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A PRIMAL-DUAL ALGORITHM FOR ROBUST fractal image coding

fractalS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2019年第7期27卷

作者： Xu, Chen Ye, Yuting Hu, Zhenwei Zou, Yuru Shen, Lixin Liu, Xiaoxia Liu, Jian Shenzhen Univ Coll Math & Stat Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Guangdong Peoples R China Syracuse Univ Dept Math Syracuse NY 13244 USA Shenzhen Univ Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Guangdong Peoples R China

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 2 x 2 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.

关键词： fractal image coding Primal-Dual Algorithm Median-Based Fisher's Classification Impulse Noise

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A fast no search fractal image coding method

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SIGNAL PROCESSING-image COMMUNICATION 2004年第5期19卷 393-404页

作者： Shen, FR Hasegawa, O Tokyo Inst Technol Dept Computat Intelligence & Syst Sci Tokyo 152 Japan Tokyo Inst Technol Imaging Sci & Engn Lab Midori Ku Tokyo 2268503 Japan

A new no search fractal image coding scheme is introduced which is able to improve the speed of fractal image compression greatly. Every time-consuming part of fractal coding is redesigned and accelerated with new techniques. Compared with the most recent scheme of Tong and Wong, this method speeds up the encoding process by 22 times and maintain the compression quality. Experiments on standard images show that the proposed scheme gets the fastest speed of fractal image coding up to the present and holds high reconstruction fidelity. For example, using PII 450 MHz PC, the proposed scheme spends 0.515 s to compress the Lena (512 x 512 x 8) with 36.04 dB PSNR decoding quality. Using Dell PIV 2.8 GHz PC, it spends only 0.078 s to finish the encoding process and gets 36.04 dB PSNR. (C) 2004 Elsevier B.V. All rights reserved.

关键词： fractal image coding no search similar degree quadtree

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Multiple same-sized block mapping for recursive fractal image coding

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OPTICAL ENGINEERING 2002年第2期41卷 328-334页

作者： Zhao, Y Wang, HX Yuan, BZ No Jiaotong Univ Inst Sci Informat Beijing 100044 Peoples R China Beijing Univ Aeronaut & Astronaut Beijing 100083 Peoples R China

In conventional fractal image coding (FIC) schemes, domain blocks are constrained to be twice as large as range blocks to ensure the convergence of their iterative decoding stage. However, this constraint has limited the fractal encoder to exploit the self-similarity at the same resolution scale of natural images. To overcome the shortcoming, a novel scheme using same-sized range and domain blocks is proposed. Further, a recursive scheme feeding the coding results back to the input during the encoding procedure is used to improve the decoded image quality. Experimental results show our method gives significant improvement over Fisher's FIC. (C) 2002 Society of Photo-Optical Instrumentation Engineers.

关键词： fractal image coding image compression

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Digital watermarking based on fractal image coding

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2000年第6期23卷 759-766页

作者： Li, CH Wang, SS Tatung Univ Dept Elect DSA Lab Taipei 104 Taiwan

With advances in computer network and multimedia technology, digital media are rapidly proliferating, and thus the issue of copyright protection for electronic publishing is receiving great attention. To achieve the goal of copyright protection, the digital watermarks are used to identify the owner of a certain image, so as to prevent illegal copying. Digital watermarking is the technique that embeds an invisible signal including owner identification and copy control information into multimedia data such as audio, video, and images. A new digital watermark approach based on fractal image coding is proposed in this paper. We present a way to use the fractal code as a means of embedding a watermark into image. The proposed approach has been shown to be resistant to general attacks, like StirMark. Moreover, someone who owns the decryption key can simply extract the digital watermark from the watermarked image without resorting to the original image.

关键词： digital watermarking invisible fractal image coding isometric transform

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Analysis of scaling-factor-quantization error in fractal image coding

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1997年第12期E80A卷 2572-2580页

作者： Lee, CH Kawamata, M Higuchi, T Tohoku Univ Grad Sch Informat Sci Sendai Miyagi 98077 Japan Tohoku Univ Grad Sch Engn Sendai Miyagi 98077 Japan

This paper proposes an analysis method of scaling-factor-quantization error in fractal image coding using a state-space approach with the statistical analysis method. It is shown that the statistical analysis method is appropriate and leads to a simple result, whereas the deterministic analysis method is not appropriate and leads to a complex result for the analysis of fractal image coding. We derive the output error variance matrix for the measure of error and define the output error variance by scalar quantity as the mean of diagonal elements of the output error variance matrix. Examples are given to show that the scaling-factor-quantization error due to iterative computation with finite-wordlength scaling factors degrades the quality of decoded images. A quantitative comparison uf experimental scaling-factor-quantization error with analytical result is made for the output error variance. The result shows that our analysis method is valid for the fractal image coding.

