CHAPTER 3
Mutual Information: A Similarity Measure
for Intensity Based Image Registration
Hua-mei Chen
3.1
Introduction
Mutual information (MI) was independently proposed in 1995 by two groups of
researchers (Maes and Collignon of Catholic University of Leuven (Collignon
et al. 1995) and Wells and Viola of MIT (Viola and Wells 1995» as a similarity
measure for intensity based registration of images acquired from different
types of sensors. Since its introduction, MI has been used widely for a variety
of applications involving image registration. These include medical imaging
(Holden et al. 2000; Maes et al. 1997; Studhilme et al. 1997; Wells et al. 1996),
remote sensing (Chen et al. 2003ab), and computer vision (Chen and Varshney
2001a). The MI registration criterion states that an image pair is geometrically
registered when the mutual information between the two images reaches its
maximum. The strength of MI as a similarity measure lies in the fact that
no assumptions are made regarding the nature of the relation between the
intensity values of the image, as long as such a relationship exists. Thus, the
MI criterion is very general and has been used in many image registration
problems in a range of applications.
The basic concept of image registration using MI as the similarity measure
may be explained with the help of Fig. 3.1. In this figure, F is referred to as the
floating image, whose pixel coordinates are to be mapped to new coordinates on
the reference image R, which are resampled according to the positions defined
by the new coordinates. x represents the coordinates of a pixel (voxel in 3D
case) in F and y represents the coordinates of a pixel in R. The transformation
model is represented by T with associated parameters a. The dependence of
T on a is indicated by the use of notation Ta. The joint histogram, which is
used to compute the mutual information, h a , between floating and reference
images, is denoted by hTa (F, R). The subscript Ta indicates that h and I are
dependent on Ta. The blocks in the shaded portion of Fig. 3.1 represent the
global optimization process used to maximize mutual information.
In this chapter, we describe the concept of image registration using MI
as a similarity measure by discussing each component of Fig. 3.1 in detail.
The application of MI based image registration methodology to multisensor
and multi-temporal remote sensing images will be discussed in Chap. 7. Two
popular methods to estimate the joint histogram for the computation of MI
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004
Mutual Information: A Similarity Measure
for Intensity Based Image Registration
Hua-mei Chen
3.1
Introduction
Mutual information (MI) was independently proposed in 1995 by two groups of
researchers (Maes and Collignon of Catholic University of Leuven (Collignon
et al. 1995) and Wells and Viola of MIT (Viola and Wells 1995» as a similarity
measure for intensity based registration of images acquired from different
types of sensors. Since its introduction, MI has been used widely for a variety
of applications involving image registration. These include medical imaging
(Holden et al. 2000; Maes et al. 1997; Studhilme et al. 1997; Wells et al. 1996),
remote sensing (Chen et al. 2003ab), and computer vision (Chen and Varshney
2001a). The MI registration criterion states that an image pair is geometrically
registered when the mutual information between the two images reaches its
maximum. The strength of MI as a similarity measure lies in the fact that
no assumptions are made regarding the nature of the relation between the
intensity values of the image, as long as such a relationship exists. Thus, the
MI criterion is very general and has been used in many image registration
problems in a range of applications.
The basic concept of image registration using MI as the similarity measure
may be explained with the help of Fig. 3.1. In this figure, F is referred to as the
floating image, whose pixel coordinates are to be mapped to new coordinates on
the reference image R, which are resampled according to the positions defined
by the new coordinates. x represents the coordinates of a pixel (voxel in 3D
case) in F and y represents the coordinates of a pixel in R. The transformation
model is represented by T with associated parameters a. The dependence of
T on a is indicated by the use of notation Ta. The joint histogram, which is
used to compute the mutual information, h a , between floating and reference
images, is denoted by hTa (F, R). The subscript Ta indicates that h and I are
dependent on Ta. The blocks in the shaded portion of Fig. 3.1 represent the
global optimization process used to maximize mutual information.
In this chapter, we describe the concept of image registration using MI
as a similarity measure by discussing each component of Fig. 3.1 in detail.
The application of MI based image registration methodology to multisensor
and multi-temporal remote sensing images will be discussed in Chap. 7. Two
popular methods to estimate the joint histogram for the computation of MI
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004