Image Interpolation Based on Weighted and Blended Rational Function

2015 ◽  
pp. 78-88
Author(s):  
Yifang Liu ◽  
Yunfeng Zhang ◽  
Qiang Guo ◽  
Caiming Zhang
Keyword(s):  
Rational Function ◽  
Image Interpolation

A Texture Preserving Image Interpolation Algorithm Based on Rational Function

2018 ◽  
Vol 9 (2) ◽  
pp. 36-56
Author(s):  
Hongwei Du ◽  
Yunfeng Zhang ◽  
Fangxun Bao ◽  
Ping Wang ◽  
Caiming Zhang
Keyword(s):  
Rational Function ◽  
State Of The Art ◽  
Image Interpolation ◽  
Rational Interpolation ◽  
Image Texture ◽  
Interpolation Algorithm ◽  
Edge Structure ◽  
Smooth Region ◽  
Pixel Value ◽  
Image Details

In this article, a type of bivariate rational interpolation function is constructed for preserving image texture structure, which integrates polynomial functions with a rational function. On the basis of this model, an image interpolation algorithm for texture preserving is proposed. First, an isoline method is employed to detect the image texture, and then the image can be divided into texture regions and smooth regions adaptively. Second, the smooth region and the textured region are interpolated by the polynomial model and the rational model, respectively. Finally, in order to preserve image texture direction, an objective function based on the gradient is constructed, and the weight of the correlation point is calculated, and the pixel value of the interpolation point is determined by convolution. Experimental results show that the proposed algorithm achieves good competitive performance compared with the state-of-the-art interpolation algorithms, especially in preserving image details and edge structure.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals The differential Galois group of the rational function field

2021 ◽  
Vol 381 ◽  
pp. 107605
Author(s):  
Annette Bachmayr ◽  
David Harbater ◽  
Julia Hartmann ◽  
Michael Wibmer
Keyword(s):  
Galois Group ◽  
Rational Function ◽  
Function Field ◽  
Differential Galois Group ◽  
Rational Function Field

scholarly journals The bifurcation set of a rational function via Newton polytopes

2021 ◽  
Author(s):  
Tat Thang Nguyen ◽  
Takahiro Saito ◽  
Kiyoshi Takeuchi
Keyword(s):  
Rational Function ◽  
Newton Polytopes ◽  
Bifurcation Set

scholarly journals Low-Cost Implementation of Bilinear and Bicubic Image Interpolation for Real-Time Image Super-Resolution

2020 ◽  
Author(s):  
Donya Khaledyan ◽  
Abdolah Amirany ◽  
Kian Jafari ◽  
Mohammad Hossein Moaiyeri ◽  
Abolfazl Zargari Khuzani ◽  
...  
Keyword(s):  
Real Time ◽  
Low Cost ◽  
Super Resolution ◽  
Image Interpolation ◽  
Real Time Image ◽  
Image Super Resolution ◽  
Time Image

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

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