In this paper we show how statistical constraints can be incorporated into the surface integration process. This problem aims to reconstruct the surface height function from a noisy field of surface normals. We propose two methods that employ a statistical model that captures variations in surface height. The first uses a coupled model that captures the variation in a training set of face surfaces in both the surface normal and surface height domain. The second is based on finding the parameters of a surface height model directly from a field of surface normals. We present experiments on ground truth face data and compare the results of the two methods with an existing surface integration technique.