Coding a Contour Graph with No Address Assignments

This work addresses the topic of coding all the contour nodes of a picture in a single code word. The set of contour nodes can be represented as a subgraph of the lattice graph. Accordingly, we demonstrate first that any set of connected contour points can be represented uniquely by a code that requires at most one absolute coordinate assignment and at most k-1 bits per contour points, where k is the highest degree of any contour node. then by the device of a relative directional assignment, we exhibit a nesting sequence of code; for arbitrary 4-connected sets, for 4-connected sets with all nodes on closed paths, and for sets further restricted so that any area bounded by contour points contains at least one non-contour (texture) lattice point. In the ifrst two cases we show that the average number of bits per contour point or per code letter is by bounded by 2.27... and 2 respectively. In the most constrained contour graph, which encloses at least one texture point in any path, a code modification leads to increase in the bound to about 2.08 bits per code letter but permits an estimate of 1.36 bits per contour point. These results are further confirmed by experimental simulations.