Tauseef ur Rehman

3D nonrigid registration via optimal mass transport on the GPU

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.

AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM

In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.

An Efficient Numerical Method for the Solution of the

In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.

L_2

In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.

Optimal Mass Transfer Problem

In this paper we present a computationally efficient Optimal Mass Transport algorithm. This method is based on the Monge-Kantorovich theory and is used for computing elastic registration and warping maps in image registration and morphing applications. This is a parameter free method which utilizes all of the grayscale data in an image pair in a symmetric fashion. No landmarks need to be specified for correspondence. In our work, we demonstrate significant improvement in computation time when our algorithm is applied as compared to the originally proposed method by Haker et al [1]. The original algorithm was based on a gradient descent method for removing the curl from an initial mass preserving map regarded as 2D vector field. This involves inverting the Laplacian in each iteration which is now computed using full multigrid technique resulting in an improvement in computational time by a factor of two. Greater improvement is achieved by decimating the curl in a multi-resolutional framework. The algorithm was applied to 2D short axis cardiac MRI images and brain MRI images for testing and comparison.

AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L(2) OPTIMAL MASS TRANSFER PROBLEM.

Presented at British Machine Vision Conference 2007, University of Warwick, UK, September 10-13, 2007.

Multigrid Optimal Mass Transport for Image Registration and Morphing

In this paper we present a novel, computationally efficient algorithm for nonrigid 2D image registration based on the work of Haker et al.[1, 2]. We formulate the registration task as an Optimal Mass Transport (OMT) problem based on the Monge-Kantorovich theory. This approach gives a number of advantages over other conventional registration methods: (1) It is parameter free and no landmarks need to be specified, (2) it is symmetrical and the energy functional has a unique minimiser, and (3) it can register images where brightness constancy is an invalid assumption. Our algorithm solves the Optimal Mass Transport program via multi-resolution, multi-grid, and parallel methodologies on a consumer graphics processing unit (GPU). Although solving the OMT problem has been shown to be computationally expensive in the past, we show that our approach is almost two orders magnitude faster than previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the quality of registration). We give results where the algorithm was used to register 2D short axis cardiac MRI images and to morph two image sets from a SOHO solar flare image sequence.