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Among the different classes of coding techniques proposed in literature, predictive schemes have proven their outstanding performance in near-lossless compression. However, these schemes are incapable of providing embedded L(infinity)-oriented compression, or, at most, provide a very limited number of potential L(infinity) bit-stream truncation points. We propose a new multidimensional wavelet-based L(infinity)-constrained scalable coding framework that generates a fully embedded L(infinity)-oriented bit stream and that retains the coding performance and all the scalability options of state-of-the-art L2-oriented wavelet codecs. Moreover, our codec instantiation of the proposed framework clearly outperforms JPEG2000 in L(infinity) coding sense.

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.

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.

In this paper we propose new filters for the contourlet transform and derive a series of trigonometric filters. Furthermore, we propose a methodology for designing new filters that are obtained from polynomial functions. Thus, we jointly derive different filters for each contourlet decomposition level, and apply them in image denoising. We show that on all the tested images and noise levels, the contourlet transform equipped with the proposed filters clearly outperforms its raised cosine filter-based counterpart in terms of denoising performance. In this sense, when employing polynomial filters, we report gains of up to 0.6dB.

A 3D extension of the standard will support cuboid volumetric data sets with no time component.

This paper reports an information-theoretic analysis of the inter-scale, inter-orientation and inter-location dependencies that exist between curvelet coefficients. We show that the marginal statistics of these coefficients can be accurately modeled using generalized Gaussian density functions. Though generally decorrelated, we find that curvelets exhibit unusually high dependencies in intra-band local micro-neighborhoods, of a magnitude not found for instance in classical wavelets. Furthermore, dependencies are subject to and decrease with increasing orientation and location differences. Finally, we conclude that intra-band coefficient dependencies are stronger than either their inter-scale or inter-direction counterparts.

In this paper, we perform a statistical analysis of curvelet coefficients, making a distinction between two classes of coefficients: those representing useful image content and those dominated by noise. By investigating the marginal statistics, we develop a mixture prior for curvelet coefficients. Through analysis of the joint intra-band statistics, we find that white Gaussian noise is transformed by the curvelet transform into noise that is correlated in one direction and decorrelated in the perpendicular direction. This enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we develop a novel denoising method, inspired by a recent wavelet domain method ProbShrink. For textured images, the new method outperforms its wavelet-based counterpart and existing curvelet-based methods. For piecewise smooth images, performances are similar as existing methods.

MESHGRID is a novel, compact, multi-scalable and animation-friendly 3D object representation method, which is part of MPEG-4, and which resides in the Animation Framework Extensions (AFX) toolset. The paper introduces the novel concept of local error control for arbitrary mesh encoding. In this sense, the paper proposes a new wavelet-based L∞-constrained coding technique for MESHGRID models, generating a fully scalable L∞-oriented bit-stream. The advantages of scalable L∞-oriented coding over L 2 coding are experimentally demonstrated.

Summary form only given. Several methods for L/sub /spl infin//-distortion constrained compression have been proposed that target a set of fixed reconstruction-error bounds. Recently, a wavelet-based L/sub /spl infin//-constrained embedded image-coding technique was proposed that guarantees the required distortion bound while retaining the coding performance and scalability option state-of-the-art wavelet-based L/sub /spl infin//-oriented codecs. The optimality of embedded deadzone scalar-quantizers for high-rate L/sub /spl infin//-constrained scalable wavelet-based coding of images was analyzed. The optimal quantizers were employed in a coding algorithm that outperforms embedded L/sub /spl infin//-oriented wavelet-coders in terms of maximum absolute error. The algorithm was briefly described and coding results were provided.

A new wavelet-based L-infinite-constrained fixed and embedded coding technique is proposed in this paper. For any desired distortion bound, the embedded bit stream can be truncated at a corresponding bit-rate, for which the required upper bound on the individual elements of the reconstruction error signal is guaranteed. The original signal can also be coded up to a fixed a priori user-defined distortion bound, ranging up to lossless coding. The proposed coding technique supports both 2D (images) and 3D (volumetric) input data.

