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image registration

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As used herein, "image registration" refers to a method, process, module, component, apparatus, and/or system that seeks to achieve precision in the alignment of two images. As used here, "image" may refer to one or more of an image of a structure or object, a time series of images such as a video or other time series, another image, or a model (e.g., a computer-based model or a physical model, in either two dimensions or three dimensions). In the simplest case of image registration, two images are aligned. One image may serve as the target image and the other as a source image; the source image is transformed, positioned, realigned, and/or modified to match the target image. An optimization procedure may be applied that updates the transformation of the source image based on a similarity value that evaluates the current quality of the alignment. An iterative procedure of optimization may be repeated until a (local) optimum is found. An example is the registration of CT and PET images to combine structural and metabolic information. 
Image registration can be used in a variety of medical applications: Studying temporal changes; Longitudinal studies may acquire images over several months or years to study long-term processes, such as disease progression. Time series correspond to images acquired within the same session (seconds or minutes). Time series images can be used to study cognitive processes, heart deformations and respiration; Combining complementary information from different imaging modalities. One example may be the fusion of anatomical and functional information. Since the size and shape of structures vary across modalities, evaluating the alignment quality can be more challenging. Thus, similarity measures such as mutual information may be used; Characterizing a population of subjects. In contrast to intra-subject registration, a one-to-one mapping may not exist between subjects, depending on the structural variability of the organ of interest. Inter-subject registration may be used for atlas construction in computational anatomy. Here, the objective may be to statistically model the anatomy of organs across subjects; Computer-assisted surgery: in computer-assisted surgery pre-operative images such as CT or MRI may be registered to intra-operative images or tracking systems to facilitate image guidance or navigation.
Image registration can be done using an intrinsic method or an extrinsic method or a combination of both. The extrinsic image registration method uses an outside object that is introduced into the physical space where the image was taken. The outside object may be referred to using different names herein such as a "reference," "visual reference," "visualization reference," "reference point," "reference marker," "patient reference," or "fiducial marker." The intrinsic image registration method uses information from the image of the patient, such as landmarks and object surfaces.
There may be several considerations made when performing image registration:

The transformation model. Common choices are rigid, affine, and deformable (i.e., nonlinear) transformation models. B-spline and thin plate spline models are commonly used for parameterized transformation fields. Non-parametric or dense deformation fields carry a displacement vector at every grid location; this may use additional regularization constraints. A specific class of deformation fields are diffeomorphisms, which are invertible transformations with a smooth inverse;

The similarity metric. A distance or similarity function is used to quantify the registration quality. This similarity can be calculated either on the original images or on features extracted from the images. Common similarity measures are sum of squared distances (SSD), correlation coefficient, and mutual information. The choice of similarity measure depends on whether the images are from the same modality; the acquisition noise can also play a role in this decision. For example, SSD may be the optimal similarity measure for images of the same modality with Gaussian noise. However, the image statistics in ultrasound may be significantly different from Gaussian noise, leading to the introduction of ultrasound specific similarity measures. Multi-modal registration may use a more sophisticated similarity measure; alternatively, a different image representation can be used, such as structural representations or registering adjacent anatomy;

The optimization procedure. Either continuous or discrete optimization is performed. For continuous optimization, gradient-based optimization techniques are applied to improve the convergence speed.(Search "medical image computing" on Wikipedia.com June 24, 2021. CC-BY-SA 3.0 Modified. Accessed June 25, 2021.)