Results 171 to 180 of about 1,271 (204)

The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolated Surfaces

Fractals, 1997
In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed. The theorem of the uniqueness of an iterated function system of bivariate fractal interpolation functions is proved.
Xie, Heping, Sun, Hongquan
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Estimating fractal dimension with fractal interpolation function models

IEEE Transactions on Medical Imaging, 1997
Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS).
Alan I. Penn, Murray H. Loew
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Resampling and reconstruction with fractal interpolation functions

IEEE Signal Processing Letters, 1998
An alternative form of the fractal interpolation function (FIF)-previously unmentioned in the signal processing literature-is noted. This form highlights a simple relationship between fractal and linear interpolation. Using this relationship, many FIF problems can be reduced to a matrix/vector expression. This expression provides a more powerful way to
Jeffery R. Price, Monson H. Hayes III
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FOURIER SERIES REPRESENTATION OF FRACTAL INTERPOLATION FUNCTION

Fractals, 2020
The purpose of this research is to show how the complicated and irregular fractal interpolation function is represented by Fourier series. First, on the closed interval [0,1], even prolongation is operated to the fractal interpolation function generated by iterated function system constituted by affine transform and Fourier cosine series ...
XUEZAI PAN, MINGGANG WANG, XUDONG SHANG
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Fractal functions and interpolation

Constructive Approximation, 1986
Consider a set of data points \(\{x_ i,y_ i)\in I\times R:i=0,...,N\}\), where \(I=[x_ 0,x_ N]\subseteq R\). The author considers continuous functions f:I\(\to R\) which interpolate the given data, i.e. \(f(x_ i)=y_ i\), and such that there exist a compact subset \(K=I\times [a,b]\subseteq R^ 2\) and continuous functions \(w_ n:K\to K\) such that the ...
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Holder property of fractal interpolation function

Approximation Theory and its Applications, 1992
Summary: The purpose of this paper is to prove a Hölder property about the fractal interpolation function \(L(x)\), \(\omega(L,\delta)=O(\delta^ \alpha)\), and an approximate estimate \(| f-L|\leq 2\{\omega(h)+{{\| f\|} \over {1-h^{2-D}}}\cdot h^{2-D}\}\), where \(D\) is a fractal dimension of \(L(x)\).
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A NEW NONLINEAR FRACTAL INTERPOLATION FUNCTION

Fractals, 2017
In this paper, we propose a new nonlinear fractal interpolation function by using the Matkowski’s fixed point theorem and Rakotch contraction. The aim of this paper is to create a method that is accurate and suitable for practical applications such as shape representation.
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3D Fractal Interpolation Functions

Nanoscience and Nanotechnology Letters, 2020
For visualizing one, two- and/or three-dimensional data, reconstruction mechanism is generally considered. In the present study, I have examined the application of iterated function systems in interpolation. I have also presented new fractal interpolation derivations for three-dimensional scalar data. The interpolations can indicate uncertainty of the
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REVIEW ON FRACTAL INTERPOLATION FUNCTIONS

Fractals
The idea of fractal interpolation dates back to the 1980s, however several recent developments on its new types and generalization frameworks have made this domain ripe for extensions, further analyses, and reliable applications. Commencing from the background of Barnsley’s fundamental fractal interpolation function, this review paper summarizes the ...
T. M. C. PRIYANKA, A. GOWRISANKAR
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Zipper Rational Quadratic Fractal Interpolation Functions

2020
Inthis article, we propose an interpolation method using a binary parameter called signature such that the graph of the interpolant is an attractor of a suitable zipper rational iterated function system. The presence of scaling factors and signature in the proposed zipper rational quadratic fractal interpolation functions (ZRQFIFs) gives the ...
Sangita Jha, A. K. B. Chand
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