Efficient error control in 3D mesh coding

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 implementation

A family of stereoscopic image compression algorithms using wavelet transforms

With the standardization of JPEG-2000, wavelet-based image and video compression technologies are gradually replacing the popular DCT-based methods. In parallel to this, recent developments in autostereoscopic display technology is now threatening to revolutionize the way in which consumers are used to enjoying the traditional 2D display based electronic media such as television, computer and movies. However, due to the two-fold bandwidth/storage space requirement of stereoscopic imaging, an essential requirement of a stereo imaging system is efficient data compression. In this thesis, seven wavelet-based stereo image compression algorithms are proposed, to take advantage of the higher data compaction capability and better flexibility of wavelets. In the proposed CODEC I, block-based disparity estimation/compensation (DE/DC) is performed in pixel domain. However, this results in an inefficiency when DWT is applied on the whole predictive error image that results from the DE process. This is because of the existence of artificial block boundaries between error blocks in the predictive error image. To overcome this problem, in the remaining proposed CODECs, DE/DC is performed in the wavelet domain. Due to the multiresolution nature of the wavelet domain, two methods of disparity estimation and compensation have been proposed. The first method is performing DEJDC in each subband of the lowest/coarsest resolution level and then propagating the disparity vectors obtained to the corresponding subbands of higher/finer resolution. Note that DE is not performed in every subband due to the high overhead bits that could be required for the coding of disparity vectors of all subbands. This method is being used in CODEC II. In the second method, DEJDC is performed m the wavelet-block domain. This enables disparity estimation to be performed m all subbands simultaneously without increasing the overhead bits required for the coding disparity vectors. This method is used by CODEC III. However, performing disparity estimation/compensation in all subbands would result in a significant improvement of CODEC III. To further improve the performance of CODEC ill, pioneering wavelet-block search technique is implemented in CODEC IV. The pioneering wavelet-block search technique enables the right/predicted image to be reconstructed at the decoder end without the need of transmitting the disparity vectors. In proposed CODEC V, pioneering block search is performed in all subbands of DWT decomposition which results in an improvement of its performance. Further, the CODEC IV and V are able to perform at very low bit rates(< 0.15 bpp). In CODEC VI and CODEC VII, Overlapped Block Disparity Compensation (OBDC) is used with & without the need of coding disparity vector. Our experiment results showed that no significant coding gains could be obtained for these CODECs over CODEC IV & V. All proposed CODECs m this thesis are wavelet-based stereo image coding algorithms that maximise the flexibility and benefits offered by wavelet transform technology when applied to stereo imaging. In addition the use of a baseline-JPEG coding architecture would enable the easy adaptation of the proposed algorithms within systems originally built for DCT-based coding. This is an important feature that would be useful during an era where DCT-based technology is only slowly being phased out to give way for DWT based compression technology. In addition, this thesis proposed a stereo image coding algorithm that uses JPEG-2000 technology as the basic compression engine. The proposed CODEC, named RASTER is a rate scalable stereo image CODEC that has a unique ability to preserve the image quality at binocular depth boundaries, which is an important requirement in the design of stereo image CODEC. The experimental results have shown that the proposed CODEC is able to achieve PSNR gains of up to 3.7 dB as compared to directly transmitting the right frame using JPEG-2000

A family of stereoscopic image compression algorithms using wavelet transforms

With the standardization of JPEG-2000, wavelet-based image and video compression technologies are gradually replacing the popular DCT-based methods. In parallel to this, recent developments in autostereoscopic display technology is now threatening to revolutionize the way in which consumers are used to enjoying the traditional 2-D display based electronic media such as television, computer and movies. However, due to the two-fold bandwidth/storage space requirement of stereoscopic imaging, an essential requirement of a stereo imaging system is efficient data compression. In this thesis, seven wavelet-based stereo image compression algorithms are proposed, to take advantage of the higher data compaction capability and better flexibility of wavelets. [Continues.

MP3D: Highly Scalable Video Coding Scheme Based on Matching Pursuit

This paper describes a novel video coding scheme based on a three-dimensional Matching Pursuit algorithm. In addition to good compression performance at low bit rate, the proposed coder allows for flexible spatial, temporal and rate scalability thanks to its progressive coding structure. The Matching Pursuit algorithm generates a sparse decomposition of a video sequence in a series of spatio-temporal atoms, taken from an overcomplete dictionary of three-dimensional basis functions. The dictionary is generated by shifting, scaling and rotating two different mother atoms in order to cover the whole frequency cube. An embedded stream is then produced from the series of atoms. They are first distributed into sets through the set-partitioned position map algorithm (SPPM) to form the index-map, inspired from bit plane encoding. Scalar quantization is then applied to the coefficients which are finally arithmetic coded. A complete MP3D codec has been implemented, and performances are shown to favorably compare to other scalable coders like MPEG-4 FGS and SPIHT-3D. In addition, the MP3D streams offer an incomparable flexibility for multiresolution streaming or adaptive decoding

