SECURE FRACTAL IMAGE CODING BASED ON FRACTAL PARAMETER ENCRYPTION

Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 149-160 ◽  
Author(s):  
SHIGUO LIAN ◽  
XI CHEN ◽  
DENGPAN YE
Keyword(s):  
Image Coding ◽  
Parameter Distribution ◽  
Self Similarity ◽  
Image Encoding ◽  
Coding Scheme ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Fractal Parameters ◽  
Fractal Encoding ◽  
Computational Resources

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.

Fractal Image Coding Based on Wavelet Transformation

2014 ◽  
Vol 1030-1032 ◽  
pp. 1713-1716
Author(s):  
Xin Wang ◽  
He Pan
Keyword(s):  
Image Coding ◽  
Wavelet Decomposition ◽  
Wavelet Transformation ◽  
Image Data ◽  
Image Encoding ◽  
Fast Encoding ◽  
Classic Problem ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Image Data Compression

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.

scholarly journals GENERALIZED FRACTAL TRANSFORMS AND SELF-SIMILARITY: RECENT RESULTS AND APPLICATIONS

2011 ◽  
Vol 30 (2) ◽  
pp. 63 ◽  
Author(s):  
Davide La Torre ◽  
Edward R. Vrscay
Keyword(s):  
Image Processing ◽  
Image Analysis ◽  
Image Coding ◽  
Function Spaces ◽  
Base Space ◽  
Self Similarity ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Recent Developments ◽  
Image Function

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.

A PRIMAL-DUAL ALGORITHM FOR ROBUST FRACTAL IMAGE CODING

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950119
Author(s):  
CHEN XU ◽  
YUTING YE ◽  
ZHENWEI HU ◽  
YURU ZOU ◽  
LIXIN SHEN ◽  
...  
Keyword(s):  
Image Coding ◽  
Dual Algorithm ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Fractal Parameters ◽  
Primal Dual ◽  
Independent Variable ◽  
M Estimation ◽  
Domain Block ◽  
Robust Prediction

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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