Two common tasks when processing point cloud data sets are surface estimation and point cloud registration. In this talk, a statistical approach is developed to solve both of these problems simultaneously. In particular, a surface is estimated from a pair of unregistered three-dimensional scans of the same spatial region. In this method, one point cloud defines the fixed coordinate system, and a rigid transformation is applied to the second cloud. Observations from both scans are considered a single realization of a Gaussian process. The registration problem is solved by jointly optimizing the likelihood over the parameters specifying the domain transformation and the mean and covariance functions. Given parameter estimates, surface estimation follows using the spatial stochastic model. While other extant approaches do not account for registration uncertainty, the likelihood-based approach to solving the registration and surface estimation problems jointly allows uncertainty in registration to be propagated to the surface prediction variance.