At the core of most image registration problems is determining a spatial transformation that relates the physical coordinates of two or more images. Registration methods have become ubiquitous in many quantitative imaging applications. They represent an essential step for many biomedical and bioengineering applications. For example, image registration is a necessary step for removing motion and distortion related artifacts in serial images, for studying the variation of biological tissue properties, such as shape and composition, across different populations, and many other applications. Here fully automatic intensity based methods for image registration are reviewed within a global energy minimization framework. A linear, shift-invariant, stochastic model for the image formation process is used to describe several important aspects of typical implementations of image registration methods. In particular, we show that due to the stochastic nature of the image formation process, most methods for automatic image registration produce answers biased towards `blurred' images. In addition we show how image approximation and interpolation procedures necessary to compute the registered images can have undesirable effects on subsequent quantitative image analysis methods. We describe the exact sources of such artifacts and propose methods through which these can be mitigated. The newly proposed methodology is tested using both simulated and real image data. Case studies using three-dimensional diffusion weighted magnetic resonance images, diffusion tensor images, and two-dimensional optical images are presented. Though the specific examples shown relate exclusively to the fields of biomedical imaging and biomedical engineering, the methods described are general and should be applicable to a wide variety of imaging problems.