Journal of Mathematical Imaging and Vision

, Volume 50, Issue 3, pp 246–260 | Cite as

Variational Image Registration Using Inhomogeneous Regularization

  • Christoph Jud
  • Marcel Lüthi
  • Thomas Albrecht
  • Sandro Schönborn
  • Thomas Vetter
Article
  • 360 Downloads

Abstract

We present a generalization of the convolution-based 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.

Keywords

Variational image registration Separable filter approximation  Nonstationary filtering Gaussian process regression 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Christoph Jud
    • 1
  • Marcel Lüthi
    • 1
  • Thomas Albrecht
    • 1
  • Sandro Schönborn
    • 1
  • Thomas Vetter
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of BaselBaselSwitzerland

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