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Journal articles on the topic 'Fractal image coding'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

LIAN, SHIGUO, XI CHEN, and DENGPAN YE. "SECURE FRACTAL IMAGE CODING BASED ON FRACTAL PARAMETER ENCRYPTION." Fractals 17, no. 02 (June 2009): 149–60. http://dx.doi.org/10.1142/s0218348x09004405.

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In recent work, various fractal image coding methods are reported, which adopt the self-similarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, produces the encrypted and encoded image. The encrypted image can only be recovered by the correct key. To maintain security and efficiency, only the suitable parameters are selected and encrypted through investigating the properties of various fractal parameters, including parameter space, parameter distribution and parameter sensitivity. The encryption process does not change the file format, keeps secure in perception, and costs little time or computational resources. These properties make it suitable for secure image encoding or transmission.

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2

Barthel, Kai Uwe. "Entropy Constrained Fractal Image Coding." Fractals 05, supp01 (April 1997): 17–26. http://dx.doi.org/10.1142/s0218348x97000607.

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In this paper we present an entropy constrained fractal coding scheme. In order to get high compression rates, previous fractal coders used hierarchical coding schemes with variable range block sizes. Our scheme uses constant range block sizes, but the complexity of the fractal transformations is adapted to the image contents. The entropy of the fractal code can be significantly reduced by introducing geometrical codebooks of variable size and a variable order luminance transformation. We propose a luminance transformation consisting of a unification of fractal and transform coding. With this transformation both inter- and intra- block redundancy of an image can be exploited to get higher coding gain. The coding results obtained with our new scheme are superior compared to conventional fractal and transform coding schemes.

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3

LU, JIAN, JIAPENG TIAN, CHEN XU, and YURU ZOU. "A DICTIONARY LEARNING APPROACH FOR FRACTAL IMAGE CODING." Fractals 27, no. 02 (March 2019): 1950020. http://dx.doi.org/10.1142/s0218348x19500208.

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In recent years, sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, this paper investigates incorporating a dictionary learning approach into fractal image coding, which leads to a new model containing three terms: a patch-based sparse representation prior over a learned dictionary, a quadratic term measuring the closeness of the underlying image to a fractal image, and a data-fidelity term capturing the statistics of Gaussian noise. After the dictionary is learned, the resulting optimization problem with fractal coding can be solved effectively. The new method can not only efficiently recover noisy images, but also admirably achieve fractal image noiseless coding/compression. Experimental results suggest that in terms of visual quality, peak-signal-to-noise ratio, structural similarity index and mean absolute error, the proposed method significantly outperforms the state-of-the-art methods.

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4

Chen, Yuanxu, Yupin Luo, and Dongcheng Hu. "Image superresolution using fractal coding." Optical Engineering 47, no. 1 (2008): 017007. http://dx.doi.org/10.1117/1.2835453.

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5

Jacquin, A. E. "Fractal image coding: a review." Proceedings of the IEEE 81, no. 10 (1993): 1451–65. http://dx.doi.org/10.1109/5.241507.

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6

Ida, T., and Y. Sambonsugi. "Image segmentation using fractal coding." IEEE Transactions on Circuits and Systems for Video Technology 5, no. 6 (1995): 567–70. http://dx.doi.org/10.1109/76.477072.

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7

Khaitu, Shree Ram, and Sanjeeb Prasad Panday. "Fractal Image Compression Using Canonical Huffman Coding." Journal of the Institute of Engineering 15, no. 1 (February 16, 2020): 91–105. http://dx.doi.org/10.3126/jie.v15i1.27718.

