Efficient error control in 3D mesh coding

Abstract

Abstract-Our recently proposed wavelet-based L-infiniteconstrained coding approach for meshes ensures that the maximum error between the vertex positions in the original and decoded meshes is guaranteed to be lower than a given upper bound. Instantiations of both L-2 and L-infinite coding approaches are demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this survey paper, we compare the novel L-infinite distortion estimator against the L-2 distortion estimator which is typically employed in 3D mesh coding systems. In addition, we show that, under certain conditions, the L-infinite estimator can be exploited to approximate the Hausdorff distance in real-time implementations.Index Terms -Distortion metric, L-infinite, L-2, MAXAD, MSE, Hausdorff, 3D mesh coding I. INTRODUCTION The diversification of content and the increasing demand in mobility has led to a proliferation of heterogeneous terminals, with diverse capabilities. Efficient storage and transmission of digital data is therefore a critical problem, which can be solved by compressing the original data based on some predefined criteria.There is a broad range of applications (e.g. in the medical area), where compact coding cannot come at the expense of information loss. A viable solution in this case is given by lossless coding, possibly coupled with multi-functionality support, such as scalability and progressive (lossy-to-lossless) reconstruction of the input data. Lossless coding is downsized however by the fairly low achievable lossless compression ratios. There are other applications, such as those in the field of remote sensing, where one can accept information loss in favor of higher compression ratios, provided that the distortions incurred are rigorously bounded. In such applications, lossy or near-lossless compression are suitable, but an appropriate distortion measure needs to be employed in order to accurately quantify and control the distortion incurred by the compression system.The ideal distortion metric in lossy coding of meshes is the Hausdorff distance, as this metric expresses the maximum local error between the original and decoded meshes. However, to compute the Hausdorff distance, considerable processing power and memory space are needed, in particular for high resolution meshes. This becomes even more critical in scalable mesh coding systems, where, in order allocate rate, one needs to determine the Hausdorff distance for all possible

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“…In the last two decades, a reasonable maturity has been achieved in what concerns 3D mesh shape compression, thanks to substantial research on two related topics. On one hand, many clever methods have been devised and published for the efficient coding of both the geometry and the topology of a static, "naked" 3D mesh (i.e., the positions and connectivity of its vertices) [Aviles and Moran 2008], On the other hand, there is a good understanding and (up to a certain extent) a common agreement on how two 3D meshes should be compared [Aspert et al 2002][Cernea et al 2010],…”