Chain codes and their linear reconstruction filters

A differential chain code implementation of the basic eight-directional and N-ring chain code for the encoding of line drawings is considered. Several distortion and rate criteria are considered, and they are evaluated for the special case of encoding infinite straight lines. These results indicate that the differential code outperforms ring codes and the ring delta code. Using a linear decoding filter for reconstructing a smoothed approximation to the original line is also considered. Optimal reconstruction filters for infinite straight lines at various angles are derived. An angle-invariant reconstruction filter that minimizes the expected square distortion taken over all angles is derived. The overall performance using this filter is close to that of the optimum filter. Furthermore, the impulse response of the angle-invariant filter is approximately rectangular, which can lead to simple hardware implementations.<>