Fractal Modelling and Analysis of Flow-Field Images

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the availability of imaging modalities that measure flow vector fields (flow-sensitive MRI and Doppler ultrasound). To study such data, we formulate estimators of the model parameters, and use them to quantify the Hurst exponent and directional properties of synthetic and real-world flow fields (measured by means of phase-contrast MRI) in 3D.

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Pouya Dehghani Tafti, Ricard Delgado Gonzalo, Michaël Unser
IEEE, 2010
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https://infoscience.epfl.ch/record/211447?ln=en

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Stochastic process

In probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has

Hurst exponent

The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of val

Parameter

A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element

Fractal Modelling And Analysis Of Flow-Field Images

Pouya Dehghani Tafti, Ricard Delgado Gonzalo, Michaël Unser

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Fractional Brownian Models For Vector Field Data

Pouya Dehghani Tafti, Michaël Unser

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have no counterpart in the scalar setting. Apart from the Hurst exponent which dictates the scale-dependent structure of the field, additional parameters of the new model control the balance between solenoidal and irrotational behaviour. This level of versatility makes these random fields potentially interesting candidates for the stochastic modelling of physical phenomena in various fields of application such as fluid dynamics, field theory, and medical image processing.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Fractional Brownian Models for Vector Field Data

Pouya Dehghani Tafti, Michaël Unser

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields—such as divergence, rotational behaviour, and interactions with coordinate transformations—that have no counterpart in the scalar setting. Apart from the Hurst exponent which dictates the scale-dependent structure of the field, additional parameters of the new model control the balance between solenoidal and irrotational behaviour. This level of versatility makes these random fields potentially interesting candidates for the stochastic modelling of physical phenomena in various fields of application such as fluid dynamics, field theory, and medical image processing.

IEEE2010