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fractal image coding with a multiscaling-domain

ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2004年第2期87卷 79-87页

作者： Furusawa, R Nakagawa, M Nagaoka Univ Technol Fac Engn Nagaoka Niigata 9402188 Japan

In order to improve the approximation capability of fractal coding, a fractal coding method using multiple domains is proposed in which an approximation is carried out by superposition of contracted images from multiple domain blocks. By combining the multidomain method with the multiscaling procedure of dividing blocks into regions and individually providing the scaling coefficients of brightness, a contraction transform with even better degrees of approximation is obtained and edge reconstruction is improved. As a result, excellent reconstructed images are obtained even for complicated images for which high reproducibility cannot be realized with the conventional fractal coding. Also, it is possible to reproduce contour regions containing edges. (C) 2003 Wiley Periodicals, Inc.

关键词： fractal coding image compression self-similarity multidomain multiscaling

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fractal image coding with regional division of a block

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2005年第8期88卷 1-8页

作者： Otsuki, S Nakagawa, M Nagaoka Univ Technol Nagaoka Niigata 9402188 Japan

fractal image coding is an image compression method that utilizes the self-similarity which is inherent in a natural image. The picture quality of the restored image depends on the detection of adequate self-similarity in the original image. However, for the conventional technique that uses square blocks, it is troublesome to detect good self-similarity in edge parts that have steep changes in gradation values. Therefore, in this paper, the authors perform regional division for each block and use separate contractive transformations in each divided region to implement superior self-similarity detection. This technique can reproduce more apparent edges than the conventional technique that uses square blocks and the SN ratio is improved by I to 2 dB at the same bit rate. Also, although the coding performance of the conventional fractal image coding technique is worse than that of JPEG, the proposed technique shows nearly equivalent PSNR to JPEG in the vicinity of 2 to 3 bpp. (c) 2005 Wiley Periodicals, Inc.

关键词： fractal coding image compression self-similarity regional division of a block

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NONLOCAL LOW RANK REGULARIZATION METHOD FOR fractal IMAGE coding UNDER SALT-AND-PEPPER NOISE

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fractalS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2023年第7期31卷 2350076-2350076页

作者： Pan, Huan Liang, Zhengyu Lu, Jian Tu, Kai Xie, Ning Shenzhen Univ Coll Math & Stat Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Peoples R China Natl Ctr Appl Math Shenzhen NCAMS Shenzhen 518055 Peoples R China Pazhou Lab Guangzhou 510335 Peoples R China Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China Shenzhen Univ Coll Elect & Informat Engn Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China

Image denoising has been a fundamental problem in the field of image processing. In this paper, we tackle removing impulse noise by combining the fractal image coding and the nonlocal self-similarity priors to recover image. The model undergoes a two-stage process. In the first phase, the identification and labeling of pixels likely to be corrupted by salt-and-pepper noise are carried out. In the second phase, image denoising is performed by solving a constrained convex optimization problem that involves an objective functional composed of three terms: a data fidelity term to measure the similarity between the underlying and observed images, a regularization term to represent the low-rank property of a matrix formed by nonlocal patches of the underlying image, and a quadratic term to measure the closeness of the underlying image to a fractal image. To solve the resulting problem, a combination of proximity algorithms and the weighted singular value thresholding operator is utilized. The numerical results demonstrate an improvement in the structural similarity (SSIM) index and peak signal-to-noise ratio.

关键词： Image Denoising fractal coding Low-Rank Regularization Salt-and-Pepper Noise

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A NONLOCAL LOW-RANK REGULARIZATION METHOD FOR fractal IMAGE coding

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fractalS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2021年第5期29卷 2150125-2150125页

作者： Zou, Yuru Hu, Huaxuan Lu, Jian Liu, Xiaoxia Jiang, Qingtang Song, Guohui Shenzhen Univ Coll Math & Stat Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Peoples R China Univ Missouri St Louis Dept Math & Stat St Louis MO 63121 USA Old Dominion Univ Dept Math & Stat Norfolk VA 23529 USA

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.

关键词： fractal coding Image Denoising Low-Rank Regularization

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A DICTIONARY LEARNING APPROACH FOR fractal IMAGE coding

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fractalS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2019年第2期27卷

作者： Lu, Jian Tian, Jiapeng Xu, Chen Zou, Yuru Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Peoples R China

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.

