This paper presents an operational rate-distortion (ORD) optimal approach for skeleton-based boundary encoding. The boundary information is first decomposed into skeleton and distance signals, by which a more efficient representation of the original boundary results. Curves of arbitrary order are utilized for approximating the skeleton and distance signals. For a given bit budget for a video frame, we solve the problem of choosing the number and location of the control points for all skeleton and distance signals and for all boundaries within a frame, so that the overall distortion is minimized. The problem is solved with the use of Lagrangian relaxation and a shortest path algorithm in a 4D directed acyclic graph (DAG) we propose. By defining a path selection pattern, we reduce the computational complexity of the 4D DAG shortest path algorithm from O(N/sup-5/) to O(N/sup-4/), where N is the number of admissible control points for a skeleton. A suboptimal solution is also presented for further reducing the computational complexity of the algorithm to O(N/sup-2/). The proposed algorithm outperforms experimentally other competing algorithms.