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Image Compression techniques have become a very important subject with the rapid growth of multimedia application. The main motivations behind the image compression are for the efficient and lossless transmission as well as for storage of digital data. Image Compression techniques are of two types; Lossless and Lossy compression techniques. Lossy compression techniques are applied for the natural images as minor loss of the data are acceptable. Entropy encoding is the lossless compression scheme that is independent with particular features of the media as it has its own unique codes and symbols. Huffman coding is an entropy coding approach for efficient transmission of data. This paper highlights the fractal image compression method based on the fractal features and searching and finding the best replacement blocks for the original image. Canonical Huffman coding which provides good fractal compression than arithmetic coding is used in this paper. The result obtained depicts that Canonical Huffman coding based fractal compression technique increases the speed of the compression and has better PNSR as well as better compression ratio than standard Huffman coding.

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8

YUEN, CHING-HUNG, and KWOK-WO WONG. "CRYPTANALYSIS ON SECURE FRACTAL IMAGE CODING BASED ON FRACTAL PARAMETER ENCRYPTION." Fractals 20, no. 01 (March 2012): 41–51. http://dx.doi.org/10.1142/s0218348x12500041.

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The vulnerabilities of the selective encryption scheme for fractal image coding proposed by Lian et al.1 are identified. By comparing multiple cipher-images of the same plain-image encrypted with different keys, the positions of unencrypted parameters in each encoded block are located. This allows the adversary to recover the encrypted depth of the quadtree by observing the length of each matched domain block. With this depth information and the unencrypted parameters, the adversary is able to reconstruct an intelligent image. Experimental results show that some standard test images can be successfully decoded and recognized by replacing the encrypted contrast scaling factor and brightness offset with specific values. Some remedial approaches are suggested to enhance the security of the scheme.

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9

Dalui, Indrani, SurajitGoon, and Avisek Chatterjee. "A NEW APPROACH OF FRACTAL COMPRESSION USING COLOR IMAGE." International Journal of Engineering Technologies and Management Research 6, no. 6 (March 25, 2020): 74–71. http://dx.doi.org/10.29121/ijetmr.v6.i6.2019.395.

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Fractal image compression depends on self-similarity, where one segment of a image is like the other one segment of a similar picture. Fractal coding is constantly connected to grey level images. The simplest technique to encode a color image by gray- scale fractal image coding algorithm is to part the RGB color image into three Channels - red, green and blue, and compress them independently by regarding each color segment as a specific gray-scale image. The colorimetric association of RGB color pictures is examined through the calculation of the relationship essential of their three-dimensional histogram. For normal color images, as a typical conduct, the connection necessary is found to pursue a power law, with a non- integer exponent type of a given image. This conduct recognizes a fractal or multiscale self-comparable sharing of the colors contained, in average characteristic pictures. This finding of a conceivable fractal structure in the colorimetric association of regular images complement other fractal properties recently saw in their spatial association. Such fractal colorimetric properties might be useful to the characterization and demonstrating of natural images, and may add to advance in vision. The outcomes got demonstrate that the fractal-based compression for the color image fills in similarly with respect to the color image.

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10

Götting, Detlef, Achim Ibenthal, and Rolf-Rainer Grigat. "Fractal Image Coding and Magnification Using Invariant Features." Fractals 05, supp01 (April 1997): 65–74. http://dx.doi.org/10.1142/s0218348x97000644.

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Fractal image coding has significant potential for the compression of still and moving images and also for scaling up images. The objective of our investigations was twofold. First, compression ratios of factor 60 and more for still images have been achieved, yielding a better quality of the decoded picture material than standard methods like JPEG. Second, image enlargement up to factors of 16 per dimension has been realized by means of fractal zoom, leading to natural and sharp representation of the scaled image content. Quality improvements were achieved due to the introduction of an extended luminance transform. In order to reduce the computational complexity of the encoding process, a new class of simple and suited invariant features is proposed, facilitating the search in the multidimensional space spanned by image domains and affine transforms.

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11

Hua, Zhen, Haicheng Zhang, and Jinjiang Li. "Image Super Resolution Using Fractal Coding and Residual Network." Complexity 2019 (November 28, 2019): 1–14. http://dx.doi.org/10.1155/2019/9419107.

