Pattern Recognition 32 1999 71 86 An overlap invariant entropy measure of 3D medical image alignment C Studholme D L G Hill D J Hawkes Department Diagnostic Radiology and Electrical Engineering Yale University BML 332 333 Cedar Street New Haven 06511 USA Computational Imaging Science Group Radiological Sciences UMDS Guys Hospital London SE1 9RT UK Received 31 October 1997 in revised form 29 April 1998 Abstract This paper is concerned with the development of entropy based registration criteria for automated 3D multi modality medical image alignment In this application where misalignment can be large with respect to the imaged field of view invariance to overlap statistics is an important consideration Current entropy measures are reviewed and a normalised measure is proposed which is simply the ratio of the sum of the marginal entropies and the joint entropy The effect of changing overlap on current entropy measures and this normalised measure are compared using a simple image model and experiments on clinical image data Results indicate that the normalised entropy measure provides significantly improved behaviour over a range of imaged fields of view 1999 Pattern Recognition Society Published by Elsevier Science Ltd All rights reserved Keywords Multi modality 3D medical images Registration criteria Information theory Entropy Mutual information Normalisation 1 Introduction Recently there has been active research into the use of voxel similarity based measures of multi modality medical image alignment 1 2 Such an approach avoids the task of identifying corresponding anatomical structures in two different modalities which is difficult to automate for a broad range of clinical data The use of image similarity measures especially those derived from information theory have been shown to allow fully automated alignment in a number of important clinical applications 3 4 In this paper we are concerned Corresponding author specifically with entropy based measures of alignment between different 3D medical modalities 5 9 In particular we examine one limitation of the measures that have so far been proposed which is their sensitivity to image overlap statistics Invariance to image overlap is an important property for this application where misalignment may be significant with respect to the volume of overlap of the images Such misalignment is illustrated by the image pair in Fig 1 The paper begins by introducing some of the ideas behind the measurement of information content in an image and how this can be used to quantify image alignment Joint entropy derived from the joint probability distribution of image values provides the starting point to relate the information content of a pair of images Its properties are examined as a measure of image alignment 0031 3203 99 19 00 0 00 1999 Pattern Recognition Society Published by Elsevier Science Ltd All rights reserved PII S 0 0 3 1 3 2 0 3 9 8 0 0 0 9 1 0 72 C Studholme et al Pattern Recognition 32 1999 71 86 Fig 1 Transaxial top and Sagittal bottom slices through clinical MR left and CT right image volumes of the brain here manually aligned illustrating the limited volume of overlap of two clinical images CT in particular can have a limited extent to reduce X Ray dose to the patient and from this a set of related measures including mutual information and normalised mutual information are developed and compared The following sections then compare the behaviour of joint entropy mutual information and the normalised measure to varying image statistics in their region of overlap This is achieved using a simple image model and also by examining the behaviour of an automated registration algorithm using these measures as the initial misalignment and field of view of the images is varied Different modalities are commonly used in clinical diagnosis and therapy planning which record different anatomical or physiological properties within the patient and can therefore delineate different structures of clinical interest for example to distinguish between tumor and non tumor tissues In order to accurately relate different structures of interest delineated by the two modalities we need to align the images into a common coordinate system In practice these modalities will delineate both common and complementary structure within the images To define alignment we wish to make use of any shared regions delineated by the two modalities 2 Information measures and image alignment 2 1 Information measures In imaging the head using a 3D medical imaging device we form an image of measurements of a physical property of material within the patient Such properties delineate regions of material for example grey matter white matter bone or tumor tissue within the patient The concept of uncertainty can provide a useful basis for developing ideas about information theory 10 If we examine the probabilities of values occurring in an image some values are rare and some are common In C Studholme et al Pattern Recognition 32 1999 71 86 73 Fig 2 The information content of a binary symmetric channel This can be equated to the information content of a binary image consisting of foreground m and background m where p m 1 p m The horizontal axis in this graph therefore corresponds to varying the ratio of background to foreground area in the images of the white circle shown below predicting what value a voxel has we can form an estimate of the uncertainty of our guess at the value given the observed distribution of probabilities If all probabilities are equal uncertainty in guessing what value a given voxel might have is largest If there is only one value in the scene then the uncertainty in guessing the value of a given voxel would be zero If we learn the value of a measurement pixel or voxel that we were very uncertain about i e it would be difficult to guess then we gain a large amount of information Conversely if we learn a value that would be easy to guess because it has a high probability of occurrence then we only gain a small amount of information If we have a set of values for example the set of voxel values occurring in an image we can then look at the average amount of information provided by the whole set Essentially we can say an image with similar numbers of each voxel value contains more information than an image where the majority of voxels have the same value There have been many plausible functions proposed to express this concept of information The most commonly used