Precision Enhancement of 3D Surfaces from Multiple Compressed Depth Maps

In texture-plus-depth representation of a 3D scene, depth maps from different camera viewpoints are typically lossily compressed via the classical transform coding / coefficient quantization paradigm. In this paper we propose to reduce distortion of the decoded depth maps due to quantization. The key observation is that depth maps from different viewpoints constitute multiple descriptions (MD) of the same 3D scene. Considering the MD jointly, we perform a POCS-like iterative procedure to project a reconstructed signal from one depth map to the other and back, so that the converged depth maps have higher precision than the original quantized versions.Comment: This work was accepted as ongoing work paper in IEEE MMSP'201

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Multiple Description Decoding of Overcomplete Expansions Using Projections onto Convex Sets

This paper presents a POCS-based algorithm for consistent reconstruction of a signal x 2 R K from any subset of quantized coefficients y 2 R N in an N \Theta K overcomplete frame expansion y = Fx, N = 2K. By choosing the frame operator F to be the concatenation of two K \Theta K invertible transforms, the projections may be computed in R K using only the transforms and their inverses, rather than in the larger space R N using the pseudo-inverse as proposed in earlier work. This enables practical reconstructions from overcomplete frame expansions based on wavelet, subband, or lapped transforms of an entire image, which has heretofore not been possible. 1 Introduction Multiple description (MD) source coding is the problem of encoding a single source fX i g into N separate binary descriptions at rates R 1 ; : : : ; RN bits per symbol such that any subset S of the descriptions may be received and together decoded to an expected distortion D S commensurate with the total b..

Efficient Quantization for Overcomplete Expansions in R^N

In this paper, we study construction of structured regular quantizers for overcomplete expansions in . Our goal is to design structured quantizers which allow simple reconstruction algorithms with low complexity and which have good performance in terms of accuracy. Most related work to date in quantized redundant expansions has assumed that the same uniform scalar quantizer was used on all the expansion coefficients. Several approaches have been proposed to improve the reconstruction accuracy, with some of these methods having significant complexity. Instead, we consider the joint design of the overcomplete expansion and the scalar quantizers (allowing different step sizes) in such a way as to produce an equivalent vector quantizer (EVQ) with periodic structure. The construction of a periodic quantizer is based on lattices in and the concept of geometrically scaled-similar sublattices. The periodicity makes it possible to achieve good accuracy using simple reconstruction algorithms (e.g., linear reconstruction or a small lookup table)

n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization

This paper is about the design and analysis of an index-assignment (IA) based multiple-description coding scheme for the n-channel asymmetric case. We use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions, which are given by the inverse IA function when all descriptions are received or otherwise by a weighted average of the received descriptions. We consider smooth sources with finite differential entropy rate and MSE fidelity criterion. As in previous designs, our construction is based on nested lattices which are combined through a single IA function. The results are exact under high-resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity. For any n, the design is asymptotically optimal within the class of IA-based schemes. Moreover, in the case of two descriptions and finite lattice vector dimensions greater than one, the performance is strictly better than that of existing designs. In the case of three descriptions, we show that in the limit of large lattice vector dimensions, points on the inner bound of Pradhan et al. can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields, in the symmetric case, a smaller rate loss than the recently proposed source-splitting approach.Comment: 49 pages, 4 figures. Accepted for publication in IEEE Transactions on Information Theory, 201