Performance bounds can be used as a performance benchmark for any image registration approach. These bounds provide insights into the accuracy limits that a registration algorithm can achieve from a statistical point of view, that is, they indicate the best achievable performance of image registration algorithms. In this chapter, we present the Cramér-Rao lower bounds (CRLBs) for a wide variety of transformation models, including translation, rotation, rigid-body, and affine transformations. Illustrative examples are presented to examine the performance of the registration algorithms with respect to the corresponding bounds.
Image registration is a crucial step in all image analysis tasks in which the final information is obtained from the combination of various data sources, as in image fusion, change detection, multichannel image restoration, and object recognition. See, for example, Brown (1992) and Zitová and Flusser (2003). The accuracy of image registration affects the performance of image fusion or change detection in applications involving multiple imaging sensors. For example, the effect of registration errors on the accuracy of change detection has been investigated by Townshend et al. (1992), Dai and Khorram (1998), and Sundaresan et al. (2007). An accurate and robust image registration algorithm is, therefore, highly desirable.
The purpose of image registration is to find the transformation parameters, so that the two given images that represent the same scene are aligned. There are many factors that might affect the performance of registration algorithms.