We present a method to globally parameterize a surface represented by height maps over a set of planes (range images). In contrast to other parametrization techniques, we do not start with a manifold mesh. The parametrization we compute defines a manifold structure, it is seamless and globally smooth, can be aligned to geometric features and shows good quality in terms of angle and area preservation, comparable to current parametrization techniques for meshes. Computing such global seamless parametrization makes it possible to perform quad remeshing, texture mapping and texture synthesis and many other types of geometry processing operations. Our approach is based on a formulation of the Poisson equation on a manifold structure defined for the surface by the range images. Construction of such global parametrization requires only a way to project surface data onto a set of planes, and can be applied directly to implicit surfaces, nonmanifold surfaces, very large meshes, and collections of range scans. We demonstrate application of our technique to all these geometry types.