This chapter discusses image registration techniques based on a finite set of parameters and/or a finite set of so-called image features. The basic idea is to determine the desired transformation for a finite number of features, any feature of the template image is mapped onto the corresponding feature on the reference image. This general notion of image features is made concrete using image landmarks. A naive approach to landmark based registration is formalized and theoretical issues such as existence and uniqueness are discussed. The naive approach is replaced by a proper regularized approach, and analytical solutions are derived using the theory of representers, radial basis functions, and thin-plate-splines. Using this advanced theoretical framework, the strict interpolation approach is further extended to a more flexible approximation approach. The various approaches (linear, quadratic, interpolating, and approximating thin-plate splines) are compared and illustrated. It is shown that landmark-based registration may not result in a meaningful one-to-one overall transformation.
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