Associated Continued Fractions-Barycentric Blending Rational Interpolation and Its Application in Image Processing

2012 ◽  
Author(s):  
Yigang Zhang ◽  
Le Zou
Keyword(s):  
Image Processing ◽  
Continued Fractions ◽  
Rational Interpolation ◽  
Associated Continued Fractions

Researches on Image Processing Technology Used in Bamboo Weaving Machine

2011 ◽  
Vol 204-210 ◽  
pp. 1070-1073
Author(s):  
Lei Zhang ◽  
Hong Li Gao ◽  
Ming Heng Xu ◽  
Shi De Xiao ◽  
Peng Du
Keyword(s):  
Image Processing ◽  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Rational Interpolation ◽  
Processing Technology ◽  
Minimum Width ◽  
Weft Direction ◽  
Image Processing Technology ◽  
Short Time

A new bamboo weaving machine, in which automatic control system is employed, is introduced in this paper. The system deals with the images firstly, and then controls bamboo weaving by means of electromotor and transmission devices. Different algorithms, such as lift wavelet, bivariate rational interpolation and Ostu are used in image processing. The minimum width of the bamboo filament is 0.7mm. The maximum number of the bamboo filament in the warp and weft direction is 360 and 430 respectively. Various beautiful bamboo artware can be weaved automatically by this machine in a short time.

scholarly journals An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Lei He ◽  
Yan Xing ◽  
Kangxiong Xia ◽  
Jieqing Tan
Keyword(s):  
Continued Fractions ◽  
State Of The Art ◽  
Signal To Noise Ratio ◽  
Subjective Evaluation ◽  
Image Inpainting ◽  
Rational Interpolation ◽  
Objective Evaluation ◽  
Experimental Results ◽  
Signal To Noise

In view of the drawback of most image inpainting algorithms by which texture was not prominent, an adaptive inpainting algorithm based on continued fractions was proposed in this paper. In order to restore every damaged point, the information of known pixel points around the damaged point was used to interpolate the intensity of the damaged point. The proposed method included two steps; firstly, Thiele’s rational interpolation combined with the mask image was used to interpolate adaptively the intensities of damaged points to get an initial repaired image, and then Newton-Thiele’s rational interpolation was used to refine the initial repaired image to get a final result. In order to show the superiority of the proposed algorithm, plenty of experiments were tested on damaged images. Subjective evaluation and objective evaluation were used to evaluate the quality of repaired images, and the objective evaluation was comparison of Peak Signal to Noise Ratios (PSNRs). The experimental results showed that the proposed algorithm had better visual effect and higher Peak Signal to Noise Ratio compared with the state-of-the-art methods.

scholarly journals ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

2017 ◽  
Vol 13 (2) ◽  
pp. 7147-7154
Author(s):  
Anthony G Shannon ◽  
Charles K Cook b ◽  
Rebecca A. Hillman c
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Fibonacci Numbers ◽  
Recursive Sequences ◽  
Essential Idea ◽  
Associated Continued Fractions ◽  
Generalized Continued Fractions

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements.

Continued Logarithms and Associated Continued Fractions

2016 ◽  
Vol 26 (4) ◽  
pp. 412-429
Author(s):  
Jonathan M. Borwein ◽  
Neil J. Calkin ◽  
Scott B. Lindstrom ◽  
Andrew Mattingly
Keyword(s):  
Continued Fractions ◽  
Associated Continued Fractions
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