Explicit B-spline regularization in diffeomorphic image registration

Nicholas J Tustison,Brian B Avants

doi:10.3389/fninf.2013.00039

Abstract

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline “flavored” diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools.

Highlights

Establishment of anatomical and functional correspondence is a crucial step toward gaining insight into biological processes
Each image was registered to its corresponding template using either Symmetric Normalization (SyN) or B-spline SyN as described previously
For the data sets used in this study, times for B-spline SyN were approximately 15–40% greater than Gaussian-based SyN using single-threading and a dense metric gradient sampling

Summary

Introduction

Establishment of anatomical and functional correspondence is a crucial step toward gaining insight into biological processes. Current research was preceded by related work for geometric modeling (Sederberg and Parry, 1986) and originated with such important contributions as Szeliski and Coughlan (1997); Thévenaz et al (1998), and Rueckert et al (1999) Continued development within this early spline-based paradigm produced additional innovations such as integrated similarity metrics (e.g., Mattes et al, 2003), additional transformation constraints (e.g., Rohlfing et al, 2003), and notable open source implementations (e.g., Ibanez et al, 2005; Klein et al, 2010b; Modat et al, 2010; Shackleford et al, 2010)

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Conclusion