Quick Answer:

One answer is shown here:

Complete Solution:

Replaces each shade in the frown and the smile by the corresponding number, as shown here:
To find the appropriate numbers for each square in the middle image, average the numbers in the matching squares of the frown and the smile.

The grid below shows the appropriate numbers and shades for the middle grid above.

To create the illusion of a smooth transition, an actual morphing uses many more shades and has many more steps.