Medical Image Registration

Maintz and Viergever have proposed a comprehensible classification of the whole registration problem based on nine main criteria [21], which include image dimensionality, the nature of the registration basis, the nature and domain of the transformation, user interaction, optimization procedures, the involved imaging modalities, the subject and the object.

All applications of image registration require the establishment of a spatial correspondence between the respective data sets. In other words, registration involves finding a spatial transformation that relates structures in one image to the corresponding structures in another image. The nature of these transformations can be classified by the dimensionality of the images to be registered and the number of parameters, or degrees of freedom, to be computed. Depending on the imaging sensor, the acquired data can be two, three or four-dimensional (three dimensions in space plus time as the fourth), so we can distinguish between:

2D-to-2D registrationIn the most simple of cases, two 2D images can be registered by determining the translation along the two axes and the rotation angle. However, clinically relevant applications of this case are rare, since changes in the geometry of image acquisition over time or from one imaging sensor to another introduce additional degrees of freedom.

2D-to-3D registrationThis case arises when a correspondence between a projection image like X-ray and a volumetric data set like CT must be established. A typical application of this would be relating an intra-operative 2D image to a preoperative 3D image for the purpose of image-aided surgery or radiotherapy. The matching of such data sets usually yields ten degrees of freedom (whereas the case of a general affine transformation would yield fifteen degrees of freedom). Four of them determine the projective transformation for the 2D image and can therefore be determined in advance by correct calibration, leaving six parameters for the volume’s translation and rotation along the three axes. Since most of the 2D-to-3D applications concern intra-operative scenarios, they are heavily time-constrained and have a strong focus on speed issues concerning the computation of the spatial pose.

3D-to-3D registrationThe registration of two volumes, is the most well developed process and a widely used method. The positions of two rigid bodies can always be related to one another by means of three translations and three rotations, but the particular conditions of imaging might impose further degrees of freedom to account for different scaling of voxels, a tilt in the gantry or a general affine transformation which is determined by twelve paramters.

Registration of time seriesTime series of images are acquired for various reasons and at various intervals. Applicationsinclude monitoring of tumor growth, post-operative monitoring of the healing process or observing the passing of injected bolus through a vessel tree. Subsequent registration of such an image series can be used to study dynamic processes such as blood flow or metabolic processes.