The original morphable model, as well as Basel Face Model, which is from the same principal researcher, do contain texture as well as geometry.
It is perfectly possible to compute the geometry part of a Morphable Model from 3D geometry data without texture. This gives you a model that captures the statistically most significant variations in the shape.
However, matching a pure-geometry model to a 2D face image is more difficult than matching a model with texture. It essentially requires you to ...
- identify (or annotate) the locations of some landmark points in your 2D face image
- optimize for the 3D pose and shape parameters that bring the respective landmarks in the 3D Morphable model close to your annotated landmarks after projection with an unknown camera.
This is an interesting problem, but not a trivial one. For step 2 I would recommend to start by assuming orthographic projection.
Regarding your output quality question: If you have a sufficiently large number of 3D models in your database, the individual scans do not have to be of particularly high quality. Noise will not show up in the principal components of the model you will actually use. Holes in the scans, however, are a problem.
Last but not least, let me shamelessly point you to a paper I wrote some years ago. It does not solve your problem, but it contains a section on fitting a 3D morphable model (geometry only) to a 2D face silhouette extracted from a photo.
