Geometrical regularization of displacement fields for histological image registration

This article tackles the registration of 2-D biomedical images (histological sections, autoradiographs, cryosections, etc.). Our goal is to adequately match anatomical features of interest without inducing biologically improbable tissue distortions. We observe that the large variety of registration applications – 3-D volume reconstruction, multimodal molecular mapping, etc. – induce a no less diverse set of requirements in terms of accuracy and robustness. In turn, these directly translate into regularization constraints on the deformation model, which should ideally be specifiable by the user. We propose an adaptive regularization approach where the rigidity constraints are informed by the registration application at hand and whose support is controlled by the geometry of the images to be registered. For each site of a sparse lattice over which a displacement field has been computed, our algorithm estimates, in a robust fashion, a rigid or affine transformation within a circular neighbourhood cut to fit the local geometry around the site. We investigate the behaviour of this technique and discuss its sensitivity to the rigidity parameter.