Consistent image registration

Abstract

Abstract-This paper presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another. This approach produces a consistent set of transformations that have less pairwise registration error, i.e., better correspondence, than traditional methods that estimate the forward and reverse transformations independently. The transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics. The transformations are parameterized by a Fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation. Results using a linear elastic material constraint are presented using both magnetic resonance and X-ray computed tomography image data. The results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity give better registration results than using either constraint alone or none at all.

Active deformation fields: Dense deformation field estimation for atlas-based segmentation using the active contour framework

“…However, such approaches do not necessarily preserve the topology, and do not guarantee the bijectivity constraint unless some explicit schemes are implemented like in Thirion (1998) and Christensen and Johnson (2002). Note that our deformation field computation is similar to the ''additive Demons iterations scheme'' of Thirion's approach (Thirion, 1998) in terms of the way the deformation field is updated, and the type of iterative scheme.…”

Image registration and atlas-based segmentation of cardiac outflow velocity profiles

“…This, along with the desire to quantify the bi-directional transformation error, are the main reasons for the additional validation using the inverse consistency test [43,44]. Each of the images from the set is registered to all the others images from the set.…”

Computing inverse optical flow

“…This is the case, for instance, in symmetric optical flow methods [2] or diffeomorphic image registration, e.g. [9], [12] or [3]. These methods introduce the inverse mapping to improve the coherence between the forward and backward flows, reducing the number of false matchings.…”

“…For instance, the diffeomorphic method presented in [9] explicitly computes the inverse mapping using an iterative algorithm: for each position, it iteratively searches for the inverse correspondence until the estimated error is below a threshold. In each iteration, the algorithm uses trilinear interpolation to compute the flow.…”