关键词： fractal image coding iterated function systems scaling-factor-quantization error state-space approach

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An improved no-search fractal image coding method based on a modified gray-level transform

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COMPUTERS & GRAPHICS-UK 2008年第4期32卷 445-450页

作者： Wang, Xing-Yuan Wang, Shu-Guo Dalian Univ Technol Sch Elect & Informat Engn Dalian 116024 Peoples R China

In this paper, we propose a fast no-search fractal image coding algorithm based on a modified gray-level transform. To improve the possibility of successful matching for a range block and a domain block, we introduce a modified gray-level transform with more transform parameters than proposed by Tong and Pi to encode the blocks. Then, we suggest a no-search fractal image coding method using two gray-level transforms, one for the large blocks and the other for the small blocks based on the quadtree partition scheme, to speed up the encoding time and improve the quality of the reconstructed images. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： fractal image coding no search quadtree gray-level transform

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Hybrid fractal image coding with quadtree-based progressive structure

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JOURNAL OF VISUAL COMMUNICATION AND image REPRESENTATION 2013年第8期24卷 1328-1341页

作者： Yuen, Ching Hung Lui, Oi Yan Wong, Kwok Wo City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

A progressive structure which takes the quadtree depth into consideration is proposed for fractal image coding. Simulation results show that its image quality at different received data rates is better than that without considering the quadtree level. Then, a hybrid fractal image coding scheme based on traditional and no-search fractal image coding with the proposed progressive structure is suggested. The image quality and compression ratio can be controlled by a threshold, which makes it downward compatible to the no-search fractal image coding. Experimental results justify that the progressive performance of the proposed scheme is better than that of traditional fractal image coding. (C) 2013 Elsevier Inc. All rights reserved.

关键词： fractal image coding Progressive image transmission image compression Quadtree partitioning Iterated function system No-search encoding Domain block and range block SSIM measure

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fractal image coding with high error tolerance

Fractal image coding with high error tolerance

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Conference on Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications

作者： Ito, Y Kimoto, T Fujii, T Tanimoto, M Nagoya Univ Grad Sch Engn Dept Informat Elect Chikusa Ku Nagoya Aichi 4648603 Japan

ISBN: (纸本)0819439843

image compression is needed to communicate image effectively. Especially, mobile communication needs high compression. It also needs high error tolerance because highly compressed data are strongly influenced by transmission errors. We found that the relation between the range block and domain block can also be applied well to the extended range blocks and domain blocks in most cases in fractal coding based on Iterated Function System. We use this feature of fractal coding and propose a new robust coding scheme, which has good error tolerance. We perform the fractal compression experiments based on the proposed scheme to verify the effectiveness of this scheme. Computational experiments show that it has nearly the same performance as conventional scheme when errors don't occur and achieve large improvement of image quality without increasing the amount of the data when errors occur.

关键词： image compression fractal image coding iterated function system error tolerance

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Recursive fractal image coding scheme with feedback structure

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CHINESE JOURNAL OF ELECTRONICS 2002年第1期11卷 16-18页

作者： Zhao, Y Yuan, BZ No Jiaotong Univ Inst Sci Informat Beijing 100044 Peoples R China

fractal image coding (FIC) has been studied for more than ten years and a lot of improvements on its fidelity performance have been proposed. In the paper, another improving scheme called recursive scheme is proposed. In the scheme, the coding results of previous range blocks are fed back to adjust the encoder parameters for the next range block. So the method can gradually reach the global optimization. Experimental results show that the method can improve the image quality about 0.5 dB higher than Fisher's quadtree scheme.

关键词： fractal image coding image compression

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Improved searching scheme for fractal image coding

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ELECTRONICS LETTERS 2002年第25期38卷 1653-1654页

作者： Lai, CM Lam, KM Siu, WC Hong Kong Polytech Univ Dept Elect & Informat Engn Ctr Multimedia Signal Proc Hong Kong Hong Kong Peoples R China

The authors propose using a non-symmetric window to search for the best matched domain block based on the local variances method. Experimental results show that the proposed scheme can achieve a speedup of 50% with on... 详细信息

关键词： image and video coding data compression nonsymmetric window fractals image coding matched domain block search problems fractal image coding speedup compression ratio improved searching PSNR image representation reconstructed image Computer vision and image processing techniques local variances method

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