In the context of compression of high resolution multi-spectral satellite image data consisting of radiances and top-of-the-atmosphere fluxes, it is vital that image calibration characteristics (luminance, radiance) must be preserved within certain limits in lossy image compression. Though existing compression schemes (SPIHT, JPEG2000, SQP) give good results as far as minimization of the global PSNR error is concerned, they fail to guarantee a maximum local error. With respect to this, we introduce a new image compression scheme, which guarantees a MAXAD distortion, defined as the maximum absolute difference between original pixel values and reconstructed pixel values. In terms of defining the Lagrangian optimization problem, this reflects in minimization of the rate given the MAXAD distortion. Our approach thus uses the l-infinite distortion measure, which is applied to the lifting scheme implementation of the 9-7 floating point Cohen-Daubechies-Feauveau (CDF) filter. Scalar quantizers, optimal in the D-R sense, are derived for every subband, by solving a global optimization problem that guarantees a user-defined MAXAD. The optimization problem has been defined and solved for the case of the 9-7 filter, and we show that our approach is valid and may be applied to any finite wavelet filters synthesized via lifting. The experimental assessment of our codec shows that our technique provides excellent results in applications such as those for remote sensing, in which reconstruction of image calibration characteristics within a tolerable local error (MAXAD) is perceived as being of crucial importance compared to obtaining an acceptable global error (PSNR), as is the case of existing quantizer design techniques.

The paper deals with the compression of multi-spectral satellite image data (high resolution data consisting of radiances and top-of—the-atmosphere TOA fluxes) investigated within the framework of the EUMETSAT project of SAP (Satellite Application Facility) on Climate Monitoring. Full multifunctionality support (quality scalability, resolution scalability, region-of-interest access) is asked for and image calibration characteristics (luminance, radiance) must be preserved within certain limits for lossy image compression, together with an excellent image quality. We analyze state-of-the-art coding techniques with respect to these requirements. Our objective is to answer two questions, namely the capability of existing state-of-the-art compression techniques to comply with our image calibration characteristics requirements and the support they offer regarding multifunctionality (in terms of quality scalability, resolution scalability and region of interest access). We propose basic modifications of these techniques so as to meet our multifunctionality requirements. We conclude from the experimental assessment of the analyzed techniques that none of the top coding algorithms available to date fully satisfy our imposed rate-distortion constraints and propose a path for future research in this field.

In this paper, we perform a statistical analysis of curvelet coefficients, distinguishing between two classes of coefficients: those that contain a significant noise-free component, which we call "signal of interest", and those that do not. By investigating the marginal statistics, we develop a prior model for curvelet coefficients. The analysis of the joint intra- and inter-band statistics enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we present a novel denoising method, inspired by a recent wavelet domain method ProbShrink. The new method outperforms its wavelet-based counterpart and produces results that are close to those of state-of-the-art denoisers.

A new wavelet-based L-infinity-constrained fixed and embedded coding technique is proposed. The embedded bit stream can be truncated for any desired distortion bound at a corresponding bit rate, so that the target upper bound on the elements of the reconstruction error signal is guaranteed. The original image can also be coded up to a fixed a priori user-defined distortion bound, ranging up to lossless coding. A lifting-based wavelet decorrelating transform is employed on the original image, and exact relations are established between spatial and wavelet domain distortions. The wavelet coefficients are quantized by symmetric uniform quantizers for fixed-distortion coding and by families of embedded uniform deadzone scalar quantizers for embedded coding. The quantized coefficients are finally losslessly encoded using a quadtree-based coding algorithm. Any floating-point lifting-based wavelet transform can be used, and a few of the popular wavelet transforms included in the JPEG2000 verification model are worked out as examples. We compare other L-infinity-constrained coding schemes and show that our proposed coder offers in addition a fully embedded L-infinity-oriented bit stream. We illustrate also that the proposed coder retains the same capabilities as the state-of-the-art embedded wavelet-based co-decs, while providing superior compression results and embeddedness with respect to the L-infinity distortion measure.

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.

In this paper, we propose a generic hybrid oriented-transform and wavelet-based image representation for intra-band image coding. We instantiate for three popular directional transforms having similar powers of approximation but different redundancy factors. For each transform type, we design a compression scheme wherein we exploit intra-band coefficient dependencies. We show that our schemes outperform alternative approaches reported in literature. Moreover, on some images, we report that two of the proposed codec schemes outperform JPEG2000 by over 1 dB. Finally, we investigate the trade-off between oversampling and sparsity and show that, at low rates, hybrid coding schemes with transform redundancy factors as high as 1.25 to 5.8 are capable in fact of outperforming JPEG2000 and its critically-sampled wavelets.

This contribution introduces an error-resilient profile for the reference-grid encoder employed in MESHGRID. An unequal error protection approach is followed, to acquaint for the different error-sensitivity levels characterizing the various resolution and quality layers produced by the reference-grid coder. In this context, a novel fast algorithm for solving the joint source and channel coding problem was developed. The experimental results demonstrate the benefits brought by error-resilient coding of the reference grid.

