Geometric distortion measurement and the associated metrics involved are integral to the Rate Distortion (RD) shape coding framework, with importantly the efficacy of the metrics being strongly influenced by the underlying measurement strategy. This has been the catalyst for many different techniques with this article presenting a comprehensive review of geometric distortion measurement, the diverse metrics applied, and their impact on shape coding. The respective performance of these measuring strategies is analyzed from both a RD and complexity perspective, with a recent distortion measurement technique based on arc-length-parameterization being comparatively evaluated. Some contemporary research challenges are also investigated, including schemes to effectively quantify shape deformation.
Traditionally the sliding window (SW) has been employed in vertex-based operational rate distortion (ORD) optimal shape coding algorithms to ensure consistent distortion (quality) measurement and improve computational efficiency. It also regulates the memory requirements for an encoder design enabling regular, symmetrical hardware implementations. This paper presents a series of new enhancements to existing techniques for determining the best SW-length within a rate-distortion (RD) framework, and analyses the nexus between SW-length and storage for ORD hardware realizations. In addition, it presents an efficient bit-allocation strategy for managing multiple shapes together with a generalized adaptive SW scheme which integrates localized curvature information (cornerity) on contour points with a bi-directional spatial distance, to afford a superior and more pragmatic SW design compared with existing adaptive SW solutions which are based on only cornerity values. Experimental results consistently corroborate the effectiveness of these new strategies.