Wavelet-based scalable L-infinity-oriented compression

Abstract

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.

Efficient error control in 3D mesh coding

“…Its statistical average, which is commonly referred to as the Mean Square Error (MSE), is then regarded as giving a good approximation of the global error. An alternative to MSE is the L-infinite distortion, which, opposite to the L-2, provides a good expression of the maximum local error [8].…”

“…For more details, the interested reader is referred to [9]. Expression (8) implies that if such a bijective mapping exists, then an L-infinite-constrained coding actually implies Hausdorff-distance-constrained coding [1]. Practically, one has the possibility to set a specific target bound on the Linfinite distortion, and due to (8), the Hausdorff distance will be guaranteed to be below that target bound.…”

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].…”

“…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]. Krivoulets proposed a lossy plus near-lossless layered compression scheme with embedded quantization of the difference signal, where the initial lossy layer is encoded with JPEG2000 [8,9].…”