scholarly journals The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2250
Author(s):  
Danilo Costarelli ◽  
Anca Croitoru ◽  
Alina Gavriluţ ◽  
Alina Iosif ◽  
Anna Rita Sambucini
Keyword(s):  
Image Coding ◽  
Detection Algorithm ◽  
Visual Signal ◽  
Lebesgue Integral ◽  
Order Continuity ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Interval Valued ◽  
Discretization Process ◽  
Lebesgue Integrability

We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the RL integral, such as monotonicity, order continuity, bounded variation, convergence are obtained. An application of interval-valued multifunctions to image processing is given for the purpose of illustration; an example is given in case of fractal image coding for image compression, and for edge detection algorithm. In these contexts, the image modelization as an interval valued multifunction is crucial since allows to take into account the presence of quantization errors (such as the so-called round-off error) in the discretization process of a real world analogue visual signal into a digital discrete one.

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.

Chaos-based encryption for fractal image coding

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

An inequality for pairs of martingales and its application to fractal image coding

1996 ◽  
Vol 33 (04) ◽  
pp. 968-973
Author(s):  
F. M. Dekking
Keyword(s):  
Image Coding ◽  
Image Data ◽  
Monotonicity Property ◽  
Fractal Image ◽  
Fractal Image Coding

We prove a monotonicity property for a function of general square integrable pairs of martingales which is useful in fractal-based algorithms for compression of image data.

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