Fractal Image Compression

Fisher, Yuval

doi:10.1142/s0218348x94000442

Cited by 93 publications

(63 citation statements)

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“…For example, for each range block R i we could consider a number of domain blocks, possibly weighting each block inversely according to the collage error that it yields. The idea of using multiple domain blocks in order to improve the accuracy of approximation has been around for some time (see, for example, [9]). However, S. Alexander [1] has recently shown that this idea can be used effectively for purposes other than simply increasing the PSNR, for example, denoising, edge detection and block classification.…”

Section: Evolution For a Convex Combination Of Contraction Mappingsmentioning

confidence: 99%

“…Indeed, such selfsimilarity properties inspired the seminal paper of M. Barnsley and S. Demko on "iterated function systems" and the inverse problem of fractal construction [4] which, in turn, led to intensive investigations into fractal image coding and compression [3,5,9].…”

Section: Introductionmentioning

confidence: 99%

“…Following the later idea of A. Jacquin [13], however, images are generally well approximated by a union of spatiallycontracted and greyscale modified copies of subsets of themselves. This is the basis of block-based fractal image coding [3,5,9] or "local IFS" methods. Indeed, recent experiments by our group [2,1] confirm that images are generally quite locally self-similar -subblocks of an image are typically well approximated by many decimated subblocks from elsewhere in the image.…”

Section: Introductionmentioning

confidence: 99%

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Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging

Vrscay

2006

Lecture Notes in Computer Science

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Abstract. Traditional fractal image coding seeks to approximate an image function u as a union of spatially-contracted and greyscale-modified copies of itself, i.e., u ≈ T u, where T is a contractive fractal transform operator on an appropriate space of functions. Consequently u is well approximated byū, the unique fixed point of T , which can then be constructed by the discrete iteration procedure un+1 = Tn. In a previous work, we showed that the evolution equation yt = Oy − y produces a continuous evolution y(x, t) toȳ, the fixed point of a contractive operator O. This method was applied to the discrete fractal transform operator, in which case the evolution equation takes the form of a nonlocal differential equation under which regions of the image are modified according to information from other regions. In this paper we extend the scope of this evolution equation by introducing additional operators, e.g., diffusion or curvature operators, that "compete" with the fractal transform operator. As a result, the asymptotic limiting function y∞ is a modification of the fixed pointū of the original fractal transform. The modification can be viewed as a replacement of traditional postprocessing methods that are employed to "touch up" the attractor functionū.

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Section: Evolution For a Convex Combination Of Contraction Mappingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging

Vrscay

2006

Lecture Notes in Computer Science

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“…These include the vector quantization [1], fractal image compression [2], wavelet image compression [3], and block truncation coding (BTC) [4]. In this study, we focus on the last one.…”

Section: Introductionmentioning

confidence: 99%

k-d Tree-Segmented Block Truncation Coding for Image Compression

Daga

Fernandez

2016

MATEC Web of Conferences

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Abstract. Block truncation coding (BTC) is a class of image compression algorithms whose main technique is the partitioning of an image into pixel blocks that are then each encoded using a representative set of pixel values. It is commonly used because of its simplicity and low computational complexity. The Quadtree-segmented BTC (QTS-BTC), which utilizes a dynamic hierarchical segmentation technique, is among the most efficient in the BTC class. In this study, we propose a new BTC variant that introduces two ideas: (1) the use of a k-d tree for segmentation and (2) the use of a Mean Squared Error (MSE) threshold for dynamically determining the granularity of the blocks. We refer to this new BTC variant as the k-d Tree Segmented BTC (KTS-BTC), and we test this against some of the existing BTC variants by running the algorithms on a standard image compression dataset. The results show that the proposed variant yields low bit rates of the compressed images, even outperforming the state-of-the-art QTS-BTC, without a significant reduction in image quality as measured using the Peak Signal-to-Noise Ratio (PSNR). The utilization of k-d tree for image segmentation is further shown to have more impact than that of employing the MSE thresholding scheme as a block activity classifier.

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“…In fractal image compression [11], the self-similarity between different parts of an image is used for image compression based on contractive mapping fixed point theorem. However, the fractal image compression focuses on contractive transform design, which makes it usually not suitable for lossless image compression.…”

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confidence: 99%

Lossless Image Compression Using Super-Spatial Structure Prediction

Zhao

2010

IEEE Signal Process. Lett.

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Abstract-We recognize that the key challenge in image compression is to efficiently represent and encode high-frequency image structure components, such as edges, patterns, and textures. In this work, we develop an efficient lossless image compression scheme called super-spatial structure prediction. This super-spatial prediction is motivated by motion prediction in video coding, attempting to find an optimal prediction of structure components within previously encoded image regions. We find that this super-spatial prediction is very efficient for image regions with significant structure components. Our extensive experimental results demonstrate that the proposed scheme is very competitive and even outperforms the state-of-the-art lossless image compression methods.Index Terms-Context-based adaptive lossless image coding (CALIC), lossless image compression, structure components, super-spatial structure prediction.

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Fractal Image Compression

Cited by 93 publications

References 0 publications

Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging

Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging

k-d Tree-Segmented Block Truncation Coding for Image Compression

Lossless Image Compression Using Super-Spatial Structure Prediction

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