Point–Based Registration Assuming Affine Motion Attila Tan´ acs 1 , G´ abor Cz´ edli 2 , K´ alm´anPal´ agyi 1 , and Attila Kuba 1 1 Department of Applied Informatics, University of Szeged, H–6701 Szeged P.O.Box 652, Hungary {tanacs,palagyi,kuba}@inf.u-szeged.hu 2 Bolyai Institute, University of Szeged, H–6720 Szeged, Aradi v´ ertan´ uk tere 1, Hungary czedli@math.u-szeged.hu Abstract. Registration is a fundamental task in image processing. Its purpose is to find a geometrical transformation that relates the points of an image to their corresponding points of another image. The determi- nation of the optimal transformation depends on the types of variations between the images. In this paper we propose a robust method based on two sets of points representing the images. One–to–one correspondence is assumed between these two sets. Our approach finds global affine trans- formation between the sets of points and can be used in any arbitrary dimension k ≥ 1. A sufficient existence condition for a unique solution is given and proven. Our method can be used to solve various registration problems emerged in numerous fields, including medical image process- ing, remotely sensed data processing, and computer vision. Keywords: registration problem; matching sets of points 1 Introduction There is an increasing number of applications that require accurate aligning of one image with another taken from different viewpoints, by different imaging devices, or at different times. The geometrical transformation is to be found that maps a floating image data set in precise spatial correspondence with a reference image data set . This process of alignment is known as registration , although other words, such as co–registration , matching , and fusion , are also used. Examples of systems where image registration is a significant component include aligning images from different medical modalities for diagnosis, matching a target with a real–time image of a scene for target recognition, monitoring global land usage using satellite images, and matching stereo images to recover shape for autonomous navigation [6,10]. The registration technique for a given task depends on the knowledge about the characteristics of the type of variations. Registration methods can be viewed as different combinations of choices for the following four components [6]: G. Sommer and Y. Y. Zeevi (Eds.): AFPAC 2000, LNCS 1888, pp. 329–338, 2000. c  Springer-Verlag Berlin Heidelberg 2000