On the Imaging of Fractal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Texture Roughness Analysis and Synthesis via Extended Self-Similar (ESS) Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
nth-order fractional Brownian motion and fractional Gaussian noises
IEEE Transactions on Signal Processing
Signal detection in fractional Gaussian noise
IEEE Transactions on Information Theory - Part 1
Spectral representation of fractional Brownian motion in n dimensions and its properties
IEEE Transactions on Information Theory
Two-channel nonseparable wavelets statistically matched to 2-D images
Signal Processing
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A first-order isotropic fractional Brownian field (IFBF) is generated by integrating a 2-dimensional (2-D) Gaussian field that has been obtained by passing a 2-D white Gaussian noise through a 2-D isotropic fractal filter. This first-order IFBF is characterized by a single parameter, the Hurst exponent H ∈[0, 1], similar to their 1-dimensional (1-D) counterpart. This paper presents a theoretical framework for the extension of a first-order IFBF to a second-order IFBF with H ∈[1, 2]. Statistical properties such as covariance functions of these fields are investigated. We observe that the Hurst exponent of a number of real life images belongs to the range [1, 2] suggesting that these images can be approximated as members of this class.