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Fractal coding techniques are an effective tool for describing image textures. Considering the shortcomings of the existing image super-resolution (SR) method, the large-scale factor reconstruction performance is poor and the texture details are incomplete. In this paper, we propose an SR method based on error compensation and fractal coding. First, quadtree coding is performed on the image, and the similarity between the range block and the domain block is established to determine the fractal code. Then, through this similarity relationship, the attractor is reconstructed by super-resolution fractal decoding to obtain an interpolated image. Finally, the fractal error of the fractal code is estimated by the depth residual network, and the estimated version of the error image is added as an error compensation term to the interpolation image to obtain the final reconstructed image. The network structure is jointly trained by a deep network and a shallow network. Residual learning is introduced to greatly improve the convergence speed and reconstruction accuracy of the network. Experiments with other state-of-the-art methods on the benchmark datasets Set5, Set14, B100, and Urban100 show that our algorithm achieves competitive performance quantitatively and qualitatively, with subtle edges and vivid textures. Large-scale factor images can also be reconstructed better.

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12

Nappi, Michele, and Daniel Riccio. "Combining Fractal Coding and Orthogonal Linear Transforms." ISRN Signal Processing 2011 (April 26, 2011): 1–9. http://dx.doi.org/10.5402/2011/359592.

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Many desirable properties make fractals a powerful mathematic model applied in several image processing and pattern recognition tasks: image coding, segmentation, feature extraction, and indexing, just to cite some of them. Unfortunately, they are based on a strong asymmetric scheme, consequently suffering from very high coding times. On the other side, linear transforms are quite time balanced, allowing them to be usefully exploited in realtime applications, but they do not provide comparable performances with respect to the image quality for high bit rates. In this paper, we investigate different levels of embedding orthogonal linear transforms in the fractal coding scheme. Experimental results show a clear improved quality for compression ratios up to 15 : 1.

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13

KAMAL, A. R. NADIRA BANU, S. THAMARAI SELVI, and HENRY SELVARAJ. "ITERATION-FREE FRACTAL CODING FOR IMAGE COMPRESSION USING GENETIC ALGORITHM." International Journal of Computational Intelligence and Applications 07, no. 04 (December 2008): 429–46. http://dx.doi.org/10.1142/s1469026808002399.

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An iteration-free fractal coding for image compression is proposed using genetic algorithm (GA) with elitist model. The proposed methodology reduces the coding process time by minimizing intensive computations. The proposed technique utilizes the GA, which greatly decreases the search space for finding the self-similarities in the given image. The performance of the proposed method is compared with the iteration-free fractal-based image coding using vector quantization method for both single block and Quad tree partition on benchmark images for parameters such as image quality and coding time. It is observed that the proposed method achieves excellent performance in image quality with reduction in computing time.

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14

ZOU, YURU, HUAXUAN HU, JIAN LU, XIAOXIA LIU, QINGTANG JIANG, and GUOHUI SONG. "A NONLOCAL LOW-RANK REGULARIZATION METHOD FOR FRACTAL IMAGE CODING." Fractals 29, no. 05 (June 25, 2021): 2150125. http://dx.doi.org/10.1142/s0218348x21501255.

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Fractal coding has been widely used as an image compression technique in many image processing problems in the past few decades. On the other hand side, most of the natural images have the characteristic of nonlocal self-similarity that motivates low-rank representations of them. We would employ both the fractal image coding and the nonlocal self-similarity priors to achieve image compression in image denoising problems. Specifically, we propose a new image denoising model consisting of three terms: a patch-based nonlocal low-rank prior, a data-fidelity term describing the closeness of the underlying image to the given noisy image, and a quadratic term measuring the closeness of the underlying image to a fractal image. Numerical results demonstrate the superior performance of the proposed model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.

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15

Wang, Dong Mei, and Jing Yi Lu. "Research of Image Compression Based on Fractal Coding." Applied Mechanics and Materials 241-244 (December 2012): 418–22. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.418.

