Registration is the determination of a geometrical transformation that aligns points in one view of an object with corresponding points in another view of that object or another object. We use the term "view" generically to include a three-dimensional image, a two-dimensional image, or the physical arrangement of an object in space. Three-dimensional images are acquired by tomographic modalities, such as computed tomography (CT), magnetic resonance (MR) imaging, single-photon emission computed tomography (SPECT), and positron emission tomography (PET). In each of these modalities, a contiguous set of two-dimensional slices provides a three-dimensional array of image intensity values. Typical two-dimensional images may be x-ray projections captured on film or as a digital radiograph or projections of visible light captured as a photograph or a video frame. In all cases, we are concerned primarily with digital images stored as discrete arrays of intensity values. In medical applications, which are our focus, the object in each view will be some anatomical region of the body. (See Volume I of this handbook for a discussion of medical imaging modalities.) The two views are typically acquired from the same patient, in which case the problem is that of intrapatient registration, but interpatient registration has application as well (see Chapter 17).
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