Hybrid multiscale landmark and deformable image registration

Paquin, Dana C.; Levy, Doron; Liu, Xing

doi:10.3934/mbe.2007.4.711

Cited by 33 publications

(20 citation statements)

References 23 publications

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“…The hierarchical, multi-layered (BV,L 2 )-decompositions (1.6) were found to be effective tools in image processing [33,8] and image registration [18,27]. They apply to image denoising in the presence of additive or multiplicative noise, to image deblurring and to image segmentation.…”

Section: Introduction -Hierarchical (Xy ) Decompositionsmentioning

confidence: 99%

Multiscale Hierarchical Decomposition of Images with Applications to Deblurring, Denoising and Segmentation

Tadmor¹,

Nezzar²,

Vese³

2007

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Abstract. We extend the ideas introduced in [33] for hierarchical multiscale decompositions of images. Viewed as a function f ∈ L 2 (Ω), a given image is hierarchically decomposed into the sum or product of simpler "atoms" u k , where u k extracts more refined information from the previous scale u k−1 . To this end, the u k 's are obtained as dyadically scaled minimizers of standard functionals arising in image analysis. Thus, starting with v −1 := f and letting v k denote the residual at a given dyadic scale, λ k ∼ 2 k , the recursive step [u k ,v k ] = arginf Q T (v k−1 ,λ k ) leads to the desired hierarchical decomposition, f ∼ P T u k ; here T is a blurring operator. We characterize such Q T -minimizers (by duality) and expand our previous energy estimates of the data f in terms of u k . Numerical results illustrate applications of the new hierarchical multiscale decomposition for blurry images, images with additive and multiplicative noise and image segmentation.

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Section: Introduction -Hierarchical (Xy ) Decompositionsmentioning

confidence: 99%

Multiscale Hierarchical Decomposition of Images with Applications to Deblurring, Denoising and Segmentation

Tadmor¹,

Nezzar²,

Vese³

2007

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“…In Ref. 12, we demonstrated that the multiscale registration algorithm is robust with respect to the location of the landmarks. In particular, the accuracy of the multiscale algorithm is not dependent on exact matching of the landmarks; due to the iterative nature of the registration method, we achieve accurate registration results even if the landmark locations are perturbed approximately 10 mm from their exact locations.…”

Section: Iib Landmark-based Registrationmentioning

confidence: 99%

“…12 to register three-dimensional rectum, head-neck, and prostate planning CT and daily CBCT volumes with one another. To evaluate the accuracy of the registration algorithm, we computed the mutual information similarity measure between the planning CT volumes and daily CBCT volumes before registration, after B-splines deformable registration, and after multiscale registration.…”

Section: Iiib2 Three-dimensional Multiscale Registrationmentioning

confidence: 99%

Multiscale registration of planning CT and daily cone beam CT images for adaptive radiation therapy

Paquin

Levy

2008

Medical Physics

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Adaptive radiation therapy ͑ART͒ is the incorporation of daily images in the radiotherapy treatment process so that the treatment plan can be evaluated and modified to maximize the amount of radiation dose to the tumor while minimizing the amount of radiation delivered to healthy tissue. Registration of planning images with daily images is thus an important component of ART. In this article, the authors report their research on multiscale registration of planning computed tomography ͑CT͒ images with daily cone beam CT ͑CBCT͒ images. The multiscale algorithm is based on the hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese ͓Multiscale Model. Simul. 2͑4͒, pp. 554-579 ͑2004͔͒. Registration is achieved by decomposing the images to be registered into a series of scales using the ͑BV, L 2 ͒ decomposition and initially registering the coarsest scales of the image using a landmark-based registration algorithm. The resulting transformation is then used as a starting point to deformably register the next coarse scales with one another. This procedure is iterated at each stage using the transformation computed by the previous scale registration as the starting point for the current registration. The authors present the results of studies of rectum, head-neck, and prostate CT-CBCT registration, and validate their registration method quantitatively using synthetic results in which the exact transformations our known, and qualitatively using clinical deformations in which the exact results are not known.

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“…This type of approaches can usually obtain more accurate registration results, since the advantages of landmark-based and intensity-based registration can be combined. Different hybrid registration models have also been proposed recently [7,17,26,27,44].…”

Section: Introductionmentioning

confidence: 99%

Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps

2015

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We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints. The standard conformality distortion defined for mappings between 2-dimensional spaces is first generalized to the n-dimensional conformality distortion K ( f ) for a mapping f between n-dimensional Euclidean spaces (n ≥ 3). We then propose a variational model involving K ( f ) to tackle the landmark-matching problem in higher dimensional spaces. The generalized conformality term K ( f ) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations. Another challenge is the high computational cost of the proposed model. To tackle this, we have also proposed a numerical method to solve the optimization problem more efficiently. Alternating direction method with multiplier is applied to split the optimization problem into two subproblems. Preconditioned conjugate gradient method with multi-grid preconditioner is applied to solve one of the sub-problems, while a fixed-point iteration is proposed to solve another subproblem. Experiments have been carried out on both synthetic examples and lung CT images to compute the diffeomorphic landmark-matching transformation with different landmark constraints. Results show the efficacy of our proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations.

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Hybrid multiscale landmark and deformable image registration

Cited by 33 publications

References 23 publications

Multiscale Hierarchical Decomposition of Images with Applications to Deblurring, Denoising and Segmentation

Multiscale Hierarchical Decomposition of Images with Applications to Deblurring, Denoising and Segmentation

Multiscale registration of planning CT and daily cone beam CT images for adaptive radiation therapy

Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps

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