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Nonlinear Approaches in Three Dimensional Medical Image Registration

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Nonlinear Approaches in Engineering Applications

Abstract

Image registration is the task of finding a spatial transformation T that aligns the objects in two or more images capturing the same or related scene. It is one of the most crucial problems of computer vision and has been studied for over three decades. The underlying task is very general and has a wide range of applications in the fields of medical imaging, machine vision, remote sensing, cartography, etc. In this chapter we focus on the application of image registration in the fields of medical imaging.

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References

  • Andronache A, Cattin P, Székely G (2006) Local intensity mapping for hierarchical non-rigid registration of multi-modal images using the cross-correlation coefficient. Biomed Image Regist 4057:26–33 [Springer]

    Article  Google Scholar 

  • Arsigny V, Pennec X, Ayache N (2005) Polyrigid and polyaffine transformations: a novel geometrical tool to deal with non-rigid deformations—application to the registration of histological slices. Med Image Anal 9:507–523

    Article  Google Scholar 

  • Arzhaeva Y, Prokop M, Murphy K, Van Rikxoort EM, de Jong PA, Gietema HA, Viergever MA, Van Ginneken B (2010) Automated estimation of progression of interstitial lung disease in CT images. Med Phys 37:63–73

    Article  Google Scholar 

  • Audette MA, Ferrie FP, Peters TM (2000) An algorithmic overview of surface registration techniques for medical imaging. Med Image Anal 4:201–217

    Article  Google Scholar 

  • Bhagalia R, Fessler JA, Boklye K (2009) Accelerated nonrigid intensity-based image registration using importance sampling. IEEE Trans Med Imaging 28:1208–1216

    Article  Google Scholar 

  • Boykov Y, Veksler O, Zabih R (2001) Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell 23:1222–1239

    Article  Google Scholar 

  • Broit C (1981) Optimal registration of deformed images. University of Pennsylvania

    Google Scholar 

  • Bro-Nielsen M, Gramkow C (1996) Fast fluid registration of medical images. In: Höhne K, Kikinis R (eds) Visualization in biomedical computing. Springer, Berlin

    Google Scholar 

  • Burschka D, Li M, Taylor R, Hager GD (2004) Scale-invariant registration of monocular endoscopic images to CT-scans for sinus surgery. In: Medical image computing and computer-assisted intervention—MICCAI 2004. Springer

    Google Scholar 

  • Cahill ND, Schnabel JA, Noble JA, Hawkes DJ (2008) Revisiting overlap invariance in medical image alignment. In: IEEE computer society conference on computer vision and pattern recognition workshops, 2008 (CVPRW’08). IEEE, pp 1–8

    Google Scholar 

  • Castillo E, Castillo R, Zhang Y, Guerrero T (2009) Compressible image registration for thoracic computed tomography images. J Med Biol Eng 29:222–233

    Google Scholar 

  • Castillo E, Castillo R, White B, Rojo J, Guerrero T (2012) Least median of squares filtering of locally optimal point matches for compressible flow image registration. Phys Med Biol 57:4827–4833

    Article  Google Scholar 

  • Christensen GE (1999) Consistent linear-elastic transformations for image matching. In: Kuba A, Šáamal M, Todd-Pokropek A (eds) Information processing in medical imaging. Springer, Berlin

    Google Scholar 

  • Christensen G, He J (2001) Consistent nonlinear elastic image registration. In: IEEE workshop on mathematical methods in biomedical image analysis, 2001 (MMBIA 2001). IEEE, pp 37–43

    Google Scholar 

  • Christensen GE, Rabbitt RD, Miller MI (1994) 3D brain mapping using a deformable neuroanatomy. Phys Med Biol 39:609

    Article  Google Scholar 

  • Christensen GE, Rabbitt RD, Miller MI (1996) Deformable templates using large deformation kinematics. IEEE Trans Image Process 5:1435–1447

