Deformable image registration based on elastodynamics

This paper presents a novel method for 2D inter-subject non-rigid image registration. It is motivated by the ideas derived from elastodynamics which is the subclass of linear elastic theory. We propose to model the non-rigid deformations as elastic waves which are characterized by elastodynamics wave equation. Our registration method is formulated in a multi-resolution manner such that it is able to recover significant deformations. The proposed scheme recovers local (non-linear) as well as global deformations. The results of image registration by the proposed technique were validated via similarity measures for real MR brain images, BrainWeb dataset and MR prostate images. We have also used overlap measures (Jaccard distance, Dice coefficient and Overlap coefficient) over the segmented deep-brain structures including: lateral and third ventricles, putamen and caudate nucleus for real image dataset to further validate our proposed registration scheme. The proposed scheme was also compared with demons, Level set and free-form deformations (cubic B-spline) algorithms implemented in ITK toolkit and symmetric normalization method available in ANTs software package. Our proposed algorithm shows marked improvement of the inter-subject non-rigid registration, both qualitatively and quantitatively, over the four above-mentioned methods. This comparison was performed on all the three types of datasets mentioned above. 2D synthetic experiments comprising of Patch-‘C’, Square–Rectangle and Circle-‘C’ were also performed with our algorithm and compared with other four methods. Both qualitative and quantitative results show that our method performs better than the other four methods. Results suggest that our proposed algorithm has improved accuracy over lemons, level set and free-form deformations (ITK implemented) and symmetric normalization method (ANTs based), tested over two types of brain and one prostate MRI. The commonly used synthetic experiments also suggest the superiority of our proposed scheme.

[1]  Dinggang Shen,et al.  HAMMER: hierarchical attribute matching mechanism for elastic registration , 2002, IEEE Transactions on Medical Imaging.

[2]  Michael Unser,et al.  Fast parametric elastic image registration , 2003, IEEE Trans. Image Process..

[3]  A. Khotanzad,et al.  A physics-based coordinate transformation for 3-D image matching , 1997, IEEE Transactions on Medical Imaging.

[4]  Kemal Tuncali,et al.  Image registration for targeted MRI‐guided transperineal prostate biopsy , 2012, Journal of magnetic resonance imaging : JMRI.

[5]  Mark Holden,et al.  A Review of Geometric Transformations for Nonrigid Body Registration , 2008, IEEE Transactions on Medical Imaging.

[6]  Mathieu De Craene,et al.  Tumour delineation and cumulative dose computation in radiotherapy based on deformable registration of respiratory correlated CT images of lung cancer patients. , 2007, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[7]  Nasser Kehtarnavaz,et al.  Symmetric deformable image registration via optimization of information theoretic measures , 2010, Image Vis. Comput..

[8]  Anup Basu,et al.  Cross-Scale Coefficient Selection for Volumetric Medical Image Fusion , 2013, IEEE Transactions on Biomedical Engineering.

[9]  C. Broit.  Optimal registration of deformed images , 1981 .

[10]  Stefan Klein,et al.  Early diagnosis of dementia based on intersubject whole-brain dissimilarities , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[11]  Xavier Geets,et al.  Impact of the type of imaging modality on target volumes delineation and dose distribution in pharyngo-laryngeal squamous cell carcinoma: comparison between pre- and per-treatment studies. , 2006, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[12]  A. Evans,et al.  MRI simulation-based evaluation of image-processing and classification methods , 1999, IEEE Transactions on Medical Imaging.

[13]  Yasuo Ohashi,et al.  Overlap coefficient for assessing the similarity of pharmacokinetic data between ethnically different populations , 2005, Clinical trials.

[14]  L. R. Dice.  Measures of the Amount of Ecologic Association Between Species , 1945 .

[15]  Stephen Breen,et al.  Biomechanical-based image registration for head and neck radiation treatment , 2010, Medical Imaging.

[16]  Gary E. Christensen,et al.  Consistent image registration , 2001, IEEE Transactions on Medical Imaging.

[17]  Arno Klein,et al.  Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration , 2009, NeuroImage.

[18]  Shu Liao,et al.  Feature Based Nonrigid Brain MR Image Registration With Symmetric Alpha Stable Filters , 2010, IEEE Transactions on Medical Imaging.

[19]  Brian B. Avants,et al.  Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain , 2008, Medical Image Anal..

[20]  Zongmin Wu,et al.  Compactly supported positive definite radial functions , 1995 .

[21]  Jean-Philippe Thirion,et al.  Image matching as a diffusion process: an analogy with Maxwell's demons , 1998, Medical Image Anal..

