A 3D morphable face model represents the complex shape and appearance structure of faces as a compact representation in a vector space. Such a model has proven extremely useful in various fields such as face recognition, facial expression synthesis, face animation, as well as in the perceptual and cognitive sciences. One of the most important steps in creating a 3D morphable model is to establish correspondence between all faces - a highly non-trivial process because of the complex topology of faces. In this paper, we propose to use implicit surfaces for this task, which enables a robust method for establishing dense 3D correspondences. This algorithm is used to build a morphable face model from a large database of Korean faces that were collected. We show that our model is in correspondence with the well-known MPI model so that our face space can be expanded from Asian to Caucasian faces. In addition, with the resulting control parameters of the model, we demonstrate realistic changes of high-level facial attributes.