    Article  Google Scholar 

  • Chun SY, Fessler JA (2008) Regularized methods for topology-preserving smooth nonrigid image registration using b-spline basis. In: 5th IEEE international symposium on biomedical imaging: from nano to macro, 2008 (ISBI 2008). IEEE, pp 1099–1102

    Google Scholar 

  • Collignon A, Maes F, Delaere D, Vandermeulen D, Suetens P, Marchal G (1995) Automated multi-modality image registration based on information theory. Inf Process Med Imaging 3:263–274

    Google Scholar 

  • Corpetti T, Mémin É, Pérez P (2002) Dense estimation of fluid flows. IEEE Trans Pattern Anal Mach Intell 24:365–380

    Article  Google Scholar 

  • Ford D, Fulkerson DR (2010) Flows in networks. Princeton University Press, Princeton

    Google Scholar 

  • Gee JC, Haynor DR, Reivich M, Bajcsy RK (1994) Finite element approach to warping of brain images. In: Medical imaging 1994. International Society for Optics and Photonics, pp 327–337

    Google Scholar 

  • Gerber N, Gavaghan KA, Bell BJ, Williamson TM, Weisstanner C, Caversaccio MD, Weber S (2013) High-accuracy patient-to-image registration for the facilitation of image-guided robotic microsurgery on the head. IEEE Trans Biomed Eng 60:960–968

    Article  Google Scholar 

  • Giger ML, Chan H-P, Boone J (2008) Anniversary paper: history and status of CAD and quantitative image analysis: the role of medical physics and AAPM. Med Phys 35:5799–5820

    Article  Google Scholar 

  • Glocker B, Komodakis N, Tziritas G, NAVAB N, Paragios N (2008) Dense image registration through MRFs and efficient linear programming. Med Image Anal 12:731–741

    Article  Google Scholar 

  • Glocker B, Sotiras A, Komodakis N, Paragios N (2011) Deformable medical image registration: setting the state of the art with discrete methods. Annu Rev Biomed Eng 13:219–244

    Article  Google Scholar 

  • Gorbunova V, Sporring J, Lo P, Loeve M, Tiddens HA, Nielsen M, Dirksen A, De Bruijne M (2012) Mass preserving image registration for lung CT. Med Image Anal 16:786–795

    Article  Google Scholar 

  • Guo W, Li Q, Boyce SJ, Mcadams HP, Shiraishi J, Doi K, Samei E (2012) A computerized scheme for lung nodule detection in multiprojection chest radiography. Med Phys 39:2001–2012

    Article  Google Scholar 

  • Haber E, Modersitzki J (2006) Intensity gradient based registration and fusion of multi-modal images. In: Medical image computing and computer-assisted intervention—MICCAI 2006. Springer

    Google Scholar 

  • Hero A, Ma B, Michel OJ, Gorman J (2002) Applications of entropic spanning graphs. IEEE Signal Process Mag 19:85–95

    Article  Google Scholar 

  • Hill DL, Batchelor PG, Holden M, Hawkes DJ (2001) Medical image registration. Phys Med Biol 46:R1

    Article  Google Scholar 

  • Holden M (2008) A review of geometric transformations for nonrigid body registration. IEEE Trans Med Imaging 27:111–128

    Article  Google Scholar 

  • Huang CH, Hsieh CH, Lee JD, Huang WC, Lee ST, Wu CT, Sun YN, Wu YT (2012) A CT-ultrasound-coregistered augmented reality enhanced image-guided surgery system and its preliminary study on brain-shift estimation. J Instrum 7, P08016

    Google Scholar 

  • Illán IA, Górriz JM, Ramírez J, Segovia F, Jiménez-Hoyuela JM, Ortega Lozano SJ (2012) Automatic assistance to Parkinsons disease diagnosis in DaTSCAN SPECT imaging. Med Phys 39:5971–5980

    Article  Google Scholar 

  • Jacobson TJ, Murphy MJ (2011) Optimized knot placement for B-splines in deformable image registration. Med Phys 38:4579–4582