[22]  Pascal Haigron,et al.  Surface-Constrained Nonrigid Registration for Dose Monitoring in Prostate Cancer Radiotherapy , 2014, IEEE Transactions on Medical Imaging.

[23]  Gary E. Christensen,et al.  Deformable Shape Models for Anatomy , 1994 .

[24]  Christos Davatzikos,et al.  Comparative Evaluation of Registration Algorithms in Different Brain Databases With Varying Difficulty: Results and Insights , 2014, IEEE Transactions on Medical Imaging.

[25]  G. Gladwell,et al.  Solid mechanics and its applications , 1990 .

[26]  Stefan Bauer,et al.  Multiscale Modeling for Image Analysis of Brain Tumor Studies , 2012, IEEE Transactions on Biomedical Engineering.

[27]  J. W. Thomas.  Numerical Partial Differential Equations: Finite Difference Methods , 1995 .

[28]  Kemal Tuncali,et al.  3T MR‐guided in‐bore transperineal prostate biopsy: A comparison of robotic and manual needle‐guidance templates , 2015, Journal of magnetic resonance imaging : JMRI.

[29]  P. Jaccard.  THE DISTRIBUTION OF THE FLORA IN THE ALPINE ZONE.1 , 1912 .

[30]  H. Hricak,et al.  Semi‐automatic deformable registration of prostate MR images to pathological slices , 2010, Journal of Magnetic Resonance Imaging.

[31]  Qiao Wei,et al.  Segmentation of Lung Lobes in High-Resolution Isotropic CT Images , 2009, IEEE Transactions on Biomedical Engineering.

[32]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[33]  Michael I. Miller,et al.  Landmark matching via large deformation diffeomorphisms , 2000, IEEE Trans. Image Process..

[34]  Max A. Viergever,et al.  Ridge-based vessel segmentation in color images of the retina , 2004, IEEE Transactions on Medical Imaging.

[35]  Xavier Geets,et al.  Adaptive biological image-guided IMRT with anatomic and functional imaging in pharyngo-laryngeal tumors: impact on target volume delineation and dose distribution using helical tomotherapy. , 2007, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[36]  Karl Rohr,et al.  Radial basis functions with compact support for elastic registration of medical images , 2001, Image Vis. Comput..

[37]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  Benoît Macq,et al.  Comparison of 12 deformable registration strategies in adaptive radiation therapy for the treatment of head and neck tumors. , 2008, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[39]  Nassir Navab,et al.  Dense image registration through MRFs and efficient linear programming , 2008, Medical Image Anal..

[40]  Nicholas Ayache,et al.  Non-parametric Diffeomorphic Image Registration with the Demons Algorithm , 2007, MICCAI.

[41]  Bill Cox.  Mathematics of wave propagation , by Julian L. Davis. Pp. 395. £36.50. 2000. ISBN 0 691 02643 2 (Princeton University Press). , 2001, The Mathematical Gazette.

[42]  Albert C. S. Chung,et al.  Non-rigid image registration of brain magnetic resonance images using graph-cuts , 2011, Pattern Recognit..

[43]  Takeo Kanade,et al.  Image Registration Using Wavelet-Based Motion Model , 2000, International Journal of Computer Vision.

[44]  G S Bauman,et al.  Tracking the dose distribution in radiation therapy by accounting for variable anatomy , 2004, Physics in medicine and biology.

[45]  David J. Hawkes,et al.  MR to Ultrasound Image Registration for Guiding Prostate Biopsy and Interventions , 2009, MICCAI.

[46]  David J. Hawkes,et al.  Voxel Similarity Measures for 3D Serial MR Brain Image Registration , 2000, IEEE Trans. Medical Imaging.

[47]  Michael I. Miller,et al.  Deformable templates using large deformation kinematics , 1996, IEEE Trans. Image Process..

[48]  Stefan Henn,et al.  A Full Curvature Based Algorithm for Image Registration , 2006, Journal of Mathematical Imaging and Vision.

[49]  Cedric X. Yu,et al.  Deformable image registration for the use of magnetic resonance spectroscopy in prostate treatment planning. , 2004, International journal of radiation oncology, biology, physics.

[50]  Y. Chen,et al.  Image registration via level-set motion: Applications to atlas-based segmentation , 2003, Medical Image Anal..

[51]  A. Ardeshir Goshtasby,et al.  A comparative study of transformation functions for nonrigid image registration , 2006, IEEE Transactions on Image Processing.

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

[53]  Simon R. Arridge,et al.  A survey of hierarchical non-linear medical image registration , 1999, Pattern Recognit..

[54]  J. Achenbach.  Wave propagation in elastic solids , 1962 .