Wavelet-based fixed and embedded L-infinite-constrained image coding

Abstract

A new wavelet-based L ∞-constrained fixed and embedded coding technique is proposed in this paper. 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 with other L ∞-constrained coding schemes and show that our proposed coder offers in addition a fully embedded L ∞oriented bit-stream. We illustrate also that the proposed coder retains the same capabilities as the state-of-the-art embedded wavelet-based codecs, while providing superior compression results and embeddedness with respect to the L ∞ distortion measure.

Scalable Joint Source and Channel Coding of Meshes

“…In other words, an L-infinite codec is capable to find the best rate allocation for which the L-infinite distortion (and consequently the Hausdorff distance) is upper-bounded by an user-defined bound, and guaranteed to be below that bound [24]- [26]. This is an interesting and unique feature in the context of 3-D object coding.…”

“…If we take as the Euclidian distance between and , then (1) This shows that optimizing the rate allocation for a given MAXAD constraint is equivalent to finding a rate allocation such that the Hausdorff distance at that resolution is upper bounded by the MAXAD bound. One benefit of such mesh coding approach is that closed-form estimates of the L-infinite distortion are readily available, following for instance similar derivations as in our approach for L-infinite coding of images [24]- [26]. Based on this, fast algorithms to solve the R-D optimization problem can be designed.…”

Statistical L-infinite distortion estimation in scalable coding of meshes

“…There are applications -see e.g. [7], [8], that require imposing a tight bound on the individual elements of the error signal, i.e. constraining the elements of the reconstruction error to be under some given thresholds.…”

Progressive lossless compression of medical images

“…The works of Avcibaş et al [3,4], Alecu et al [5,6,7] and Krivoulets [8,9] are remarkable exceptions, since they address the problem of generating embedded bit-streams that minimize the L∞-norm of the reconstruction error. Avcibaş et al proposed an approach that relies on a predictive-based method that successively refines the probability density function (pdf) used to estimate each pixel and by restricting the region of support of the pdf to fixed size intervals, which have to be predefined before encoding [3,4].…”

“…Avcibaş et al proposed an approach that relies on a predictive-based method that successively refines the probability density function (pdf) used to estimate each pixel and by restricting the region of support of the pdf to fixed size intervals, which have to be predefined before encoding [3,4]. Almost simultaneously, Alecu et al proposed a wavelet-based scheme that allows full L∞ scalability [5,6,7]. This algorithm was compared with JPEG2000 in terms of L∞ rate-distortion, showing better results [7].…”