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The EZW and Fractal Coding were researched and simulated in this paper. And two drawbacks were discovered in these algorithm:the coding time is too long and the effect of reconstructed image is not ideal. Therefore, The paper studied the wavelet transformation in the fractal coding application, The wavelet coefficients of an image present two characteristics when the image is processed by wavelet transform: first characteristic is that the energy of an image is strongly concentrated in low frequency sub-image, second characteristic is that there is a similarity between the same direction in high frequency sub-images.but the fractal coding essence was precisely uses the similarity of wavelet transform image. The paper designed one kind of new Image Compression based on Fractal Coding in wavelet domain. The theoretical analysis and the simulation experiment indicated that, to some extent the method can reduce the coding time and reduce the MSE and enhance compression ratio of the reconstructed image and improve PSNR of the reconstructed image..

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16

Popescu, Dan C. "Fractal image coding - achievements and prospects." Annales Des Télécommunications 53, no. 5-6 (May 1998): 219–28. http://dx.doi.org/10.1007/bf02997678.

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17

WANG, XING-YUAN, FAN-PING LI, and ZHI-FENG CHEN. "AN IMPROVED FRACTAL IMAGE CODING METHOD." Fractals 17, no. 04 (December 2009): 451–57. http://dx.doi.org/10.1142/s0218348x09004545.

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This paper presents a fast fractal image coding method based on quadtree division, improved neighbor search and asymptotic strategy. We search the optimal matched domain block of a range block in its five nearest neighbor blocks and make asymptotic moves along the direction of potential optimal solution. If the optimal solution can not be improved, we carry out quadtree division for this range block until it caters to our demand or reaches greatest division level. The experimental results show that the coding speed of the proposed method declined slightly, but it has a better quality of reconstructed image and higher compression ratio in comparisons with no search method.

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18

Kim, Taekon, Robert E. Van Dyck, and David J. Miller. "Hybrid fractal zerotree wavelet image coding." Signal Processing: Image Communication 17, no. 4 (April 2002): 347–60. http://dx.doi.org/10.1016/s0923-5965(02)00003-6.

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19

齐, 凌云. "An Improved Fractal Image Coding Method." Computer Science and Application 07, no. 11 (2017): 1052–58. http://dx.doi.org/10.12677/csa.2017.711119.

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20

Yin, Zhongke, Shaoguo Yang, and Deren Gu. "A new fractal image coding method." Journal of Electronics (China) 15, no. 2 (April 1998): 125–29. http://dx.doi.org/10.1007/s11767-998-0046-3.

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21

Furao, Shen, and Osamu Hasegawa. "Fractal Image Coding with Simulated Annealing Search." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 1 (January 20, 2005): 80–88. http://dx.doi.org/10.20965/jaciii.2005.p0080.

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The main shortcomings of fractal image coders are (1) the slow speed for searching domain block pool, and (2) known fast algorithms leading to a loss of image quality. We propose efficient fractal image coding using simulated annealing method. Compared to previous schemes, our proposal greatly increases the search speed of domain block pool with almost no image quality loss. Experimental results indicate the high feasibility of the proposed method, which is, furthermore, extendable to other fractal coders.

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22

Гулаков, Василий, Vasiliy Gulakov, Сергей Клепинин, and Sergey Klepinin. "Using subfractals for coding and image recognition." Bulletin of Bryansk state technical university 2014, no. 3 (September 30, 2014): 108–13. http://dx.doi.org/10.12737/23139.

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Considered fractal image coding for image recognition, analyzed the spatial distribution of matching domain and rank blocks received during the encoding process. A new method of con-struction of fractal code that is designed to minimize the influence of defects in image recogni-tion quality.

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23

Ali, Ahmed Huaasin, Ali Nihad Abbas, Loay Edwar George, and Mohd Rosmadi Mokhtar. "Image and audio fractal compression: comprehensive review, enhancements and research directions." Indonesian Journal of Electrical Engineering and Computer Science 15, no. 3 (September 1, 2019): 1564. http://dx.doi.org/10.11591/ijeecs.v15.i3.pp1564-1570.