关键词： fractal coding Image Denoising Learned Dictionary

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A Fast fractal Image coding Technique

A Fast Fractal Image Coding Technique

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1998 Fourth International Conference Signal Processing

作者： Li Wenjing Li Wangchao Department of Computer Science & Engineering Hebei University of Technology Senior Member IEEEDepartment of Computer Science & EngineeringHebei University of Technology

fractal coding is a very promising technique for image ***,it has not been widely used because of its long encoding time and high computational *** paper presents a fast fractal image coding technique and its algorith... 详细信息

关键词： fractal coding image compression quadtree partition block classification

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Split decision functions in fractal image coding based on 1uadtree

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Jisuanji Gongcheng/Computer Engineering 2005年第3期31卷 54-56页

作者： Li, Junli Chen, Gang Chi, Zheru Sch. of Info. Sci. and Eng. Ningbo Univ. Ningbo 315211 China Ctr. for Multimedia Signal Proc. Dept. of Electron. and Info. Eng Hongkong Polytech. Univ. Hongkong Hong Kong

Quadtree partitions are often used in fractal image compression to achieve variable bit rates. This paper proposes a fuzzy integral based split decision function-fuzzy mean error that can improve image coding quality ... 详细信息

关键词： fractal coding Fuzzy integral Quadtree Split decision function

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Research of Neighborhood Searching fractal Image coding Algorithm based on Ant Colony Optimization

Research of Neighborhood Searching Fractal Image Coding Algo...

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SAI Intelligent Systems Conference

作者： Li Lou Yong Li School of electronics and information Northwest Polytechnical University

ISBN: (纸本)9781467376075

A kind of fractal improved coding algorithms based on Ant Colony Optimization and neighborhood search matching way is presented in this paper. The compression ratio of this algorithm is higher than that of Jacquin's as well as the coding speed is faster than that of Jacquin's on the premise of similar signal-to-noise ratio. Experimental results show that the compression ratio of this neighborhood searching fractal image coding algorithm based on ant colony optimization can reach to 14.33, the PSNR can reach to 29.7dB, encoding time decreases to 120s and decoding time is 28s.

关键词： Ant Colony Optimization fractal coding Neighborhood Range Block

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Still image coding based on vector quantization and fractal approximation

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1996年第4期5卷 587-597页

作者： Kim, IK Park, RH Department of Electronic Engineering Sogang University Seoul South Korea

In this paper, we propose a coding algorithm for still images using vector quantization (VQ) and fractal approximation, in which low-frequency components of an input image are approximated by VQ, and its residual is coded by fractal mapping, The conventional fractal coding algorithms indirectly used the gray patterns of an original image with contraction mapping, whereas the proposed fractal coding method employs an approximated and then decimated image as a domain pool and uses its gray patterns, Thus, the proposed algorithm utilizes fractal approximation without the constraint of contraction mapping, For approximation of an original image, we employ the discrete cosine transform (DCT) rather than conventional polynomial-based transforms. In addition, for variable block-size segmentation, we use the fractal dimension of a block that represents the roughness of the gray surface of a region, Computer simulations with several test images show that the proposed method shows better performance than the conventional fractal coding methods for encoding still pictures.

关键词： fractals approximation image coding discrete cosine transforms original image Vector quantization Still images contraction mapping still image coding fractal coding

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Variable tree size fractal compression for wavelet pyramid image coding

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SIGNAL PROCESSING-IMAGE COMMUNICATION 1999年第3期14卷 195-208页

作者： Zhang, Y Po, LM City Univ Hong Kong Dept Elect Engn CityU Image Proc Lab Tat Chee Ave Kowloon Peoples R China

Pyramidal wavelet decomposition provides a hierarchical data structure for image representation which is suitable for further quantization and compression. Through discrete wavelet transform, image signals are decomposed into multiresolution and multi-frequency subbands with a set of tree-structured coefficients. The coefficients which have the same spatial location but with different resolution and different orientation can be organized into wavelet subtree. This efficient representation of image signals has achieved superior coding performance in wavelet-based image compression. In this paper, a novel variable tree partition algorithm is introduced which can efficiently split the wavelet subtrees according to the local details. Then a new variable size wavelet-subtree-based fractal coding algorithm is proposed to obtain a good trade-off between image quality and compression ratio. The self-similarities among wavelet subtrees are successfully exploited in the fractal coding method by predicting the coefficients at finer scales from those at coarser scales through proper affine transformation. Experimental results show a gain over JPEG of 5-6 dB in PSNR with even a slightly higher compression ratio (around 60 : 1 to 70 : 1). A slight gain in terms of coding efficiency is also achieved when compared to a method proposed by Davis, which also applies variable tree size wavelet fractal coding, but the complexity has been significantly reduced by avoiding iterative optimization procedures. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： wavelet transform fractal coding hybrid coding

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