A New Equation for Nonlinear Image Registration with Control over the Vortex Structure in the Displacement Field

Abstract

The goal of nonparametric image registration lies in the solution of highly nonlinear partial differential equations. We present a new partial differential equation for the nonlinear image registration that can be used for the registration of images with textured and complex shaped motifs. The new equation allows to control the vortex structure in the registration field. For many image registration problems, the required transformation should not contain vortices. The application field of the new equation is not restricted to biomedical imaging.

Process flow for classification and clustering of fruit fly gene expression patterns

“…This is done in two steps: first, we apply a rigid registration [13] and second, a nonlinear registration onto the ellipse [14, 15]. This minimizes the distortions produced by the nonlinear registration.…”

Automatic Classification of Embryonic Fruit Fly Gene Expression Patterns

“…This is done in two steps: first, we apply a rigid registration [19] and second, a nonlinear registration onto the ellipse [20,21]. The found transformations onto an ellipse, computed from the registration of the embryo outlines, are then applied to the masked embryo images to obtain the expression pattern mapped onto an ellipse.…”

Projection Technique for Vortex-Free Image Registration

“…This is appropriable in cases where it is known that the solution does not contain vortices. The method presented in [3] has several drawbacks compared to our new approach:…”

“…A first workaround for the vortex problem was presented by Kuska and Braumann [3]. Their method includes the suppression of vortices as weighted term in the variational problem.…”