one individual or from different individuals. Such combination or comparison requires the registration of images or
We present a methodology for alignment of multidimensional data sets that is based on the Euclidean distance transform volumetric data sets. This involves the determination of the and the Marquardt-Levenberg optimization algorithm. The geometric transformation between images and subsequent proposed approach operates on pixel or voxel descriptions of transformation of one or both data sets into a common objects to be matched and estimates the parameters of a space coordinate system. This paper deals with the determination transformation for optimal alignment of objects. The computaof the geometrical transformation required to align two tional cost of an algorithm developed with this method is estidata sets. mated. The methodology is tested by developing an algorithm Image registration techniques have recently been refor rigid body transformation alignment of three-dimensional viewed by van der Elsen et al. [1] who give a comprehensive data sets. Tests with synthetic and real objects indicate that and insightful overview of the work in this field. Among the method is accurate, reliable, and robust. Β© 1997 Academic Press the categories used for classifying image registration methods it is most cogent to concentrate on the type of data and the type of transformation used for image 1. INTRODUCTION matching.
The types of data range from extrinsic features, such as Image alignment or registration is a common task in image processing. It is encountered in many fields such as fiducial objects introduced into the field of view to provide coordinates of alignment, to intrinsic features, namely remote sensing, where two-dimensional data sets must be registered, and biomedical imaging, where two-or three-structures which are normally present in objects being matched. While extrinsic features are preferable since they dimensional images are collated. This problem arises when data collected at different times or with different modalities can provide unambiguous and controlled fiducial information, the introduction of these structures may complicate are to be correlated. For example, in medicine a body can be imaged through computer tomography (CT), magnetic the data acquisition process adding cost and time. In many cases, such as when viewing the interior of an intact organ-resonance imaging (MRI), positron emission tomography (PET), single photon emission computed tomography ism or in remote sensing, it is just not feasible to use extrinsic features. Another issue is the type of intrinsic (SPECT), and ultrasound. Since these methods generally provide complementary information, synthesis of data feature to be used. A traditional approach to image alignment relies on correlation, where the gray value distribu-gathered by more than one method can give synergistic information. Such synthesis allows the combination of ana-tions of the images or data sets are compared. This, however, is not feasible if there is a qualitative difference tomical (e.g., CT and MRI) and functional (PET, SPECT) information in two-or three-dimensional images. Such vi-between the gray scales, such as in multimodality imaging.
Under these conditions a viable strategy is to preprocess sualization can be very helpful to evaluate the location and type of pathology under examination. Another task the images to extract homologous geometric features in the data sets to be registered, such as points, lines, or facilitated by combining images is the comparison of studies in one modality but collected at different times from surfaces. These features may then be registered and the 373