Ilya Baran has permitted me to host online his and Jaakko Lehtinen's technical report from 2009, Notes on Inflating Curves.
The clever "trick" in this approach is rather than to set the height as the solution to a Poisson equation, to set the square of the height to the solution to a Poisson equation. This ensures that the surface normals are in plane at the boundary so the inflated surface may be glued to itself and turned into a closed "pillow" surface. This idea was leveraged and expanded upon in Ink-and-Ray: Bas-Relief Meshes for Adding Global Illumination Effects to Hand-Drawn Characters.
You could cite this note as:
@techreport{Baran:NIC:2009,
author = {Baran, Ilya and Lehtinen, Jaakko},
title = {Notes on inflating curves},
institution = {MIT},
year = {2009},
}