In this paper a new morphological interpolation technique is presented. It is applied to the coding of the smooth (primary) component in a sketch-based image compression approach for very low bit-rates. The interpolation technique is intended to perform two dimensional interpolation from any set of initial pixels and, in particular, from sketch data. It makes intensive use of geodesic dilation, a morphological operator that may be implemented by means of FIFO queues. This results in a very efficient process compared to those that perform interpolation by linear filtering on the initial image. For the application of this method to interpolative image coding, the sketch data is extracted as a set of maximum curvature lines by means of the watershed algorithm. From such information, the interpolation technique obtains a fair reconstruction of both the smooth texture component and the main transitions of the image signal at low bit-rate cost.