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<p>This study aims to review the recent techniques in digital multimedia compression with respect to fractal coding techniques. It covers the proposed fractal coding methods in audio and image domain and the techniques that were used for accelerating the encoding time process which is considered the main challenge in fractal compression. This study also presents the trends of the researcher's interests in applying fractal coding in image domain in comparison to the audio domain. This review opens directions for further researches in the area of fractal coding in audio compression and removes the obstacles that face its implementation in order to compare fractal audio with the renowned audio compression techniques.</p>

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24

Wang, Xin, and He Pan. "Fractal Image Coding Based on Wavelet Transformation." Advanced Materials Research 1030-1032 (September 2014): 1713–16. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.1713.

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The classic problem of the existence of fractal coding time is too long, a kind of fast encoding algorithm was proposed in this paper, which is based on Wavelet and Fractal combined, using wavelet decomposition characteristics. This method reduces the amount of image data compression effectively, shorts coding time and improve the image encoding quality.

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25

WANG, XING-YUAN, and ZHI-FENG CHEN. "A FAST FRACTAL CODING IN APPLICATION OF IMAGE RETRIEVAL." Fractals 17, no. 04 (December 2009): 441–50. http://dx.doi.org/10.1142/s0218348x09004557.

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Aiming at content-based image retrieval (CBIR) in fractal domain, this paper puts forward a fast fractal encoding method to extract image features, which is based on a novel non-searching and adaptive quadtree division. As a result, it enhances fractal coding speed sharply, only needs 0.0485 seconds on average for a 256 × 256 image and is approximately 70 times faster than algorithm in addition to good reconstructed image quality. Furthermore, this paper improves image matching algorithm, consequently enhancing the accuracy of query results. In addition, we present a method to further accelerate image retrieval based on the analysis to fractal codes distance and number. Experimental results show that our proposed method is performs highly in retrieval speed and feasible in retrieval accuracy.

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26

Yang, Jie. "Multiple Description Wavelet-Based Image Coding Using Iterated Function System." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/924274.

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Recent literature highlights the multiple description coding (MDC) as a promising method to solve the problem of resilient image coding over error-prone networks, where packet losses occur. In this paper, we introduce a novel multiple description wavelet-based image coding scheme using fractal. This scheme exploits the fractal’s ability, which is to describe the different resolution scale similarity (redundancy) among wavelet coefficient blocks. When one description is lost, the lost information can be reconstructed by the proposed iterated function system (IFS) recovering scheme with the similarity and some introduced information. Compared with the referenced methods, the experimental results suggest that the proposed scheme can achieve better performance. Furthermore, it is substantiated to be more robust for images transmission and better subjective quality in reconstructed images even with high packet loss ratios.

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27

WANG, Qiang, De-qun LIANG, and Sheng BI. "Prediction on decoded image quality for fractal image coding." Journal of Computer Applications 30, no. 12 (January 5, 2011): 3255–57. http://dx.doi.org/10.3724/sp.j.1087.2010.03255.

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28

Lai, Cheung-Ming, Kin-Man Lam, and Wan-Chi Siu. "Improved searching scheme for fractal image coding." Electronics Letters 38, no. 25 (2002): 1653. http://dx.doi.org/10.1049/el:20021175.

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29

Davoine, Franck, Etienne Bertin, and Jean-Marc Chassery. "An Adaptive Partition for Fractal Image Coding." Fractals 05, supp01 (April 1997): 243–56. http://dx.doi.org/10.1142/s0218348x97000796.

