Nonlinear binary wavelet transforms and their application to binary image compression

Kamstra, Lute

doi:10.1109/icip.2002.1039040

Cited by 6 publications

(5 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since it does not require the existence of the Fourier transform, it can be extended to any finite field, including the binary field [13]. Furthermore, this wavelet transform does not depend on the field structure of binary numbers and nonlinear transforms can also be involved [19].…”

Section: Theory Of Bwtmentioning

confidence: 99%

“…The filter length has an important impact on the performance of a BWT-based compression system. It is shown in [19] that short filters perform better for synthetic images, such as character images, which comprise uniform areas with shape boundaries. In contrast, long filters perform well on images that are the dithered version of grey-level images, with a limited number of grey levels.…”

Section: Constraints On Filter Designmentioning

confidence: 99%

See 1 more Smart Citation

Lossless image compression using binary wavelet transform

2007

View full text Add to dashboard Cite

A binary wavelet transform (BWT) has several distinct advantages over a real wavelet transform when applied to binary data. No quantisation distortion is introduced and the transform is completely invertible. Since all the operations involved are modulo-2 arithmetic, it is extremely fast. The outstanding qualities of the BWT make it suitable for binary image-processing applications. The BWT, originally designed for binary images, is extended to the lossless compression of grey-level images. An in-place implementation structure of the BWT is explored. Then, a simple embedded lossless BWT-based image-coding algorithm called progressive partitioning binary wavelet-tree coder (PPBWC) is proposed. The proposed algorithm is simple in concept and implementation, but achieves promising lossless compression efficiency as compared with the conventional bitplane scanning methods. Small alphabets in the arithmetic coding, non-causal adaptive context modelling and source division are the major factors that contribute to the gain of compression efficiency of the PPBWC. Experimental results show that the PPBWC outperforms most of other embedded coders in terms of coding efficiency.

show abstract

Section: Theory Of Bwtmentioning

confidence: 99%

Section: Constraints On Filter Designmentioning

confidence: 99%

Lossless image compression using binary wavelet transform

2007

View full text Add to dashboard Cite

show abstract

“…single-scaled) binary variables in multiscales, we employ the BWT [10,18] used in signal processing. Although BWT has been explained from the viewpoint of filters, we describe BWT from the following permutation viewpoint, which appears suitable for the development of multiscale genetic operations.…”

Section: Appendix A: Multiscale Representation Of Binary Variablesmentioning

confidence: 99%

Multiscale multiresolution genetic algorithm with a golden sectioned population composition

Kim

Jung

Kim

2007

Numerical Meth Engineering

View full text Add to dashboard Cite

A new genetic algorithm (GA) strategy called the multiscale multiresolution GA is proposed for expediting solution convergence by orders of magnitude. The motivation for this development was to apply GAs to a certain class of large optimization problems, which are otherwise nearly impossible to solve. For the algorithm, standard binary design variables are binary wavelet transformed to multiscale design variables. By working with the multiscale variables, evolution can proceed in multiresolution; converged solutions at a low resolution are reused as a part of individuals of the initial population for the next resolution evolution. It is shown that the best solution convergence can be achieved if three initial population groups having different fitness levels are mixed at the golden section ratio. An analogy between cell division and the proposed multiscale multiresolution strategy is made. The specific applications of the developed method are made in topology optimization problems.The optimal choice for the population size increase is still a subject of further studies, the overall GA performance will not be significantly affected if the size increase is not too small.

show abstract

“…But the BWT spreads out an edge over the neighborhood, which degrades the coding efficiency. Kamstra [13,14] generalized the BWT by making it independent on the field structure of binary numbers and including nonlinear transforms as well. As a result, the increase of freedom in choosing a particular transform can be useful in binary image compression.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, this symbol expansion dramatically increases the ''model cost" [11] of a highorder context-based entropy coder in the compression of grayscale images that are usually represented by only eight alphabets. There have been several attempts to generalize wavelet transform to finite fields in order to take into account the image characteristics [12][13][14][15][16][17][18][19][20]. Swanson and Tewfik [12] introduced a new sequencebased transform applicable to sequences over GF (2).…”

Section: Introductionmentioning

confidence: 99%