To produce the morph, the positions of the keyframe polylines are interpolated between the initial and end image. At each frame, the elastic mesh is relaxed to a minimum energy state. The texture on each triangle in the intial frame and the final frame are then color interpolated and displayed on the matching intermediate triangle in the morph frame.
Since the pixel interpolation is local to the triangle, it can be done very efficiently. The mesh relaxation is global, but contains few elements compared to the number of pixels and can also be solved quickly. And frame-to-frame coherence speeds convergence as well.
Mpegs of morphs are available online. Some of these morphs were done during a one day workshop for high school students sponsored by our group. Can you recognize the halfway mix of Barney and Elvis done by one of the students in the top right image?