Ricci flow has been applied to computer vision (e.g., to 3D shape matching),
and to computer graphics (e.g., surface parametrization):
Wei Zeng, Samaras, D., Gu, D. ,
"Ricci Flow for 3D Shape Analysis,"
IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(4) 2010 662-677.
Yang, Guo, Luo, Hu, Gu,
"Generalized Discrete Ricci Flow,"
Computer Graphics Forum, Volume 28, Issue 7, pages 2005–2014, October 2009.
If you classify the eikonal equation as a geometric evolution equation, then there
are many applications to the computer vision problem known as "shape from shading": deriving
the 3D shape of an object from shading variation. For example:
Anna R. Bruss,
"The eikonal equation: Some results applicable to computer vision,"
J. Math. Phys. 23, 890 (1982).
Ron Kimmel , James A. Sethian,
"Optimal Algorithm for Shape from Shading and Path Planning,"
Journal of Mathematical Imaging and Vision,Volume 14 Issue 3, May 2001.
And in fact Sethian's book,
Level Set Methods:
Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science,
Cambridge University Press, 1996.
is filled with applications of the eikonal equation (and its variants):
"The text includes applications from physics, chemistry, fluid mechanics, combustion, image processing, material science, seismology, fabrication of microelectronic components, computer vision and control theory."