Our recently proposed wavelet-based L-infinite-constrained 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.

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

This paper investigates the novel concept of local error control in arbitrary mesh encoding, and proposes a new L-infinite mesh coding approach implementing this concept. In contrast to traditional mesh coding systems that use the mean-square error as distortion measure, the proposed approach employs the L-infinite distortion as target distortion metric. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum local error between the original and decoded meshes is lower than a given upper-bound. Additionally, the proposed system achieves scalability in L-infinite sense, that is, the L-infinite distortion upper-bound can be accurately estimated when decoding any layer from the input stream. Moreover, a distortion estimation approach is proposed, expressing the L-infinite distortion in the spatial domain as a statistical estimate of quantization errors produced in the wavelet domain. An instantiation of the proposed L-infinite coding approach is demonstrated for MESHGRID, which is a scalable 3D object coding system, part of MPEG-4 AFX. The proposed L-infinite coding approach guarantees that the maximum error is upper-bounded, it enables a fast real-time implementation of the rate-allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

This paper proposes a new approach for joint source and channel coding (JSCC) of meshes, simultaneously providing scalability and optimized resilience against transmission errors. An unequal error protection approach is followed, to cope with the different error-sensitivity levels characterizing the various resolution and quality layers produced by the input scalable source codec. The number of layers and the protection levels to be employed for each layer are determined by solving a joint source and channel coding problem. In this context, a novel fast algorithm for solving the optimization problem is conceived, enabling a real-time implementation of the JSCC rate-allocation. An instantiation of the proposed JSCC approach is demonstrated for MeshGrid, which is a scalable 3-D object representation method, part of MPEG-4 AFX. In this context, the L-inflnite distortion metric is employed, which is to our knowledge a unique feature in mesh coding. Numerical results show the superiority of the L-inflnite norm over the classical L-2 norm in a JSCC setting. One concludes that the proposed joint source and channel coding approach offers resilience against transmission errors, provides graceful degradation, enables a fast real-time implementation, and preserves all the scalability features and animation capabilities of the employed scalable mesh codec.