A New Approach for Fractal Image Coding: Self-similarity at Smallest Scale

Author(s):  
Ashish Awasthi ◽  
Manish Kumar
Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 149-160 ◽  
Author(s):  
SHIGUO LIAN ◽  
XI CHEN ◽  
DENGPAN YE

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.


2009 ◽  
Vol 5 (3) ◽  
pp. 183-189 ◽  
Author(s):  
Nadia M.G. Al-Saidi ◽  
Muhammad Rushdan Md. Said

2011 ◽  
Vol 30 (2) ◽  
pp. 63 ◽  
Author(s):  
Davide La Torre ◽  
Edward R. Vrscay

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.


2012 ◽  
Vol 21 (1) ◽  
pp. 010502 ◽  
Author(s):  
Ching-Hung Yuen ◽  
Kwok-Wo Wong

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