Mark P. Wachowiak

High-performance medical image registration using new optimization techniques

Optimization of a similarity metric is an essential component in intensity-based medical image registration. The increasing availability of parallel computers makes parallelizing some registration tasks an attractive option to increase speed. In this paper, two new deterministic, derivative-free, and intrinsically parallel optimization methods are adapted for image registration. DIviding RECTangles (DIRECT) is a global technique for linearly bounded problems, and multidirectional search (MDS) is a recent local method. The performance of DIRECT, MDS, and hybrid methods using a parallel implementation of Powells method for local refinement, are compared. Experimental results demonstrate that DIRECT and MDS are robust, accurate, and substantially reduce computation time in parallel implementations

A real time finite element based tissue simulation method incorporating nonlinear elastic behavior

This paper presents a new finite element simulation approach for surgical simulators. Based on the solution of the algebraic equations derived from a nonlinear elastic model, we propose a real time simulation rule based on the implicit relation between the displacements of contacted and free nodes. This rule is an analytic expression in the linear case, and an approximation of the implicit relation in the non-linear case. We also remove some of the restrictions on flexibility exhibited by previous linear and nonlinear approaches. In the linear case, real time reconfiguration of the contacted nodes and the boundary constraints is realized using the simulation rule, while in the nonlinear case, a similar result is obtained by employing affine mapping. These methods allow nonlinear material properties to be applied to real time tissue simulation, with an efficiency comparable to that of the tensor matrix method for linear elastic models.

Registration of two-dimensional cardiac images to preprocedural three-dimensional images for interventional applications

To evaluate the accuracy and efficiency of rigid‐body registration of two‐dimensional fast cine and real‐time cardiac images to high‐resolution and SNR three‐dimensional preprocedural reference volumes for application during MRI‐guided interventional procedures.

Multiresolution Biomedical Image Registration Using Generalized Information Measures

In addition to the widely-used Shannon mutual information, generalized information-theoretic similarity metrics have properties that make them conducive to biomedical image registration. The mutual information based on Havrda-Charvat and Renyi entropy measures are compared to Shannon mutual information, normalized mutual information, the correlation ratio, and other generalized metrics. Single slice/3D registration results on brain and heart volumes show that generalized metrics that deviate slightly from the Shannon metrics can improve registration outcomes based on success rate, and have competitive computation times. The results also suggest that these metrics may be used with Shannon (and other) measures in a complementary manner.

Compact support radial basis functions for soft tissue deformation

We describe the use of compact support radial basis functions (CSRBFs) for simulation of soft tissue deformation. CSRBFs allow surface and volumetric deformations to be computed in near real time. In comparison to other spline functions, CSRBFs effect local deformations. In addition, CSRBF matrices are guaranteed to be positive definite and invertible. Visual realism can be achieved by utilizing different CSRBFs with deformation behaviour approximating specific soft tissue characteristics, and by a locality parameter. Computations can also be performed in parallel for increased efficiency. The efficacy of this deformation model is demonstrated on data from a 3D prostate image for the application of needle insertion for implanting radioactive seeds for brachytherapy.

Parallel Optimization Approaches for Medical Image Registration

Optimization of a similarity metric is an essential component in most medical image registration approaches based on image intensities. The increasing availability of parallel computers makes parallelizing some registration tasks an attractive option. In this paper, two relatively new, deterministic, direct optimization algorithms are parallelized for distributed memory systems, and adapted for image registration. DIRECT is a global technique, and the multidirectional search is a recent local method. The performance of several variants are compared. Experimental results show that both methods are robust, accurate, and, in parallel implementations, can significantly reduce computation time.

Registration of fast cine cardiac MR slices to 3D preprocedural images: toward real-time registration for MRI-guided procedures

Interventional cardiac magnetic resonance (MR) procedures are the subject of an increasing number of research studies. Typically, during the procedure only two-dimensional images of oblique slices can be presented to the interventionalist in real time. There is a clear benefit to being able to register the real-time 2D slices to a previously acquired 3D computed tomography (CT) or MR image of the heart. Results from a study of the accuracy of registration of 2D cardiac images of an anesthetized pig to a 3D volume obtained in diastole are presented. Fast cine MR images representing twenty phases of the cardiac cycle were obtained of a 2D slice in a known oblique orientation. The 2D images were initially mis-oriented at distances ranging from 2 to 20 mm, and rotations of +/-10 degrees about all three axes. Images from all 20 cardiac phases were registered to examine the effect of timing between the 2D image and the 3D pre-procedural image. Linear registration using mutual information computed with 64 histogram bins yielded the highest accuracy. For the diastolic phases, mean translation and rotation errors ranged between 0.91 and 1.32 mm and between 1.73 and 2.10 degrees. Scans acquired at other phases also had high accuracy. These results are promising for the use of real time MR in image-guided cardiac interventions, and demonstrate the feasibility of registering 2D oblique MR slices to previously acquired single-phase volumes without preprocessing.

Adaptive finite element technique for cutting in surgical simulation (Cum Laude Poster Award)

Pre-computed finite element methods are valuable because of their extreme speed and high accuracy for soft tissue modeling, but they are not suitable for surgical incision simulation. In this paper we present an adaptive algorithm for finite element computation based on a preprocessing approach. It inverts the global stiffness matrix in a pre-computing stage and then simulates each cutting step by updating two lists of basic components iteratively with some localization techniques. This method allows a fast and physically accurate simulation of incision procedures.

Estimation of generalized entropies with sample spacing

In addition to the well-known Shannon entropy, generalized entropies, such as the Renyi and Tsallis entropies, are increasingly used in many applications. Entropies are computed by means of nonparametric kernel methods that are commonly used to estimate the density function of empirical data. Generalized entropy estimation techniques for one-dimensional data using sample spacings are proposed. By means of computational experiments, it is shown that these techniques are robust and accurate, compare favorably to the popular Parzen window method for estimating entropies, and, in many cases, require fewer computations than Parzen methods.

Combining global and local parallel optimization for medical image registration

Optimization is an important component in linear and nonlinear medical image registration. While common non-derivative approaches such as Powells method are accurate and efficient, they cannot easily be adapted for parallel hardware. In this paper, new optimization strategies are proposed for parallel, shared-memory (SM) architectures. The Dividing Rectangles (DIRECT) global method is combined with the local Generalized Pattern Search (GPS) and Multidirectional Search (MDS) and to improve efficiency on multiprocessor systems. These methods require no derivatives, and can be used with all similarity metrics. In a multiresolution framework, DIRECT is performed with relaxed convergence criteria, followed by local refinement with MDS or GPS. In 3D-3D MRI rigid registration of simulated MS lesion volumes to normal brains with varying noise levels, DIRECT/MDS had the highest success rate, followed by DIRECT/GPS. DIRECT/GPS was the most efficient (5-10 seconds with 8 CPUs, and 10-20 seconds with 4 CPUs). DIRECT followed by MDS or GPS greatly increased efficiency while maintaining accuracy. Powells method generally required more than 30 seconds (1 CPU) with a low success rate (0.3 or lower). This work indicates that parallel optimization on shared memory systems can markedly improve registration speed and accuracy, particularly for large initial misorientations.