A Fast Distortion Measurement Using Chord-Length Parameterisation within the Vertex- Based Operational Rate-Distortion Optimal Shape Coding Framework

Existing vertex-based operational rate-distortion (ORD) optimal shape coding algorithms use the shortest absolute distance (SAD) or alternatively either the distortion band (DB) or tolerance band (TB) as their distortion measuring technique. Each approach however can lead to inaccurate distortion measurements, though these can be avoided by employing the accurate distortion measurement technique for shape coding (ADMSC). From a computational time perspective, an N point contour requires ( ) 2 N O time for DB and TB for both polygon and B-spline based encoding, while SAD and ADMSC incur order ( ) N O time for polygonal encoding, but ( ) 2 N O complexity for B-spline based encoding, thereby rendering ORD optimal algorithms computationally inefficient. This paper presents a novel distortion measurement strategy based on chord-length parameterisation (DMCLP) of a boundary that incurs order ( ) N O complexity for both polygon and B-spline based encoding, while preserving an analogous rate-distortion performance to the original ORD optimal shape coding algorithms, when it is embedded within the ORD framework.