Theoretical distortion estimation in L-infinite wavelet-based coding of semi-regular meshes

Subdivision-based wavelet coding techniques yield state-of-the-art performance in scalable compression of semi-regular meshes. However, all these codecs make use of the L-2 distortion metric, which gives only a good approximation of the global error produced by lossy coding of the wavelet coefficients. The L-infinite metric has been proven to be a suitable metric for applications where controlling the local, maximum error on each vertex is of critical importance. In this context, an upper bound formulation for the L-infinite distortion for a wavelet-based coding scheme operating on semi-regular meshes is derived. In addition, we propose a rate-distortion optimization algorithm that minimizes the rate for any target L-infinite distortion. It is shown that our L-infinite coding system outperforms the state-of-the-art and that an L-2 driven coding approach for semi-regular meshes loses ground to its L-infinite driven version when the goal is to have a tight control on the local reconstruction error.