Wavelet-Based ${L_\infty }$ Semi-regular Mesh Coding
Polygonal meshes are popular three-dimensional virtual representations employed in a wide range of applications. Users have very high expectations with respect to the accuracy of these virtual representations, fueling a steady increase in the processing power and performance of graphics processing hardware. This accuracy is closely related to how detailed the virtual representations are. The more detailed these representations become, the higher the amount of data that will need to be displayed, stored, or transmitted. Efficient compression techniques are of critical importance in this context. State-of-the-art compression performance of semi-regular mesh coding systems has been achieved through the use of subdivision-based wavelet coding techniques. However, the vast majority of these codecs are optimized with respect to the <inline-formula><tex-math notation="LaTeX">${L_2}$</tex-math></inline-formula> distortion metric, i.e., the average error. This makes them unsuitable for applications where each input signal sample has a certain significance. To alleviate this problem, we propose to optimize the mesh codec with respect to the <inline-formula><tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> metric, which allows for the control of the local reconstruction error. This paper proposes novel data-dependent formulations for the <inline-formula><tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> distortion. The proposed <inline-formula><tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> estimators are incorporated in a state-of-the-art wavelet-based semi-regular mesh codec. The resulting coding system offers scalability in <inline-formula><tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> sense. The experiments demonstrate the advantages of <inline-formula><tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> coding in providing a tight control on the local reconstruction error. Furthermore, the proposed data-dependent <inline-formula> <tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> approaches significantly improve estimation accuracy, reducing the classical low-rate gap between the estimated and actual <inline-formula> <tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> distortion observed for previous <inline-formula> <tex-math notation="LaTeX">${L_\infty }$</tex-math></inline-formula> estimators.