distortion analytically and introduce rank-regularized SSD (RRSSD). This new similarity measure is a modified SSD based on singular values of difference image in mono-modal imaging. In fact, image registration and distortion correction are performed simultaneously in the proposed model. Based on our experiments, the RRSSD similarity measure achieves clinically acceptable registration results, and outperforms other state-of-the-art similarity measures, such as the well-known method of residual complexity.

[1]  Emad Fatemizadeh,et al.  RISM: Single-Modal Image Registration via Rank-Induced Similarity Measure , 2015, IEEE Transactions on Image Processing.

[2]  Zhuowen Tu,et al.  Robust $L_{2}E$ Estimation of Transformation for Non-Rigid Registration , 2015, IEEE Transactions on Signal Processing.

[3]  J. Alison Noble,et al.  MAP MRF joint segmentation and registration of medical images , 2003, Medical Image Anal..

[4]  Lingfeng Wang,et al.  Nonrigid medical image registration with locally linear reconstruction , 2014, Neurocomputing.

[5]  Christian Jutten,et al.  Recovery of Low-Rank Matrices Under Affine Constraints via a Smoothed Rank Function , 2013, IEEE Transactions on Signal Processing.

[6]  Nicholas Ayache,et al.  Unifying maximum likelihood approaches in medical image registration , 2000 .

[7]  Hamid Soltanian-Zadeh,et al.  Medical image registration using sparse coding of image patches , 2016, Comput. Biol. Medicine.

[8]  Nassir Navab,et al.  Manifold Learning for Multi-Modal Image Registration , 2010, BMVC.

[9]  Nassir Navab,et al.  Entropy and Laplacian images: Structural representations for multi-modal registration , 2012, Medical Image Anal..

[10]  Paul A. Viola,et al.  Multi-modal volume registration by maximization of mutual information , 1996, Medical Image Anal..

[11]  Daniel Rueckert,et al.  Nonrigid registration using free-form deformations: application to breast MR images , 1999, IEEE Transactions on Medical Imaging.

[12]  William R. Brody,et al.  Digital Subtraction Angiography , 1982, IEEE Transactions on Nuclear Science.

[13]  Emad Fatemizadeh,et al.  Sparse-induced similarity measure: mono-modal image registration via sparse-induced similarity measure , 2014, IET Image Process..

[14]  R. Castillo,et al.  A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets , 2009, Physics in medicine and biology.

[15]  Emad Fatemizadeh,et al.  Manifold learning based registration algorithms applied to multimodal images , 2014, 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[16]  Andriy Myronenko,et al.  Registration of Microscopic Iris Image Sequences Using Probabilistic Mesh , 2006, MICCAI.

[17]  D. Louis Collins,et al.  Self-similarity Weighted Mutual Information: A New Nonrigid Image Registration Metric , 2012, MICCAI.

[18]  James S. Duncan,et al.  Estimation of 3-D left ventricular deformation from medical images using biomechanical models , 2002, IEEE Transactions on Medical Imaging.

[19]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[20]  Paul Suetens,et al.  Nonrigid Image Registration Using Conditional Mutual Information , 2007, IPMI.

[21]  Nicholas Ayache,et al.  The Correlation Ratio as a New Similarity Measure for Multimodal Image Registration , 1998, MICCAI.

[22]  Mohamed M. Fouad,et al.  Image Registration Under Illumination Variations Using Region-Based Confidence Weighted $M$-Estimators , 2012, IEEE Transactions on Image Processing.

[23]  D. Louis Collins,et al.  Nonrigid Registration of Ultrasound and MRI Using Contextual Conditioned Mutual Information , 2014, IEEE Transactions on Medical Imaging.

[24]  Alan C. Evans,et al.  BrainWeb: Online Interface to a 3D MRI Simulated Brain Database , 1997 .

[25]  Yong Ma,et al.  Image Feature Matching via Progressive Vector Field Consensus , 2015, IEEE Signal Processing Letters.

[26]  Colin Studholme,et al.  Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change , 2006, IEEE Transactions on Medical Imaging.

[27]  Andriy Myronenko,et al.  Adaptive Regularization of Ill-Posed Problems: Application to Non-rigid Image Registration , 2009, ArXiv.

[28]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[29]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[30]  Emmanuel J. Candès,et al.  Matrix Completion With Noise , 2009, Proceedings of the IEEE.

[31]  Zhuowen Tu,et al.  Robust Point Matching via Vector Field Consensus , 2014, IEEE Transactions on Image Processing.

[32]  John Wright,et al.  RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images , 2012, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[34]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[35]  Jamshid Shanbehzadeh,et al.  An efficient approach for robust multimodal retinal image registration based on UR-SIFT features and PIIFD descriptors , 2013, EURASIP J. Image Video Process..

[36]  F. Zana,et al.  A region merging algorithm using mathematical morphology: application to macula detection , 1998 .

[37]  A. Lewis.  The Convex Analysis of Unitarily Invariant Matrix Functions , 1995 .

[38]  Konstantinos Konstantinides,et al.  Statistical analysis of effective singular values in matrix rank determination , 1988, IEEE Trans. Acoust. Speech Signal Process..

[39]  Javad Alirezaie,et al.  Brain-shift compensation by non-rigid registration of intra-operative ultrasound images with preoperative MR images based on residual complexity , 2015, International Journal of Computer Assisted Radiology and Surgery.

[40]  Ji Zhao,et al.  Nonrigid Image Deformation Using Moving Regularized Least Squares , 2013, IEEE Signal Processing Letters.

[41]  Nikos Paragios,et al.  Deformable Medical Image Registration: A Survey , 2013, IEEE Transactions on Medical Imaging.

[42]  Hang Zhou,et al.  Registration of Pre- and Postresection Ultrasound Volumes With Noncorresponding Regions in Neurosurgery , 2016, IEEE Journal of Biomedical and Health Informatics.

[43]  Yi Ma,et al.  TILT: Transform Invariant Low-Rank Textures , 2010, ACCV.

[44]  David Atkinson,et al.  Respiratory motion correction in dynamic MRI using robust data decomposition registration - Application to DCE-MRI , 2014, Medical Image Anal..

[45]  Andriy Myronenko,et al.  Intensity-Based Image Registration by Minimizing Residual Complexity , 2010, IEEE Transactions on Medical Imaging.

[46]  Emad Fatemizadeh,et al.  Robust Huber similarity measure for image registration in the presence of spatially-varying intensity distortion , 2015, Signal Process..

[47]  Khadijeh Aghajani,et al.  A robust image registration method based on total variation regularization under complex illumination changes , 2016, Comput. Methods Programs Biomed..

[48]  Mohsen Shirpour,et al.  Intensity based image registration by minimizing the complexity of weighted subtraction under illumination changes , 2016, Biomed. Signal Process. Control..

[49]  Lexin Li,et al.  Regularized matrix regression , 2012, Journal of the Royal Statistical Society. Series B, Statistical methodology.