Variational Image Registration Using Inhomogeneous Regularization

Abstract

We present a generalization of the convolutionbased variational image registration approach, in which different regularizers can be implemented by conveniently exchanging the convolution kernel, even if it is nonseparable or nonstationary. Nonseparable kernels pose a challenge because they cannot be efficiently implemented by separate 1D convolutions. We propose to use a low-rank tensor decomposition to efficiently approximate nonseparable convolution. Nonstationary kernels pose an even greater challenge because the convolution kernel depends on, and needs to be evaluated for, every point in the image. We propose to pre-compute the local kernels and efficiently store them in memory using the Tucker tensor decomposition model. In our experiments we use the nonseparable exponential kernel and a nonstationary landmark kernel. The exponential kernel replicates desirable properties of elastic image registration, while the landmark kernel incorporates local prior knowledge about corresponding points in the images. We examine the trade-off between the computational resources needed and the approximation accuracy of the tensor decomposition methods. Furthermore, we obtain very smooth displacement fields even in the presence of large landmark displacements.

A fractional-order decomposition model of image registration and its numerical algorithm

“…To deduce staircase effect, Zhang and Chen (2015) extended TV regularization into fractional-order regularization R(u) = ∇ α u L 1 (Ω) (1 < α < 2). Moreover, there are also many other papers concerning image registration model and numerical simulation (Beg et al 2005;Bruveris et al 2011;Chen et al 2009;Dupuis et al 1998;Goldstein and Osher 2009;Han and Zhou 2017;Thirion 1998;Haber and Modersitzki 2007;Ibrahim and Chen 2017;Alahyane et al 2018Alahyane et al , 2019Lederman et al 2016;Jud et al 2014). Ibrahim and Chen (2017) put forward a unifying framework for decomposition models.…”