Fast Distortion Measurement Using Chord-Length Parameterization Within the Vertex-Based Rate-Distortion Optimal Shape Coding Framework

Existing vertex-based operational rate-distortion (ORD) optimal shape coding algorithms can use a number of different distortion measurement techniques, including the shortest absolute distance (SAD), the distortion band (DB), the tolerance band (TB), and the accurate distortion measurement technique for shape coding (ADMSC). From a computational time perspective, an N-point contour requires O(N
²
) time for DB and TB for both polygon and B-spline-based encoding, while SAD and ADMSC incur O(N) time for polygonal encoding but O(N
²
) for B-spline based encoding, thereby rendering the ORD optimal algorithms computationally inefficient. This letter presents a novel distortion measurement strategy based on chord-length parameterization (DMCLP) of a boundary that incurs order O(N) complexity for both polygon and B-spline-based encoding while preserving a comparable rate-distortion performance to the original ORD optimal shape coding algorithms