We present an extension of the conventional computational anatomy framework to account for confounding variations due to selection of parameters and templates, by learning the equivalence class derived from the multitude of representations of an individual anatomy. A morphological appearance manifold obtained by varying parameters of the template warping procedure is estimated. Group-wise registration and statistical analysis is then based on a constrained optimization framework, which employs a minimum variance criterion to perform manifold walking, i.e. to traverse each individual's morphological appearance manifold until group variance is minimal. Effectively, this process removes the aforementioned confounding effects and potentially leads to morphological representations that reflect purely underlying biological variations, instead of variations introduced by modeling assumptions and parameter settings. The nonlinearity of a morphological appearance manifold is treated via local linear approximations of the manifold via PCA.