14. COFIR: Coarse and Fine Image Registration
Jan Modersitzki, Eldad Haber · Society for Industrial and Applied Mathematics eBooks · 2007
14.1 Introduction Image registration is one of today's challenging image processing problems. The problem can be formulated as follows: Given two images, find a “reasonable” transformation such that a transformed version of the so-called template image becomes “similar” to the so-called reference image. Image registration is applied whenever images resulting from different times, devices, and/or perspectives need to be compared or integrated; see, e.g., [20, 26] and the references therein. A registration procedure is typically based on two main building blocks. The first one is a distance measure. The distance measure quantifies the meaning of similarity or proximity of images. A distance measure can be based on image features (e.g., moments [1], landmarks [20, 23], or markers [19]), on image intensities (e.g., L2-norm or sum of squared differences [7], correlation, mutual information [10, 25]), on image surfaces [3, 4], on level sets [11], or on combinations thereof [8, 13]. For an overview and comparisons, see also [17, 20, 22]. The second building block is a regularizing term. Since image registration is an ill-posed problem, regularization is inevitable and becomes a central topic [20]. Typical regularization techniques are a restriction to a low-dimensional transformation space (e.g., the space of rigid or affine linear transformations) or an explicit regularization of the problem.