Diffeomorphic demons: efficient non-parametric image registration.

TLDR: An efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm that provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

About: This article is published in NeuroImage.The article was published on 2009-03-01 and is currently open access. It has received 1432 citations till now. The article focuses on the topics: Image registration.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Diffeomorphic demons: efficient non-parametric image registration" ?

The authors propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion ’ s demons algorithm. In the first part of this paper, the authors show that Thirion ’ s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The authors provide strong theoretical roots to the different variants of Thirion ’ s demons algorithm. The authors show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, the authors adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. 

Q2. What have the authors stated for future works in "Diffeomorphic demons: efficient non-parametric image registration" ?

Nevertheless, the framework the authors proposed showed to be versatile enough to be extended to many types of images such as DTI ( Yeo et al., 2008c ), Cortical surfaces ( Yeo et al., 2008b ) or 4D time series of cardiac images ( Peyrat et al., 2008 ). 

Q3. What is the name of the group that tested their registration scheme?

Thanks to their open-source implementation of the diffeomorphic demons algorithm (Vercauteren et al., 2007b), their registration scheme has also been tested by an independent group, cf. (Urschler et al., 2007). 

Q4. What is the main reason why diffeomorphisms are considered an important topic?

With the development of computational anatomy and in the absence of a justified physical model of inter-subject variability, statistics on diffeomorphisms also become an important topic (Arsigny et al., 2006; Lepore et al., 2008; Vaillant et al., 2004; Xue et al., 2006). 

Q5. How many independent groups have tested their algorithm?

Thanks to the open-source implementation of their diffeomorphic demons the authors proposed in (Vercauteren et al., 2007b), their algorithm has been successfully tested by several independent groups. 

Q6. What is the interesting conclusion of the derivations?

One of the most interesting conclusions of these derivations was to show that the symmetric forces could be linked to the efficient second-order minimization (ESM) framework. 

Q7. What is the way to deal with diffeomorphisms?

The authors have seen that the parameterization of diffeomorphic transformations through a stationary speed vector field presented in (Arsigny et al., 2006), provides a very efficient framework for dealing with diffeomorphisms. 

Q8. What is the emphasis on the comparison of the various schemes?

Since the emphasis is on the comparison of the various schemes and not on the final performance, no multi-resolution scheme was used. 

Q9. What is the way to evaluate the diffeomorphic demons?

As a first test to evaluate the usefulness of the diffeomorphic demons with respect to the additive demons, the authors have used the classical “Circle to C” registration problem. 

Q10. What is the way to compute the exponential of a smooth vector field?

Using this property in a recursive manner, this yields the following efficient algorithm for the computation of vector fields exponentials:Algorithm 3 (Fast Vector Field Exponentials) • Choose N such that 2−Nu is close enough to 0, e.g. maxp ∥ ∥2−Nu(p) ∥ ∥ ≤ 0.5• Perform an explicit first order integration: v(p)← 2−Nu(p) for all pixels. 

Q11. What is the advantage of using a parametric approach?

Since the composition and inversion of B-spline transformations cannot be expressed on a B-spline basis, the advantage of using a parametric approach is not clear in this case. 

Q12. What is the main limitation of the additive and compositive demons algorithms?

One of the main limitations of both the additive and compositive demons algorithm is that it does not ensure the invertibility of the output transformations contrarily to diffeomorphic image registration algorithms. 

Q13. What is the way to investigate the image of the exponential map?

When using a single parameterization in the Lie algebra, it might therefore be useful to investigate the image of the exponential map.