PDE-constrained Stokes Large Deformation Diffeomorphic Metric Mapping (LDDMM) is a particularly interesting framework of physically meaningful diffeomorphic registration methods. PDE-constrained Stokes-LDDMM is formulated as a constrained variational problem, where the different physical models can be introduced using the associated partial differential equations as hard constraints. Newton--Krylov optimization has shown an excellent numerical accuracy and an extraordinarily fast convergence rate in this framework. However, the most significant limitation of PDE-constrained Stokes LDDMM is the huge computational complexity, which hinders the extensive use in Computational Anatomy applied studies. In previous work, we proposed a time-efficient approximation of PDE-constrained Stokes-LDDMM formulating the constrained variational problem in the space of band-limited vector fields and performing the computations in the GPU. The parameterization in the space of band-limited vector fields dramatically reduced the computation time. However, the method still showed a considerable memory load, and the performance was low for the smallest and most interesting domain sizes. In this work, we propose two novel variants of Newton--Krylov PDE-constrained Stokes-LDDMM parameterized in the space of band-limited vector fields. The variants are better suited for the band-limited vector field parameterization, yielding efficient methods in terms of time and memory. We have performed a comparative study of the performance of our proposed methods with our previous contribution and the state-of-the-art methods most related to our work. The results have shown that some configurations of the proposed variants outperform the state-of-the-art methods in terms of accuracy and computational complexity. The proposed variants can be regarded as a potentially useful contribution to the set of physically meaningful LDDMM registration methods.

The class of registration methods proposed in the framework of Stokes large deformation diffeomorphic metric mapping (LDDMM) is a particularly interesting family of physically meaningful diffeomorphic registration methods. Stokes-LDDMM methods are formulated as constrained variational problems, where the different physical models are imposed using the associated partial differential equations as hard constraints. The most significant limitation of Stokes-LDDMM framework is its huge computational complexity. The objective of this paper is to promote the use of Stokes-LDDMM in computational anatomy applications with an efficient approximation of the original variational problem. Thus, we propose a novel method for efficient Stokes-LDDMM diffeomorphic registration. Our method poses the constrained variational problem in the space of band-limited vector fields and it is implemented in the GPU. The performance of band-limited Stokes-LDDMM has been compared and evaluated with original Stokes-LDDMM, EPDiff-LDDMM, and band-limited EPDiff-LDDMM. The evaluation has been conducted in 3-D with the nonrigid image registration evaluation project database. Since the update equation in Stokes-LDDMM involves the action of low-pass filters, the computational complexity has been greatly alleviated with a modest accuracy lose. We have obtained a competitive performance for some method configurations. Overall, our proposed method may make feasible the extensive use of novel physically meaningful Stokes-LDDMM methods in different computational anatomy applications. In addition, our results reinforce the usefulness of band-limited vector fields in diffeomorphic registration methods involving the action of low-pass filters in the optimization, even in algorithmically challenging environments such as Stokes-LDDMM.

Non-rigid image registration is a highly ill-posed problem. This means that a number of qualitatively different transformations can achieve the same image similarity after registration. This justifies the vast literature on image registration methods with differences on transformation characterization, regularizers, image similarity metrics, optimization methods, and additional constraints [3]. In the last decade, diffeomorphic registration has arisen as a powerful paradigm for non-rigid image registration, with application to Computational Anatomy. Large Deformation Diffeomorphic MetricMapping (LDDMM) [1] and Diffeomorphic Demons [4] are among the most widespread methods for diffeomorphic registration. In both methods, transformations are characterized to belong to an infinite dimensional Riemannian manifold of diffeomorphisms, parameterized by flows of smooth vector fields in the tangent space. The invertibility of the transformations is numerically guaranteed by the use of sufficiently smooth regularizers. Customarily, these methods regularize the problem with the L-norm of some physically meaningful differential expression of the vector fields, or with the Gaussian smoothing of the vector fields. Simultaneously to the development of the diffeomorphic registration paradigm, the computer vision community has shown a growing interest in robust regularizers based on the Total Variation (TV) norm. The popularity of these regularizers has increased thanks to the availability of optimization methods for solving this challenging problem. The ability of TV based regularizers to preserve discontinuities has led these methods to occupy top positions in optical flow benchmark studies and non-rigid image registration evaluations. The purpose of this article is to propose a method for primal-dual optimization of convexified LDDMM problems, formulated with robust regularizers and image similarity norms related to the TV norm. The method is based on Chambolle and Pock algorithm with diagonal preconditioning [2]. Let Di f f (Ω) be the manifold of diffeomorphisms. Let V be the corresponding tangent space at the identity. Let L= Id − γ∆ be the autoadjoint Laplacian operator associated to the scalar product in V , providing the Riemannian metric in Di f f (Ω). The LDDMM variational problem is given by the minimization of the energy functional

Computational Anatomy aims for the study of the statistical variability in anatomical structures. Variability is encoded by the transformations existing among populations of anatomical images. These transformations are usually computed from diffeomorphic registration based on the large deformation paradigm. In this framework diffeomorphisms are usually computed as end points of paths on the Riemannian manifold of diffeomorphisms parameterized by non-stationary vector fields. Recently, an alternative parameterization based on stationary vector fields has been developed. In this article we propose to use this stationary parameterization for diffeomorphic registration. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. We evaluate the performance of the non-stationary vs the stationary parameterizations in real and synthetic 3D-MRI datasets. Compared to the non-stationary parameterization, our proposal provides similar accuracy in terms of image matching and deformation smoothness while drastically reducing memory and time requirements.

A Java monitor is a Java class that defines one or more synchronized methods. Unlike a regular object, a Java monitor object is intended to be accessed by multiple threads simultaneously. Thus, testing a Java monitor can be significantly different from testing a regular class. In this paper, we propose a state exploration-based approach to testing a Java monitor. A novel aspect of our approach is that during exploration, threads are introduced on-the-fly, and as needed, to simulate race conditions that can occur when multiple threads try to access a monitor object at the same time. Furthermore, each transition is defined in a way such that the behavior of the threads along each path can be precisely characterized and controlled. We describe a prototype tool called MonitorExplorer and report three case studies that are designed to provide an initial evaluation of our approach