Morphometric analysis and anatomical correspondence across MR images is important in understanding neurological diseases as well as brain function. By registering shape models to unseen data, we will be able to segment the brain into its sub-cortical regions. A Bayesian cost function was derived for this purpose and serves to minimize the residuals to a planar intensity model. The aim of this paper is to explore the properties and justify the use of the cost function. In addition to apure residual term (similar to correlation ratio) there are three additional terms, one of which is a growth term. We show the benefit of incorporating an additional growth term into a purely residual cost function. The growth term minimizes the size of the structure in areas of high residual variance. We further show the cost function's dependence on the local intensity contrast estimate for a given structure.