    Article  Google Scholar 

  • Jaya J, Thanushkodi K (2011) Implementation of computer aided diagnosis system based on parallel approach of ant based medical image segmentation. J Comput Sci 7:291–297

    Article  Google Scholar 

  • Kim J (2004) Intensity based image registration using robust similarity measure and constrained optimization: applications for radiation therapy. Citeseer

    Google Scholar 

  • Klein S, Staring M, Pluim JPW (2007) Evaluation of optimization methods for nonrigid medical image registration using mutual information and B-splines. IEEE Trans Image Process 16:2879–2890

    Article  MathSciNet  Google Scholar 

  • Klein S, Van der Heide UA, Lips IM, Van Vulpen M, Staring M, Pluim JP (2008) Automatic segmentation of the prostate in 3D MR images by atlas matching using localized mutual information. Med Phys 35:1407–1417

    Article  Google Scholar 

  • Kleinberg J, Tardos E (2002) Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields. J ACM 49:616–639

    Article  MathSciNet  Google Scholar 

  • Ko JP, Betke M (2001) Chest CT: automated nodule detection and assessment of change over time-preliminary experience. Radiology 218(1):267–273

    Article  Google Scholar 

  • Kolmogorov V (2006) Convergent tree-reweighted message passing for energy minimization. IEEE Trans Pattern Anal Mach Intell 28:1568–1583

    Article  Google Scholar 

  • Kolmogorov V, Zabin R (2004) What energy functions can be minimized via graph cuts? IEEE Trans Pattern Anal Mach Intell 26:147–159

    Article  Google Scholar 

  • Komodakis N, Tziritas G, Paragios N (2007) Fast, approximately optimal solutions for single and dynamic MRFs. In: IEEE conference on computer vision and pattern recognition, 2007 (CVPR’07), 17–22 June 2007, pp 1–8

    Google Scholar 

  • Kschischang FR, Frey BJ, Loeliger H-A (2001) Factor graphs and the sum-product algorithm. IEEE Trans Inf Theory 47:498–519

    Article  MathSciNet  MATH  Google Scholar 

  • Kwon D, Lee KJ, Yun ID, Lee SU (2011) Nonrigid image registration using higher-order MRF model with dense local descriptor. In: Computer vision and pattern recognition workshop, 2011

    Google Scholar 

  • Kybic J, Unser M (2003) Fast parametric elastic image registration. IEEE Trans Image Process 12:1427–1442

    Article  Google Scholar 

  • Lee KJ, Kwon D, Yun ID, Lee SU (2008) Deformable 3D volume registration using efficient MRFs model with decomposed nodes. In: BMVC 2008, pp 1–10

    Google Scholar 

  • Lester H, Arridge SR (1999) A survey of hierarchical non-linear medical image registration. Pattern Recogn 32:129–149

    Article  Google Scholar 

  • Liang Y, Ryan NS, Schott JM, Fox NC (2013) Imaging the onset and progression of Alzheimer’s disease: implications for prevention trials. J Alzheimers Dis 33:S305–S312

    Google Scholar 

  • Likar B, Pernuš F (2001) A hierarchical approach to elastic registration based on mutual information. Image Vis Comput 19:33–44

    Article  Google Scholar 

  • Linte CA, White J, Eagleson R, Guiraudon GM, Peters TM (2010) Virtual and augmented medical imaging environments: enabling technology for minimally invasive cardiac interventional guidance. IEEE Rev Biomed Eng 3:25–47

    Article  Google Scholar 

  • Loeckx D, Slagmolen P, Maes F, Vandermeulen D, Suetens P (2010) Nonrigid image registration using conditional mutual information. IEEE Trans Med Imaging 29:19–29

    Article  Google Scholar 

  • Maintz JBA, Viergever MA (1998) A survey of medical image registration. Med Image Anal 2: 1–36

    Article  Google Scholar 

  • Mirota DJ, Hanzi W, Taylor RH, Ishii M, Gallia GL, Hager GD (2012) A system for video-based navigation for endoscopic endonasal skull base surgery. IEEE Trans Med Imaging 31:963–976

