An efficient boundary following algorithm for coding segmented images is presented. The segmented images are obtained by a graph theoretic image segmentation algorithm which has the objective of minimising the sum squared error (SSE) of the representation. The representation of regions by zero, first and second order two-dimensional polynomials is investigated. The authors compare this coding algorithm with a well established transform coding technique that optimises the same measure. The results of this comparison show that, in terms of the objective SSE measure, the segmented-image coder performs better than the transform coder at high compression ratios, and favourably over the entire useful range of rates. In contrast to the transform coder, which has parameters that have to be carefully chosen to give optimal performance, the segmented-image coder has no external parameters. The subjective quality of the resulting images is discussed.