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In this paper we present a flexible partitioning scheme for fractal image compression, based on the Delaunay triangles. The aim is to have the advantage of triangular blocks over squares, in terms of adaptivity to the image content. In a first step, the triangulation is computed so that the triangles are more densely distributed in regions containing interesting features such as corners and edges, or so that they tend to run along the strong edges in the image. In a second step we merge adjacent triangles into quadrilaterals, in order to decrease the number of blocks. Quadrilaterals permit a reduction of the number of local contractive affine transformations composing the fractal transform, and thus to increase the compression ratio, while preserving the visual quality of the decoded image.

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30

Chen, Rong‐Jian, and Bin‐Chang Chieu. "Adaptive fractal image coding in subband domain." Journal of the Chinese Institute of Engineers 19, no. 3 (April 1996): 417–27. http://dx.doi.org/10.1080/02533839.1996.9677803.

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31

Li, Cheng‐Hao, and Shuenn‐Shyang Wang. "Digital watermarking based on fractal image coding." Journal of the Chinese Institute of Engineers 23, no. 6 (September 2000): 759–66. http://dx.doi.org/10.1080/02533839.2000.9670597.

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32

Chitra, A., Aravind Krishnaswamy, and S. N. Sivanandam. "A Parallel Algorithm for Fractal Image Coding." IFAC Proceedings Volumes 30, no. 25 (September 1997): 307–12. http://dx.doi.org/10.1016/s1474-6670(17)41341-3.

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33

Xu, Chang-man, and Zhao-yang Zhang. "A fast fractal image compression coding method." Journal of Shanghai University (English Edition) 5, no. 1 (March 2001): 57–59. http://dx.doi.org/10.1007/s11741-001-0029-1.

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34

Yuen, Ching-Hung, and Kwok-Wo Wong. "Chaos-based encryption for fractal image coding." Chinese Physics B 21, no. 1 (January 2012): 010502. http://dx.doi.org/10.1088/1674-1056/21/1/010502.

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35

Popescu, D. C., A. Dimca, and Hong Yan. "A nonlinear model for fractal image coding." IEEE Transactions on Image Processing 6, no. 3 (March 1997): 373–82. http://dx.doi.org/10.1109/83.557339.

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36

Chang-Su Kim, Rin-Chul Kim, and Sang-Uk Lee. "A fractal vector quantizer for image coding." IEEE Transactions on Image Processing 7, no. 11 (1998): 1598–602. http://dx.doi.org/10.1109/83.725366.

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Hürtgen, B. "Contractivity of fractal transforms for image coding." Electronics Letters 29, no. 20 (1993): 1749. http://dx.doi.org/10.1049/el:19931165.

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38

Distasi, R., M. Polvere, and M. Nappi. "Split decision functions in fractal image coding." Electronics Letters 34, no. 8 (1998): 751. http://dx.doi.org/10.1049/el:19980597.

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39

Chatterjee, Shoma, and K. K. Biswas. "A Technique for Faster Fractal Image Coding." IETE Journal of Research 46, no. 3 (May 2000): 147–55. http://dx.doi.org/10.1080/03772063.2000.11416150.

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40

Furusawa, Ryuji, and Masahiro Nakagawa. "Fractal image coding with a multiscaling-domain." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 87, no. 2 (2003): 79–87. http://dx.doi.org/10.1002/ecjc.10081.

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41

SANKARAGOMATHI, B., L. GANESAN, and S. ARUMUGAM. "ENCODING VIDEO SEQUENCES IN FRACTAL-BASED COMPRESSION." Fractals 15, no. 04 (December 2007): 365–78. http://dx.doi.org/10.1142/s0218348x0700371x.