    Article  Google Scholar 

  • Modersitzki J (2004) Numerical methods for image registration (numerical mathematics and scientific computation). Oxford University Press, Oxford

    Google Scholar 

  • Modersitzki J (2008) FLIRT with rigidity—image registration with a local non-rigidity penalty. Int J Comput Vis 76:153–163

    Article  Google Scholar 

  • Mostayed A, Garlapati RR, Joldes GR, Wittek A, Roy A, Kikinis R, Warfield SK, Miller K (2013) Biomechanical model as a registration tool for image-guided neurosurgery: evaluation against bspline registration. Ann Biomed Eng 41:2409–2425

    Article  Google Scholar 

  • Musse O, Heitz F, Armspach J-P (2001) Topology preserving deformable image matching using constrained hierarchical parametric models. IEEE Trans Image Process 10:1081–1093

    Article  MATH  Google Scholar 

  • Myronenko A, Xubo S (2010) Intensity-based image registration by minimizing residual complexity. IEEE Trans Med Imaging 29:1882–1891

    Article  Google Scholar 

  • Noblet V, Heinrich C, Heitz F, Armspach J-P (2005) 3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization. IEEE Trans Image Process 14:553–566

    Article  MathSciNet  Google Scholar 

  • Oliveira FP, Tavares JM (2014) Medical image registration: a review. Comput Methods Biomech Biomed Eng 17:73–93

    Article  Google Scholar 

  • Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Francisco

    Google Scholar 

  • Pennec X, Stefanescu R, Arsigny V, Fillard P, Ayache N (2005) Riemannian elasticity: a statistical regularization framework for non-linear registration. In: Medical image computing and computer-assisted intervention—MICCAI 2005. Springer

    Google Scholar 

  • Pitiot A, Malandain G, Bardinet E, Thompson PM (2003) Piecewise affine registration of biological images. In: Biomedical image registration. Springer

    Google Scholar 

  • Pluim JP, Maintz JA, Viergever MA (2000) Image registration by maximization of combined mutual information and gradient information. In: Medical image computing and computer-assisted intervention—MICCAI 2000. Springer, pp 452–461

    Google Scholar 

  • Pluim JP, Maintz JA, Viergever MA (2003) Mutual-information-based registration of medical images: a survey. IEEE Trans Med Imaging 22:986–1004

    Article  Google Scholar 

  • Rabbitt RD, Weiss JA, Christensen GE, Miller MI (1995) Mapping of hyperelastic deformable templates using the finite element method. In: SPIE’s 1995 international symposium on optical science, engineering, and instrumentation. International Society for Optics and Photonics, pp 252–265

    Google Scholar 

  • Rivaz H, Collins DL (2012) Self-similarity weighted mutual information: a new nonrigid image registration metric. Med Image Comput Comput Assist Interv 15:91–98

    Google Scholar 

  • Robertson S, Weiss E, Hugo GD (2013) Deformable mesh registration for the validation of automatic target localization algorithms. Med Phys 40(7):071721

    Article  Google Scholar 

  • Rohde GK, Aldroubi A, Dawant BM (2003) The adaptive bases algorithm for intensity-based nonrigid image registration. IEEE Trans Med Imaging 22:1470–1479

    Article  Google Scholar 

  • Rueckert D, Aljabar P (2010) Nonrigid registration of medical images: theory, methods, and applications [applications corner]. IEEE Signal Process Mag 27:113–119

    Article  Google Scholar 

  • Rueckert D, Sonoda LI, Hayes C, Hill DLG, Leach MO, Hawkes DJ (1999) Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans Med Imaging 18:712–721

    Article  Google Scholar 

  • Rueckert D, Clarkson M, Hill D, Hawkes DJ (2000) Non-rigid registration using higher-order mutual information. In: Medical imaging 2000. International Society for Optics and Photonics, pp 438–447

