Abstract: In this paper, we present a new shape-coding approach, which decouples the shape information into two independent signal data sets; the skeleton and the boundary distance from the skeleton. The major benefit of this approach is that it allows for a more flexible trade-off between approximation error and bit budget. Curves of arbitrary order can be utilized for approximating both 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 of all boundaries within a frame, so that the overall distortion is minimized. An operational rate-distortion (ORD) optimal approach using Lagrangian relaxation and a four-dimensional Direct Acyclic Graph (DAG) shortest path algorithm is developed for solving the problem. To reduce the computational complexity from O(N 5) to O(N 3), where N is the number of admissible control points for a skeleton, a suboptimal greedy-trellis search algorithm is proposed and compared with the optimal algorithm. In addition, an even more efficient algorithm with computational complexity O(N 2) that finds an ORD optimal solution using a relaxed distortion criterion is also proposed and compared with the optimal solution. Experimental results demonstrate that our proposed approaches outperform existing ORD optimal approaches, which do not follow the same decomposition of the source data. EDICS: IP 1.1 Coding 1.

Abstract—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 5) to O(N 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 2). The proposed algorithm outperforms experimentally other competing algorithms.

In this paper, we consider the rate-distortion optimal encoding of shape information using a skeleton decomposition and the minmum maximum (MINMAX) distortion criterion. For bit budget constrained video communication applications, whose goal is to achieve as low as possible but almost constant distortion, the MINMAX criterion is the natural choice. We propose a 4D DAG (directed acyclic graph) shortest path algorithm implemented by dynamic programming to solve the minimum rate problem, and also provide a solution for the dual minimum distortion problem. Experimental results indicate that our algorithm has an outstanding performance compared with existing methods. 1.