The adaptive bases algorithm for intensity-based nonrigid image registration

Abstract

Abstract-Nonrigid registration of medical images is important for a number of applications such as the creation of population averages, atlas-based segmentation, or geometric correction of functional magnetic resonance imaging (fMRI) images to name a few. In recent years, a number of methods have been proposed to solve this problem, one class of which involves maximizing a mutual information (MI)-based objective function over a regular grid of splines. This approach has produced good results but its computational complexity is proportional to the compliance of the transformation required to register the smallest structures in the image. Here, we propose a method that permits the spatial adaptation of the transformation's compliance. This spatial adaptation allows us to reduce the number of degrees of freedom in the overall transformation, thus speeding up the process and improving its convergence properties. To develop this method, we introduce several novelties: 1) we rely on radially symmetric basis functions rather than B-splines traditionally used to model the deformation field; 2) we propose a metric to identify regions that are poorly registered and over which the transformation needs to be improved; 3) we partition the global registration problem into several smaller ones; and 4) we introduce a new constraint scheme that allows us to produce transformations that are topologically correct. We compare the approach we propose to more traditional ones and show that our new algorithm compares favorably to those in current use.Index Terms-Adaptive bases algorithm, mutual information, nonrigid image registration.

A Variational Formulation for Discrete Registration

“…at any spatial location x ∈ Ω T can found through interpolation of the nodal probabilities [L * m ] N m=1 based on the finite element approximation in equation (9). Then, the estimated displacement field U(x) at x ∈ Ω T is obtained by choosing the displacement value d k with the highest optimal probability at that spatial location, i.e., U(x) = d k where k = argmax r∈{1,2,...,K} L * r (x).…”

“…Alternatively, a demons minimization strategy can be used, where the smoothing of the displacement field is decoupled from the minimization of the data term [6], [7], [8]. In parametric approaches, regularization is enforced in an implicit manner through the parametrization of the displacement field using a finite set of basis functions, such as radial basis functions (RBF) [9], B-spline based free form deformations (FFD) [10], finite element method (FEM) basis functions [11].…”

Development of 2dTCA for the detection of irregular, transient bold activity

“…Using a combination of rigid body [Li, 2001;Maes et al, 1997;Wells et al, 1996] and nonrigid intensity-based registration algorithms Hartmann et al, 1999;Rohde et al, 2003], all the images in a real subject fMRI time series of 100 volumes were registered to each other. The transformations computed with this technique served as an estimator for the motion occurring during the scan.…”

Cortical Shift Tracking Using a Laser Range Scanner and Deformable Registration Methods

“…In this paper, a deformable registration extension is explored to allow for shift tracking based on serial laser-range scan data. The deformable registration is provided by local support radial basis functions [11] and mutual information optimization [12]. Once calculated, the deformation field allows for easy calculation of surface shift in serial range scans.…”