A maximum likelihood estimate for two-variable fractal surface

Adil S. Balghonaim; James M. Keller

doi:10.1109/83.730389

A maximum likelihood estimate for two-variable fractal surface

Adil S. Balghonaim^*, James M. Keller

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.

Original language	English
Pages (from-to)	1746-1753
Number of pages	8
Journal	IEEE Transactions on Image Processing
Volume	7
Issue number	12
DOIs	https://doi.org/10.1109/83.730389
State	Published - 1998

Keywords

Fractal dimension
Fractional Brownian motion
Maximum likelihood
Parameter estimation

ASJC Scopus subject areas

Software
Computer Graphics and Computer-Aided Design

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10.1109/83.730389

Cite this

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title = "A maximum likelihood estimate for two-variable fractal surface",

abstract = "The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.",

keywords = "Fractal dimension, Fractional Brownian motion, Maximum likelihood, Parameter estimation",

author = "Balghonaim, \{Adil S.\} and Keller, \{James M.\}",

year = "1998",

doi = "10.1109/83.730389",

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volume = "7",

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T1 - A maximum likelihood estimate for two-variable fractal surface

AU - Balghonaim, Adil S.

AU - Keller, James M.

PY - 1998

Y1 - 1998

N2 - The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.

AB - The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.

KW - Fractal dimension

KW - Fractional Brownian motion

KW - Maximum likelihood

KW - Parameter estimation

UR - https://www.scopus.com/pages/publications/0032296812

U2 - 10.1109/83.730389

DO - 10.1109/83.730389

M3 - Article

AN - SCOPUS:0032296812

SN - 1057-7149

VL - 7

SP - 1746

EP - 1753

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

IS - 12

ER -

A maximum likelihood estimate for two-variable fractal surface

Abstract

Keywords

ASJC Scopus subject areas

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