Mass Preserving Mappings and Image Registration

Haker, Steven; Tannenbaum, Allen; Kikinis, Ron

doi:10.1007/3-540-45468-3_15

Cited by 29 publications

(33 citation statements)

References 19 publications

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“…Apart from its use in different theoretical studies [2,11,[13][14][15]38]) potential "industrial" applications also emerge, for instance in medical imaging, astronomy, meteorology etc. [9,21,23,26,29,31,32,34]. The design of efficient numerical methods is therefore already an issue for the applied mathematicians [1, 3, 4, 6-8, 17, 26, 27].…”

Section: Introductionmentioning

confidence: 99%

Numerical resolution of an “unbalanced” mass transport problem

Benamou¹

2003

ESAIM: M2AN

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Abstract.We introduce a modification of the Monge-Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this "unbalanced" problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.Mathematics Subject Classification. 35J60, 65K10, 78A05, 90B99.

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Section: Introductionmentioning

confidence: 99%

Numerical resolution of an “unbalanced” mass transport problem

Benamou¹

2003

ESAIM: M2AN

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“…Previous authors [15,16] have noted that this assumption can lead to violations of the basic physical properties of the subject which are present despite changes in illumination. To address this they use mass or volumetric constraints specific to their given applications.…”

Section: Related Workmentioning

confidence: 99%

Membrane Nonrigid Image Registration

Oxholm

Nishino

2010

Computer Vision – ECCV 2010

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Abstract. We introduce a novel nonrigid 2D image registration method that establishes dense and accurate correspondences across images without the need of any manual intervention. Our key insight is to model the image as a membrane, i.e., a thin 3D surface, and to constrain its deformation based on its geometric properties. To do so, we derive a novel Bayesian formulation. We impose priors on the moving membrane which act to preserve its shape as it deforms to meet the target. We derive these as curvature weighted first and second order derivatives that correspond to the changes in stretching and bending potential energies of the membrane and estimate the registration as the maximum a posteriori. Experimental results on real data demonstrate the effectiveness of our method, in particular, its robustness to local minima and its ability to establish accurate correspondences across the entire image. The results clearly show that our method overcomes the shortcomings of previous intensity-based and feature-based approaches with conventional uniform smoothing or diffeomorphic constraints that suffer from large errors in textureless regions and in areas in-between specified features.

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“…More recently, optimal mass transport has found applications in medical image registration problems (Haker et al, 2004, 2001). Although there have been a number of algorithms in the literature for computing an optimal mass transport, the method proposed in Haker et al (2004, 2001) computes the optimal warp from a first order partial differential equation, which is a computational improvement over earlier proposed higher order methods and computationally complex discrete methods based on linear programming. However, at large grid sizes and especially for 3D registration the computational cost of even this method is significant.…”

Section: Introductionmentioning

confidence: 99%

3D nonrigid registration via optimal mass transport on the GPU

Rehman

Haber

Pryor

et al. 2009

Medical Image Analysis

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In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.

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Mass Preserving Mappings and Image Registration

Cited by 29 publications

References 19 publications

Numerical resolution of an “unbalanced” mass transport problem

Numerical resolution of an “unbalanced” mass transport problem

Membrane Nonrigid Image Registration

3D nonrigid registration via optimal mass transport on the GPU

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