3D image registration using a fast noniterative algorithm

This note describes the implementation of a three-dimensional (3D) registra tion algorithm, generalizing a previous 2D version [Alexander, Int J Imagin g Systems and Technology 1999;10:242-57]. The algorithm solves an integrate d form of linearized image matching equation over a set of 3D rectangular s ub-volumes ('patches') in the image domain. This integrated form avoids num erical instabilities due to differentiation of a noisy image over a lattice , and in addition renders the algorithm robustness to noise. Registration i s implemented by first convolving the unregistered images with a set of com putationally fast [O(N)] filters, providing four bandpass images for each i nput image, and integrating the image matching equation over the given patc h. Each filter and each patch together provide an independent set of constr aints on the displacement field derived by solving a set of linear regressi on equations. Furthermore, the filters are implemented at a variety of spat ial scales, enabling registration parameters at one scale to be used as an input approximation for deriving refined values of those parameters at a fi ner scale of resolution. This hierarchical procedure is necessary to avoid false matches occurring. Both downsampled and oversampled (undecimating) fi ltering is implemented. Although the former is computationally fast, it lac ks the translation invariance of the latter. Oversampling is required for a ccurate interpolation that is used in intermediate stages of the algorithm to reconstruct the partially registered from the unregistered image. Howeve r, downsampling is useful, and computationally efficient, for preliminary s tages of registration when large mismatches are present. The 3D registratio n algorithm was implemented using a 12-parameter affine model for the displ acement: u(x) = Ax + b. Linear interpolation was used throughout. Accuracy and timing results for registering various multislice images, obtained by s canning a melon and human volunteers in various stationary positions, is de scribed. The algorithm may be generalized to more general models of the dis placement field, and is also well suited to parallelprocessing. (C) 2000 El sevier Science Inc. All rights reserved.