MURPHY -- A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids

We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach provides a consistent handling of non-lifted and lifted interpolating wavelets of arbitrary order demonstrated using second, fourth, and sixth order wavelets, combined with standard finite-difference based discretization operators. We first validate that the wavelet family used provides strict and explicit error control when coarsening the grid, and show that lifting wavelets increase the grid compression rate while conserving discrete moments across levels. Further, we demonstrate that high-order PDE discretization schemes combined with sufficiently high order wavelets retain the expected convergence order even at resolution jumps. We then simulate the advection of a scalar to analyze convergence for the temporal evolution of a PDE. The results shows that our wavelet-based refinement criterion is successful at controlling the overall error while the coarsening criterion is effective at retaining the relevant information on a compressed grid. Our software exploits a block-structured grid data structure for efficient multi-level operations, combined with a parallelization strategy that relies on a one-sided MPI-RMA communication approach with active PSCW synchronization. Using performance tests up to 16,384 cores, we demonstrate that this leads to a highly scalable performance. The associated code is available under a BSD-3 license at https://github.com/vanreeslab/murphy.Comment: submitted to SIAM Journal of Scientific Computing (SISC) on Dec 1

Learning-based Wavelet-like Transforms For Fully Scalable and Accessible Image Compression

The goal of this thesis is to improve the existing wavelet transform with the aid of machine learning techniques, so as to enhance coding efficiency of wavelet-based image compression frameworks, such as JPEG 2000. In this thesis, we first propose to augment the conventional base wavelet transform with two additional learned lifting steps -- a high-to-low step followed by a low-to-high step. The high-to-low step suppresses aliasing in the low-pass band by using the detail bands at the same resolution, while the low-to-high step aims to further remove redundancy from detail bands by using the corresponding low-pass band. These two additional steps reduce redundancy (notably aliasing information) amongst the wavelet subbands, and also improve the visual quality of reconstructed images at reduced resolutions. To train these two networks in an end-to-end fashion, we develop a backward annealing approach to overcome the non-differentiability of the quantization and cost functions during back-propagation. Importantly, the two additional networks share a common architecture, named a proposal-opacity topology, which is inspired and guided by a specific theoretical argument related to geometric flow. This particular network topology is compact and with limited non-linearities, allowing a fully scalable system; one pair of trained network parameters are applied for all levels of decomposition and for all bit-rates of interest. By employing the additional lifting networks within the JPEG2000 image coding standard, we can achieve up to 17.4% average BD bit-rate saving over a wide range of bit-rates, while retaining the quality and resolution scalability features of JPEG2000. Built upon the success of the high-to-low and low-to-high steps, we then study more broadly the extension of neural networks to all lifting steps that correspond to the base wavelet transform. The purpose of this comprehensive study is to understand what is the most effective way to develop learned wavelet-like transforms for highly scalable and accessible image compression. Specifically, we examine the impact of the number of learned lifting steps, the number of layers and the number of channels in each learned lifting network, and kernel support in each layer. To facilitate the study, we develop a generic training methodology that is simultaneously appropriate to all lifting structures considered. Experimental results ultimately suggest that to improve the existing wavelet transform, it is more profitable to augment a larger wavelet transform with more diverse high-to-low and low-to-high steps, rather than developing deep fully learned lifting structures

Joint coding-denoising optimization of noisy images

In this paper, we propose to study the problem of noisy source coding/denoising. The challenge of this problem is that a global optimization is usually difficult to perform as the global fidelity criterion needs to be optimized in the same time over the sets of both coding and denoising parameters. Most of the bibliography in this domain is based on the fact that, for a specific criterion, the global optimization problem can be simply separated into two independent optimization problems: The noisy image should be first optimally denoised and this denoised image should then be optimally coded. In many applications however, the layout of the acquisition imaging chain is fixed and cannot be changed, that is a denoising step cannot be inserted before coding. For this reason, we are concerned here with the problem of global joint optimization in the case the denoising step is performed, as usual, after coding/decoding. In this configuration, we show how to express the global distortion as a function of the coding and denoising parameters. We present then an algorithm to minimize this distortion and to get the optimal values of these parameters. We show results of this joint optimization algorithm on classical test images and on a high dynamic range image, visually and in a rate-distortion sense

Joint coding-denoising optimization of noisy images

In this paper, we propose to study the problem of noisy source coding/denoising. The challenge of this problem is that a global optimization is usually difficult to perform as the global fidelity criterion needs to be optimized in the same time over the sets of both coding and denoising parameters. Most of the bibliography in this domain is based on the fact that, for a specific criterion, the global optimization problem can be simply separated into two independent optimization problems: The noisy image should be first optimally denoised and this denoised image should then be optimally coded. In many applications however, the layout of the acquisition imaging chain is fixed and cannot be changed, that is a denoising step cannot be inserted before coding. For this reason, we are concerned here with the problem of global joint optimization in the case the denoising step is performed, as usual, after coding/decoding. In this configuration, we show how to express the global distortion as a function of the coding and denoising parameters. We present then an algorithm to minimize this distortion and to get the optimal values of these parameters. We show results of this joint optimization algorithm on classical test images and on a high dynamic range image, visually and in a rate-distortion sense

Context-based bit plane golomb coder for scalable image coding

Master'sMASTER OF ENGINEERIN