Simultaneous optimal boundary encoding and variable-length code selection

This paper describes efficient and optimal encoding and representation of object contours. Contours are approximated by connected second-order spline segments, each defined by three consecutive control points. The placement of the control points is done optimally in the rate-distortion (RD) sense and jointly with their entropy encoding. We utilize a differential scheme for the rate and an additive area-based metric for the distortion to formulate the problem as a Lagrangian minimization. We investigate the sensitivity of the resulting operational RD curve on the variable length codes used and propose an iterative procedure arriving at the entropy representation of the original boundary for any given rate-distortion tradeoff.