    Google Scholar 

  • Ruhaak J, Konig L, Hallmann M, Papenberg N, Heldmann S, Schumacher H, Fischer B (2013) A fully parallel algorithm for multimodal image registration using normalized gradient fields. In: 2013 IEEE 10th international symposium on biomedical imaging (ISBI), 7–11 April 2013, pp 572–575

    Google Scholar 

  • Rui L, Li Z, Ying S, Shun M, Chefd’hotel C (2013) A review of recent advances in registration techniques applied to minimally invasive therapy. IEEE Trans Multimed 15:983–1000

    Article  Google Scholar 

  • Rynne BP, Youngson MA (2008) Linear functional analysis. Springer, London

    Book  MATH  Google Scholar 

  • Sadeghi Naini A, Patel RV, Samani A (2010) CT-enhanced ultrasound image of a totally deflated lung for image-guided minimally invasive tumor ablative procedures. IEEE Trans Biomed Eng 57:2627–2630

    Article  Google Scholar 

  • Shekhovtsov A, Kovtun I, Hlaváč V (2008) Efficient MRF deformation model for non-rigid image matching. Comput Vis Image Underst 112:91–99

    Article  Google Scholar 

  • Shiraishi J, Abe H, Li F, Engelmann R, Macmahon H, Doi K (2006) Computer-aided diagnosis for the detection and classification of lung cancers on chest radiographs. ROC analysis of radiologists’ performance. Acad Radiol 13:995–1003

    Article  Google Scholar 

  • Sluimer I, Schilham A, Prokop M, Van Ginneken B (2006) Computer analysis of computed tomography scans of the lung: a survey. IEEE Trans Med Imaging 25:385–405

    Article  Google Scholar 

  • So R, Chung A (2009) Multi-level non-rigid image registration using graph-cuts. In: IEEE international conference on acoustics, speech and signal processing, 2009 (ICASSP 2009), 19–24 April 2009, pp 397–400

    Google Scholar 

  • So RWK, Tang TWH, Chung ACS (2011) Non-rigid image registration of brain magnetic resonance images using graph-cuts. Pattern Recogn 44:2450–2467

    Article  Google Scholar 

  • Sotiras A, Davatzikos C, Paragios N (2013) Deformable medical image registration: a survey. IEEE Trans Med Imaging 32:1153–1190

    Article  Google Scholar 

  • Staring M, van der Heide UA, Klein S, Viergever MA, Pluim JP (2009) Registration of cervical MRI using multifeature mutual information. IEEE Trans Med Imaging 28:1412–1421

    Article  Google Scholar 

  • Studholme C, Hill DL, Hawkes DJ (1999) An overlap invariant entropy measure of 3D medical image alignment. Pattern Recogn 32:71–86

    Article  Google Scholar 

  • Studholme C, Drapaca C, Iordanova B, Cardenas V (2006) Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change. IEEE Trans Med Imaging 25:626–639

    Article  Google Scholar 

  • Szeliski R, Zabih R, Scharstein D, Veksler O, Kolmogorov V, Agarwala A, Tappen M, Rother C (2008) A comparative study of energy minimization methods for Markov random fields with smoothness-based priors. IEEE Trans Pattern Anal Mach Intell 30:1068–1080

    Article  Google Scholar 

  • Tennakoon RB, Bab-Hadiashar A, Cao Z, De Bruijne M (2014) Nonrigid registration of volumetric images using ranked order statistics. IEEE Trans Med Imaging 33:422–432

    Article  Google Scholar 

  • Timp S, Varela C, Karssemeijer N (2007) Temporal change analysis for characterization of mass lesions in mammography. IEEE Trans Med Imaging 26:945–953

    Article  Google Scholar 

  • Uneri A, Nithiananthan S, Schafer S, Otake Y, Stayman JW, Kleinszig G, Sussman MS, Prince JL, Siewerdsen JH (2013) Deformable registration of the inflated and deflated lung in cone-beam CT-guided thoracic surgery: initial investigation of a combined model- and image-driven approach. Med Phys 40

