The aim of this paper is to present a new interpolation technique intended for spatial interpolation from sparse data sets. The proposed implementation, which is based on non-linear morphological operators, overperforms linear interpolation by means of diffusion processes performing iterative space-variant filtering on the initial image. Morphological interpolation is applied to sketch-based image coding. We put forward a perceptually motivated two-component image model that strongly relies on morphological operators. The watershed is used to detect strong edge features in the first component of the model. The smooth areas of the image are recovered from the extracted edge information by morphological interpolation. The residual component, containing fine textures, is separately coded by a subband coding scheme.