This paper describes a new surface normal smoothing process which can be used in conjunction with shape-fromshading. Rather than directly smoothing the surface normal vectors, we exert control over their directions by smoothing the field of principal curvature vectors. To do this we develop a topography sensitive smoothing process which overcomes the problems of singularities in the field of principal curvature directions at the locations of umbilics and saddles. The method is evaluated on both synthetic and real-world images