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With the rapid increase in the use of computers and the Internet, the demand for higher transmission and better storage is increasing as well. This paper describes the different techniques for data (image-video) compression in general and, in particular, the new compression technique called fractal image compression. Fractal image compression is based on self-similarity, where one part of an image is similar to the other part of the same image. Low bit rate color image sequence coding is very important for video transmission and storage applications. The most significant aspect of this work is the development of color images using fractal-based color image compression, since little work has been done previously in this area. The results obtained show that the fractal-based compression works for the color images works as well as for the gray-scale images. Nevertheless, the encoding of the color images takes more time than the gray-scale images. Color images are usually compressed in a luminance-chrominance coordinate space, with the compression performed independently for each coordinate by applying the monochrome image processing techniques. For image sequence compression, the design of an accurate and efficient algorithm for computing motion to exploit the temporal redundancy has been one of the most active research areas in computer vision and image compression. Pixel-based motion estimation algorithms address pixel correspondence directly by identifying a set of local features and computing a match between these features across the frames. These direct techniques share the common pitfall of high computation complexity resulting from the dense vector fields produced. For block matching motion estimation algorithms, the quad-tree data structure is frequently used in image coding to recursively decompose an image plane into four non-overlapping rectangular blocks.

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Bi, Sheng, and Qiang Wang. "Fractal Image Coding Based on a Fitting Surface." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/634848.

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A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI) is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.

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XU, CHEN, YUTING YE, ZHENWEI HU, YURU ZOU, LIXIN SHEN, XIAOXIA LIU, and JIAN LU. "A PRIMAL-DUAL ALGORITHM FOR ROBUST FRACTAL IMAGE CODING." Fractals 27, no. 07 (November 2019): 1950119. http://dx.doi.org/10.1142/s0218348x19501196.

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The essence of Huber fractal image coding (HFIC) is to predict the fractal code of a noiseless image as accurately as possible from its corrupted observation with outliers by adopting Huber M-estimation technique. However, the traditional HFIC is not quite satisfactory mainly due to the absence of contractivity restriction for the estimate of the fractal parameters (actually, it is a fundamental requirement in the theory of fractal image coding). In this paper, we introduce a primal-dual algorithm for robust fractal image coding (PD-RFIC), which formulates the problem of robust prediction of the fractal parameters with contractivity condition as a constrained optimization model and then adopts a primal-dual algorithm to solve it. Furthermore, in order to relieve using the corrupted domain block as the independent variable in the proposed method, instead of using the mean operation on a [Formula: see text] subblock in the traditional HFIC, we apply a median operation on a larger subblock to obtain the contracted domain blocks for achieving the robustness against outliers. The effectiveness of the proposed method is experimentally illustrated on problems of image denoising with impulse noise (specifically, salt & pepper noise and random-valued noise). Remarkable improvements of the proposed method over conventional HFIC are demonstrated in terms of both numerical evaluations and visual quality. In addition, a median-based version of Fisher classification method is also developed to accelerate the encoding speed of the proposed method.

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Park, Jaehong, Cheolwoo Park, and Wonseok Yang. "Fractal Image Coding for Improve the Quality of Medical Images." Journal of the Korean Society of Radiology 8, no. 1 (January 30, 2014): 19–26. http://dx.doi.org/10.7742/jksr.2014.8.1.19.

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Takezawa, Megumi, and Miki Haseyama. "Quality Improvement of JPEG Images Based on Fractal Image Coding." Journal of the Institute of Image Information and Television Engineers 58, no. 9 (2004): 1317–23. http://dx.doi.org/10.3169/itej.58.1317.

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Al-Saidi, Nadia M. G., Mohamad Rushdan Md Said, and Wan Ainun M. Othman. "Password Authentication Based on Fractal Coding Scheme." Journal of Applied Mathematics 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/340861.

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Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.

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Hu, Hong Tao, and Qi Fei Liu. "Improvement of Fractal Image Compression Coding Based on Quadtree." Advanced Materials Research 532-533 (June 2012): 1157–61. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.1157.

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The goal of image compression is to represent an image with as few number of bits as possible while keeping the quality of the original image. With the characteristics of higher compression ratio, fractal image coding has received much attention recently. However, conventional fractal compression approach needs more time to code the original image. In order to overcome the time-consuming issue, a Quadtree-based partitioning and matching scheme is proposed. During the partitioning phase, an image frame is partitioned into tree-structural segments. And during a matching phase, a rang block only searches its corresponding domain block around previous matched domain block. Such local matching procedures will not stop until a predefined matching threshold is obtained. The preliminary experimental results show that such sub-matching rather than a global matching scheme dramatically decreases the matching complexity, while preserving the quality of an approximate image to the original after decoding process. In particular, the proposed scheme improves the coding process up to 2 times against the conventional fractal image coding approach.

