1. A method for reconstructing an image, comprising: using a computer to perform receiving an original image f defined on a coordinate space; receiving input selecting a region of the original image f within the coordinate space; receiving a reference to a texture image g; generating a first intermediate image I 1 by dividing f by g, wherein the division is performed over the region and its boundary such that I 1 =f/g; solving the Laplace equation ΔI 2 =0 or the biharmonic equation ∇ 4 I 2 =0 to determine a solution I 2 on the region, subject to the constraint that the solution I 2 agrees with the first intermediate image I 1 on the boundary of the region, wherein the solution I 2 defines a second intermediate image; multiplying I 2 by g to produce an image h, wherein the multiplication is performed over the region such that h=I 2 g; and determining new pixel values for the original image f using values of h on the region.