Numerical experiments with smooth surface extension and image inpainting
using harmonic and biharmonic functions are carried out. The boundary data used
for constructing biharmonic functions are the values of the Laplacian and
normal derivatives of the functions on the boundary. Finite difference schemes
for solving these harmonic functions are discussed in detail.Comment: Revised 21 July, 2017. Revised 12 January, 2018. To appear in
International Journal of Mathematics and Mathematical Science
