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We present two edge encoding schemes, namely 8-sector scheme and 16-sector scheme, for the operational rate-distortion (ORD) optimal shape coding framework. Different from the traditional 8-direction scheme that can only encode edges with angles being an integer multiple of Â¿/4, our proposals can encode edges with arbitrary angles. We partition the digital coordinate plane into 8 and 16 sectors, and design the corresponding differential schemes to encode the short and the long component of each vertex. Experiment results demonstrate that our two proposals can reduce a large number of encoding vertices and therefore reduce 10%~20% bits for the basic ORD optimal algorithms and 10%~30% bits for all the ORD optimal algorithms under the same distortion thresholds, respectively. Moreover, the reconstruction contours are more compact compared with those using the traditional 8-direction edge encoding scheme.