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Li, Xiangjun, Shuili Zhang, and Haibo Zhao. "A Fast Image Compression Algorithm Based on Wavelet Transform." International Journal of Circuits, Systems and Signal Processing 15 (July 30, 2021): 809–19. http://dx.doi.org/10.46300/9106.2021.15.89.

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With multimedia becoming widely popular, the conflict between mass data and finite memory devices has been continuously intensified; so, it requires more convenient, efficient and high-quality transmission and storage technology and meanwhile, this is also the researchers’ pursuit for highly efficient compression technology and it is the fast image transmission that is what people really seek. This paper mainly further studies wavelet analysis and fractal compression coding, proposes a fast image compression coding method based on wavelet transform and fractal theory, and provides the theoretical basis and specific operational approaches for the algorithm. It makes use of the smoothness of wavelet, the high compression ratio of fractal compression coding and the high quality of reconstructed image. It firstly processes the image through wavelet transform. Then it introduces fractal features and classifies the image according to the features of image sub-blocks. Each class selects the proper features. In this way, for any sub-block, it only needs to search the best-matched block in a certain class according to the corresponding features. With this method, it can effectively narrow the search in order to speed up coding and build the relation of inequality between the sub-block and the matching mean square error. So, it can effectively combine wavelet transform with fractal theory and further improves the quality of reconstructed image. By comparing the simulation experiment, it objectively analyzes the performance of algorithm and proves that the proposed algorithm has higher efficiency.

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LIAN, SHIGUO. "IMAGE AUTHENTICATION BASED ON FRACTAL FEATURES." Fractals 16, no. 04 (December 2008): 287–97. http://dx.doi.org/10.1142/s0218348x08004034.

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In this paper, the fractal features of natural images are used to construct an image authentication scheme, which can detect whether an image is maliciously tampered (cutting, wiping, modification, etc.) or not and can even locate the tampered regions. For the original image, the fractal transformation is applied to each of the image blocks, and some of the transformation parameters are quantized and used as the authentication code. The authentication code can be stored or transmitted secretly. To authenticate an image, the new authentication code is computed from the image with the similar method, and then compared with the stored or received code. A metric is proposed to decide whether an image block is tampered or not. Comparative experiments show that the authentication scheme can detect malicious tampering, is robust against such common signal processing as JPEG compression, fractal coding, adding noise or filtering, and thus, obtains competent performances compared with existing image authentication schemes.

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La Torre, Davide, and Edward R. Vrscay. "GENERALIZED FRACTAL TRANSFORMS AND SELF-SIMILARITY: RECENT RESULTS AND APPLICATIONS." Image Analysis & Stereology 30, no. 2 (June 30, 2011): 63. http://dx.doi.org/10.5566/ias.v30.p63-76.

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Most practical as well as theoretical works in image processing and mathematical imaging consider images as real-valued functions, u : X → ℝg, where X denotes the base space or pixel space over which the images are defined and ℝg ⊂ ℝ is a suitable greyscale space. A variety of function spaces ℱ(X) may be considered depending on the application. Fractal image coding seeks to approximate an image function as a union of spatially-contracted and greyscale-modified copies of subsets of itself, i.e., u ≈ Tu, where T is the so-called Generalized Fractal Transform (GFT) operator. The aim of this paper is to show some recent developments of the theory of generalized fractal transforms and how they can be used for the purpose of image analysis (compression, denoising). This includes the formulation of fractal transforms over various spaces of multifunctions, i.e., set-valued and measure-valued functions. The latter may be useful in nonlocal image processing.

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