Kluwer - Handbook of Biomedical Image Analysis Vol

challenges, and previous methods of image registration in the prostate. Then the chapter describes a three-dimensional mutual information rigid body registration algorithm with special features. The chapter also discusses the threedimensional nonrigid registration algorithm. Many interactively placed control points are independently optimized using mutual information and a thin plate spline transformation is established for the warping of image volumes. Nonrigid method works better than rigid body registration whenever the subject position or condition is greatly changed between acquisitions.

This chapter will cover 1D, 2D, and 3D registration approaches both rigid and elastic. Mathematical foundation for surface and volume registration approaches will be presented. Applications will include plastic surgery, lung cancer, and multiple sclerosis.

Flow-mediated dilation (FMD) offers a mechanism to characterize endothelial function and therefore may play a role in the diagnosis of cardiovascular diseases. Computerized analysis techniques are very desirable to give accuracy and objectivity to the measurements. Virtually all methods proposed up to now to measure FMD rely on accurate edge detection of the arterial wall, and they are not always robust in the presence of poor image quality or image artifacts. A novel method for automatic dilation assessment based on a global image analysis strategy is presented. We model interframe arterial dilation as a superposition of a rigid motion model and a scaling factor perpendicular to the artery. Rigid motion can be interpreted as a global compensation for patient and probe movements, an aspect that has not been sufficiently studied before. The scaling factor explains arterial dilation. The ultrasound (US) sequence is analyzed in two phases using image registration to recover both transformation models. Temporal continuity in the registration parameters along the sequence is enforced with a Kalman filter since the dilation process is known to be a gradual physiological phenomenon. Comparing automated and gold standard measurements we found a negligible bias (0.04%) and a small standard deviation of the differences (1.14%). These values are better than those obtained from manual measurements (bias = 0.47%, SD = 1.28%). The proposed method offers also a better reproducibility (CV = 0.46%) than the manual measurements (CV =

1.40%).

This chapter will focus on nonrigid registration techniques. Nonrigid registration is needed to correct for deformations that occur in various contexts: respiration or organ motion, disease progression over time, tissue deformation

due to surgical procedure, intersubject comparison to build anatomical atlases, etc. Numerous registration techniques have been developed and can be broadly decomposed into intensity-based (photometric) and landmark-based (geometrical) techniques. This chapter will present up-to-date methods.

This chapter will then present how segmentation and registration methods can cooperate: accurate and fast segmentation can be obtained using nonrigid registration; nonrigid registration methods can be constrained by segmentation methods. Results of these cooperation schemes will be given.

This chapter will finally be concerned with validation of nonrigid registration methods. More specifically, an objective evaluation framework will be presented in the particular context of intersubject registration.

This chapter concerns elastic image registration for biomedical applications. We start with an overview and classification of existing registration techniques. We revisit the landmark interpolation and add some generalisations. We develop a general elastic image registration algorithm. It uses a grid of uniform B-splines to describe the deformation. It also uses B-splines for image interpolation. Multiresolution in both image and deformation model spaces yields robustness and speed. We show various applications of the algorithm on MRI, CT, SPECT and ultrasound data. A semiautomatic version of the registration algorithm is capable of accepting expert hints in the form of soft landmark constraints.

The chapter will include algorithms based on landmark and intensity-based image registration. It will compare traditional unidirectional registration algorithms to those that are bidirectional and minimize the inverse consistency error. It will discuss how small deformation models can nonrigidly be used for medical image registration in the brain, skull, and inner ear. It will also discuss how to extend the small deformation model to the large deformation model to accommodate locally large deformation image registration problems. We will provide examples using phantom images and brain images to demonstrate the large deformation case.

Another example of the use of medical image registration is in neurosurgery where it is useful to identify tumors with magnetic resonance images (MRI), yet the established stereotaxy technology uses computed tomography (CT) images. Being able to register these two modalities allows one to transfer the coordinates of tumors from the MR images into the CT stereotaxy. It is similarly useful to transfer functional information from SPECT or positron-emission tomography (PET) into MR or CT for anatomical reference, and for stereotactic exploitation.

The currently used imaging modalities can be generally divided into two main categories, one related to the anatomy being imaged and the other to the functionality represented in the image. The first one includes X-ray, CT

[1] provided a good survey on different classification criteria. In this section we will summarize seven basic classification criteria commonly used (for more details and further reading see the Maintz and Viergever review).

The seven criteria are:

1.Dimensionality

2.Nature of registration basis

3.Nature of transformation

4.Interaction

5.Optimization procedure

6.Modalities involved

7.Subject

1.2.1 Dimensionality

The main division here is either the scope of the registration involves spatial dimension only or is time series also involved. For spacial registration, there are the (i) 3D/3D registration where two or more volumes of interest are to be aligned together, the (ii) 2D/2D registration where two medical images are to be aligned together. In general, 2D/2D registration is less complex than the 3D/3D registration. A more complex one is the (iii) 2D/3D registration which involves the direct alignment of spatial data to projective data (e.g., a preoperative CT image to an intraoperative X-ray image), or the alignment of a single tomographic slice to spatial data. Time can be another dimension involved when the patient’s images and volumes are to be tracked with time for analysis or monitoring.

1.2.2 Nature of Registration Basis

In this category registration can be divided into extrinsic, i.e., based on foreign objects introduced into the imaged space, and intrinsic methods, i.e., based on the image information as generated by the patient. Extrinsic methods rely on artificial objects attached to the patient, objects which are designed to be well visible and accurately detectable in all of the pertinent modalities. As such,

the registration of the acquired images is comparatively easy, fast, can usually be automated, and, since the registration parameters can often be computed explicitly, has no need for complex optimization algorithms. The main drawback of extrinsic registration is that, for good accuracy, invasive maker (e.g., stereotactic frame or screw markers) objects are used. Non-invasive markers (e.g., skin markers individualized foam moulds, head holder frames, or dental adapters) can be used, but as a rule are less accurate.

Intrinsic registration can rely on landmarks in the images or volumes to be aligned. These landmarks can be anatomical based on morphological points on some visible anatomical organ(s), or pure geometrical based. Intrinsic registration can also be based on segmentation results. Segmentation in this case can be rigid where anatomically the same structures (mostly surfaces) are extracted from both images to be registered, and used as sole input for the alignment procedure. They can also be deformable model based where an extracted structure (also mostly surfaces, and curves) from one image is elastically deformed to fit the second image. The rigid model based approaches are probably the most popular methods due to its easy implementation and fast results. A drawback of rigid segmentation based methods is that the registration accuracy is limited to the accuracy of the segmentation step. In theory, rigid segmentation based registration is applicable to images of many areas of the body, yet, in practice, the application areas have largely been limited to neuroimaging and orthopedic imaging.

Another example of intrinsic registration are the voxel based registration methods that operate directly on the image gray values, without prior data reduction by the user or segmentation. There are two distinct approaches: the first is to immediately reduce the image gray value content to a representative set of scalars and orientations, the second is to use the full image content throughout the registration process. Principal axes and moments based methods are the prime examples of reductive registration methods. Within these methods the image center of gravity and its principal orientations (principal axes) are computed from the image zeroth and first order moments. Registration is then performed by aligning the center of gravity and the principal orientations. The result is usually not very accurate, and the method is not equipped to handle differences in scanned volume well. Despite its drawbacks, principal axes methods are widely used in registration problems that require no high accuracy, because of the automatic and very fast nature of its use, and the easy implementation. On the other hand, voxel based registration using full image content is more