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# Geometry, Imaging and Computing

## Volume 1 (2014)

### Number 4

### A novel variational model for image registration using Gaussian curvature

Pages: 417 – 446

DOI: http://dx.doi.org/10.4310/GIC.2014.v1.n4.a2

#### Authors

#### Abstract

Image registration is one important task in many image processing applications. It aims to align two or more images so that useful information can be extracted through comparison, combination or superposition. This is achieved by constructing an optimal transformation which ensures that the template image becomes similar to a given reference image. Although many models exist, designing a model capable of modelling a large and smooth deformation field continues to pose a challenge. This paper proposes a novel variational model for image registration using the Gaussian curvature as a regulariser. The model is motivated by the surface restoration work in geometric processing [Elsey and Esedoglu, *Multiscale Model. Simul.*, (2009), pp. 1549–1573]. An effective numerical solver is provided for the model using an augmented Lagrangian method. Numerical experiments can show that the new model outperforms three competing models based on, respectively, a linear curvature [Fischer and Modersitzki, *J. Math. Imaging Vis.*, (2003), pp. 81–85], the mean curvature [Chumchob, Chen and Brito, *Multiscale Model. Simul.*, (2011), pp. 89–128] and the diffeomorphic demon model [Vercauteren at al., *NeuroImage*, (2009), pp. 61–72] in terms of robustness and accuracy.

#### Keywords

image registration, non-parametric image registration, regularisation, Gaussian curvature, surface mapping