In this paper, we perform an inter-sub-band statistical analysis of curvelet coefficients, making a distinction between two classes of coefficients: those representing useful image content and those dominated by noise. This analysis enables us to develop an appropriate inter-sub-band local spatial activity indicator (LSAI) for curvelets. We use this LSAI in our recently developed curvelet-based denoising method ProbShrinkCurv. The results demonstrate that the new method outperforms the wavelet-based ProbShrink estimator as well as the existing curvelet-based methods, both for textured and for piecewise smooth images.

A new wavelet-based embedded image coding technique is proposed. For any desired L/sub /spl infin//-distortion bound, the bit stream can be truncated at a corresponding bit rate, so that the target upper bound on the absolute values of the pixels of the reconstruction error image is guaranteed. The algorithm outperforms embedded L/sub 2/-oriented wavelet coders in terms of maximum absolute error.

The heterogeneous nature of modern communications stems from the need of transmitting digital information through various types of mediums to a large variety of end-user terminals. In this context, simultaneously providing a scalable source representation and resilience against transmission errors is of primary importance. MESHGRID, which is part of the MPEG-4 AFX standard, is a scalable 3D object representation method especially designed to address the heterogeneous nature of networks and clients in modern communication systems. A MESHGRID object comprises one or several surface layers attached to and located within a volumetric reference-grid. In this paper we focus on the errorresilience aspects of MESHGRID and propose a novel approach for scalable error-resilient coding of MESHGRID's reference-grid. An unequal error protection approach is followed, to acquaint for the different error-sensitivity levels characterizing the various resolution and quality layers produced by the reference-grid coder. The code rates to be employed for each layer are determined by solving a joint source and channel coding problem. The L-infinite distortion metric is employed instead of the classical L-2 norm, typically used in case of images and video. In this context, a novel fast algorithm for solving the optimization problem is proposed. The proposed approach allows for real-time implementations. The experimental results demonstrate the benefits brought by error resilient coding of the reference grid. We conclude that the proposed approach offers resilience against transmission errors while preserving all the scalability features and animation capabilities that characterize MESHGRID.

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This paper reports an information-theoretic analysis of the dependencies that exist between curvelet coefficients. We show that strong dependencies exist in local intra-band micro-neighborhoods, and that the shape of these neighborhoods is highly anisotropic. With this respect, it is found that the two immediately adjacent neighbors that lie in a direction orthogonal to the orientation of the subband convey the most information about the coefficient. Moreover, taking into account a larger local neighborhood set than this brings only mild gains with respect to intra-band mutual information estimations. Furthermore, we point out that linear predictors do not represent sufficient statistics, if applied to the entire intra-band neighborhood of a coefficient. We conclude that intra-band dependencies are clearly the strongest, followed by their inter-orientation and inter-scale counterparts; in this respect, the more complex intra-band/inter-scale or intra-band/inter-orientation models bring only mild improvements over intra-band models. Finally, we exploit the coefficient dependencies in a curvelet-based image coding application and show that the scheme is comparable and in some cases even outperforms JPEG2000.

MESHGRID is a scalable 3D object representation method which is part of MPEG-4 AFX. This paper proposes a new approach for optimized protection of MESHGRID-represented objects against transmission errors occurring over error-prone channels. An unequal error protection approach is followed, to cope with the different error-sensitivity levels characterizing the various resolution and quality layers produced by MESHGRID. The protection level to be employed for each layer is determined by solving a joint source and channel coding problem. The L-infinite distortion metric is used, and its superiority over the classical L-2 norm is proven. In this context, a novel fast algorithm for solving the optimization problem is conceived. The proposed joint source and channel coding approach offers resilience against transmission errors, enables a real-time implementation, and preserves all the scalability features and animation capabilities that characterize MESHGRID.

MESHGRID is a novel, compact, multi-scalable and animation-friendly 3D object representation method, which is part of MPEG-4, and which resides in the Animation Framework Extensions (AFX) toolset. The paper introduces the novel concept of local error control for arbitrary mesh encoding. In this sense, the paper proposes a new wavelet-based L-infinity-constrained coding technique for MESHGRID models, generating a fully scalable L-infinity-oriented bit-stream. The advantages of scalable L-infinity-oriented coding over L2 coding are experimentally demonstrated.