A Novel Nonrigid Registration Algorithm and Applications

Abstract

In this paper we describe a new algorithm for nonrigid registration of brain images based on an elastically deformable model. The use of registration methods has become an important tool for computer-assisted diagnosis and surgery. Our goal was to improve analysis in various applications of neurology and neurosurgery by improving nonrigid registration. A local gray level similarity measure is used to make an initial sparse displacement field estimate. The field is initially estimated at locations determined by local features, and then a linear elastic model is used to infer the volumetric deformation across the image. The associated partial differential equation is solved by a finite element approach. A model of empirically observed variability of the brain was created from a dataset of 154 young adults. Both homogeneous and inhomogeneous elasticity models were compared. The algorithm has been applied to medical applications including intraoperative images of neurosurgery showing brain shift and a study of gait and balance disorder.

Robust nonrigid registration to capture brain shift from intraoperative MRI

“…These surface-based methods showed very good accuracy near the boundary conditions, but suffered from as lack of data inside the brain [6]. Rexilius et al [25] followed Ferrant's efforts by incorporating block-matching estimated displacements as internal boundary condition to the FEM model (leading to the solution presented in Section II-C2). However, the method proposed by Rexilius was not robust to outliers.…”

“…The numerical scheme of (17) can be written as (25) Since is nonsingular, we can write the system in the form (26) This system converges if and only if the eigenvalues of satisfy: , . From (20) and (21) Now that we proved the convergence, one can have the equation of the displacement field U after convergence (27) which implies that (28) Equation (28) is exactly the solution of the matching energy minimization (4), meaning that the proposed scheme solves the interpolation problem.…”

Hybrid Formulation of the Model-Based Non-rigid Registration Problem to Improve Accuracy and Robustness

“…Rohr et al [4] combined elastic regularization with an improved block matching (BM) algorithm relying on relevant anatomical landmarks and taking into account the anisotropic matching error. In 2001, Rexilius [5] combined feature point correspondences with a finite element biomechanical model in an approximation formulation to capture brain shift.…”

A Framework for the Generation of Realistic Brain Tumor Phantoms and Applications

“…In this work, we simulate the three-dimensional tumor growth based on a linear elastic model, which was previously also used to capture shape changes of the brain during neurosurgery [11,12]. Since a rigid model can be assumed for surrounding tissue such as the dura mater, the model is constrained at the boundaries of a brain mask generated by a modified watershed transform [13], so that motion is restricted to areas inside the brain.…”

“…The resulting equation is solved by a finite element approach [14]. A fast parallel implementation was proposed in [12] as part of a nonrigid registration approach. In order to also simulate the process of tumor growth, we initially start with a deformation restricted to the boundary of a downsampled (factor 5) phantom, with its center of gravity placed at the same position as for the full-scale tumor phantom.…”