AN IMPROVED METHOD OF “DEMONS” NON-RIGID IMAGE REGISTRATION
ALGORITHM

Xiangbo LIN*,†, Tianshuang QIU*1, Frédéric Nicolier†, Su RUAN†
(*.Department of Electronic Engineering, Dalian University of Technology, Dalian 116024, China;
†. Dept. GE&II, IUT de Troyes, Université de Reims Champagne. Ardnne, 10026 Troyes Cedex, France;)

ABSTRACT1

In this paper the force formulation based on optical
flow of the Demons non-rigid registration algorithm is
analyzed. It is indicated that the force formulation has some
limitations in certain circumstances, which may be the
reason that the topology structure can’t be preserved in the
whole deformation region. In order to solve the problem, a
more reasonable modified Demons algorithm is proposed,
which is approved by the experiment results.
Keywords: non-rigid registration; optical flow; topology;

1. INTRODUCTION

Image registration is the process to find the spatial
transformation applied to the source image so that it can be
aligned to the target. In medical applications, registration
can be used to monitor tumor development or treatment over
time, to make an operation plan, or to compare images from
different subjects. The physical characteristics of soft tissue
determine that the non-rigid registration is more suitable for
medical images. The non-rigid registration is a developing
research and a few reviews can be found in [1-5].
In this paper, an intensity-based non-rigid registration
method, Demons algorithm [6], is discussed and the
modification to this algorithm is provided. Although this
method has been widely studied [7-10], what we want to
discuss in this paper has not been paid enough attention
before. The detailed analysis and the modified algorithm can
be found in section 3 and 4, and section 5 gives the
validation by a simple experiment.
2. METHODS
2.1 Demons Registration (D) and Active Demons

1 Corresponding author: Tel: +86 411 84709573; Fax: +86 411 84709573;
E-mail address: qiutsh@dlut.edu.cn(T. QIU).
Registration (AD)
The main idea of the Demons registration algorithm is
to consider the non-rigid registration as a diffusion process.
A ‘demon’ is a selective effector situated in a point P of the
boundary of an object O in the reference image (S). The
moving image (M) is considered to be a deformable grid,
whose vertex is labeled ‘inside’ or ‘outside’. The role of a
‘demon’ is to push M inside O if the corresponding point of
M is labeled ‘inside’, and outside O if it is labeled ‘outside’.
The inside/outside attribute determines the force direction of
a grid vertex. Suppose the spatial coordinate of a ‘demon’ is
p with an intensity s(p), and the intensity of the
corresponding point in M is m(p). If ( ) ( )m s<p p , this point
is labeled ‘inside’ and pushed toward s−∇ . If ( ) ( )m s>p p ,
this point is labeled ‘outside’ and pushed toward s+∇ .
Although the behavior of a ‘demon’ can be designed in
different ways, implementation method based on the optical
flow theory is used for most medical image analysis. The
basic force formulation is
2 2
( )
|| || ( )
m s s
s m s
− ∇
=
∇ + −
K
f (1)
When
K
f is obtained, the moving image can be registered to
the reference image.
It can be seen from equation (1) that the gradient
information driving the deformation is taken from the static
image only. Wang et al[9] made some modification to the
original Demons algorithm to make the registration more
efficient, which can be called Active Demons registration
algorithm. Assuming that the diffusion is bi-directional, a
‘demon’ at any point in the image space will produce not
only a force that allows a deformable moving object to
diffuse into a corresponding static object, but also produce a
force that allows the static object to diffuse into the
corresponding moving object. So a new force based on
Newton’s third law of motion is combined to equation (1),
which results
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