3D image registration using a fast noniterative algorithm
Magnetic Resonance Imaging, 18 (9):
1143--1150 (2000)Abstract
This note describes the implementation of a three-dimensional (3D)
registration algorithm, generalizing a previous 2D version Alexander,
Int J Imaging Systems and Technology 1999;10:242-57. The algorithm
solves an integrated form of linearized image matching equation over
a set of 3D rectangular sub-volumes ('patches') in the image domain.
This integrated form avoids numerical instabilities due to differentiation
of a noisy image over a lattice, and in addition renders the algorithm
robustness to noise. Registration is implemented by first convolving
the unregistered images with a set of computationally fast O(N)
filters, providing four bandpass images for each input image, and
integrating the image matching equation over the given patch. Each
filter and each patch together provide an independent set of constraints
on the displacement field derived by solving a set of linear regression
equations. Furthermore, the filters are implemented at a variety
of spatial scales, enabling registration parameters at one scale
to be used as an input approximation for deriving refined values
of those parameters at a finer scale of resolution. This hierarchical
procedure is necessary to avoid false matches occurring. Both downsampled
and oversampled (undecimating) filtering is implemented. Although
the former is computationally fast, it lacks the translation invariance
of the latter. Oversampling is required for accurate interpolation
that is used in intermediate stages of the algorithm to reconstruct
the partially registered from the unregistered image. However, downsampling
is useful, and computationally efficient, for preliminary stages
of registration when large mismatches are present. The 3D registration
algorithm was implemented using a 12-parameter affine model for the
displacement: u(x) = Ax + b. Linear interpolation was used throughout.
Accuracy and timing results for registering various multislice images,
obtained by scanning a melon and human volunteers in various stationary
positions, is described. The algorithm may be generalized to more
general models of the displacement field, and is also well suited
to parallel processing. (C) 2000 Elsevier Science Inc.