    Google Scholar 

  • Van Ginneken B, Ter Haar Romeny BM, Viergever MA (2001) Computer-aided diagnosis in chest radiography: a survey. IEEE Trans Med Imaging 20:1228–1241

    Article  Google Scholar 

  • van Herk M (2007) Different styles of image-guided radiotherapy. Semin Radiat Oncol 17: 258–267

    Article  Google Scholar 

  • Vercauteren T, Pennec X, Perchant A, Ayache N (2007) Non-parametric diffeomorphic image registration with the demons algorithm. In: Medical image computing and computer-assisted intervention—MICCAI 2007. Springer

    Google Scholar 

  • Viola P, Wells WM III (1997) Alignment by maximization of mutual information. Int J Comput Vis 24:137–154

    Article  Google Scholar 

  • Wainwright MJ, Jaakkola TS, Willsky AS (2005) MAP estimation via agreement on trees: message-passing and linear programming. IEEE Trans Inf Theory 51:3697–3717

    Article  MathSciNet  Google Scholar 

  • Wang J, Jiang T (2007) Nonrigid registration of brain MRI using NURBS. Pattern Recogn Lett 28:214–223

    Article  Google Scholar 

  • Wei J, Chan HP, Sahiner B, Zhou C, Hadjiiski LM, Roubidoux MA, Helvie MA (2009) Computer-aided detection of breast masses on mammograms: dual system approach with two-view analysis. Med Phys 36:4451–4460

    Article  Google Scholar 

  • Worm ES, Hansen AT, Petersen JB, Muren LP, Præstegaard LH, Høyer M (2010) Inter- and intrafractional localisation errors in cone-beam CT guided stereotactic radiation therapy of tumours in the liver and lung. Acta Oncol 49:1177–1183

    Article  Google Scholar 

  • Wu Y-T, Kanade T, Li C-C, Cohn J (2000) Image registration using wavelet-based motion model. Int J Comput Vis 38:129–152

    Article  MATH  Google Scholar 

  • Xishi H, Jing R, Guiraudon G, Boughner D, Peters TM (2009) Rapid dynamic image registration of the beating heart for diagnosis and surgical navigation. IEEE Trans Med Imaging 28: 1802–1814

    Article  Google Scholar 

  • Yedidia JS, Freeman WT, Weiss Y (2000) Generalized belief propagation. In: NIPS 2000, pp 689–695

    Google Scholar 

  • Yin Y, Hoffman EA, Lin C-L (2009) Mass preserving nonrigid registration of CT lung images using cubic B-spline. Med Phys 36:4213

    Article  Google Scholar 

  • Yuanjie Z, Kambhamettu C, Bauer T, Steiner K (2009) Accurate estimation of pulmonary nodule’s growth rate in CT images with nonrigid registration and precise nodule detection and segmentation. In: IEEE computer society conference on computer vision and pattern recognition workshops 2009 (CVPR workshops 2009), 20–25 June 2009, pp 101–108

    Google Scholar 

  • Zitova B, Flusser J (2003) Image registration methods: a survey. Image Vis Comput 21:977–1000

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, VIC, 3122, Australia

    Ruwan Tennakoon & Zhenwei Cao

  2. School of Aerospace, Mechanical and Manufacturing, RMIT University, Melbourne, VIC, 3001, Australia

    Alireza Bab-Hadiashar

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  1. Ruwan Tennakoon
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  2. Alireza Bab-Hadiashar
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  3. Zhenwei Cao
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Correspondence to Ruwan Tennakoon .

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Editors and Affiliations

  1. Industrial Systems Engineering, University of Regina, Regina, Saskatchewan, Canada

    Liming Dai

  2. Aerospace, Mechanical and Manufacturing Engineering, RMIT University Bundoora East Campus, Bundoora, Victoria, Australia

    Reza N. Jazar

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Tennakoon, R., Bab-Hadiashar, A., Cao, Z. (2015). Nonlinear Approaches in Three Dimensional Medical Image Registration. In: Dai, L., Jazar, R. (eds) Nonlinear Approaches in Engineering Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-09462-5_10

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