Greens Theorem

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Esmaile, Maher Faik - One of the best experts on this subject based on the ideXlab platform.

  • Thyroid volume estimation from ultrasound extend field of view images using star algorithm with green's Theorem
    2013
    Co-Authors: Esmaile, Maher Faik
    Abstract:

    Area calculation is regarded as an important step in many applications (e.g. industry, medicine, biology). GreensTheorem is one of the methods that can be applied to calculate the area with the advantages: it evaluates a double integral over the region of an object by a simple integration along the boundary of the object, and it can result in high accuracy for the area calculations by increasing the edge’s point of the object. In this work a modified Star algorithm is incorporated with GreensTheorem (SAGT) to calculate the area of an arbitrary shape. As an application to this modification, it has been applied in medical field to calculate the actual area of thyroid gland from ultrasound extend field of view (EFOV) images and for several slices along the neck. Then area summation technique will be used to estimate the volume of thyroid gland. Diagnosis of thyroid gland diseases and correct radioiodine dosage depend on the correct thyroid gland volume estimation. Different approaches used to determine thyroid size including ultrasound, scintigraphy, SPECT, CT scan, and MRI. Recently, ultrasonography is the preferred aid in clinical diagnosis. The use of ultrasound to estimate thyroid volume involves several disadvantages. First; the application of ellipsoid formula with thyroid gland ultrasound images to evaluate thyroid volume which is applied to irregular shape is reported to be inaccurate and may result in underestimation or overestimation. Second; the thyroid lobe length is sometimes difficult to be measured, because most modern transducers are available with a footpad of 4 cm or less which is less than the adult’s thyroid lobe length. Third; the accuracy of ultrasound thyroid gland volume estimation depends on operator skill. A new methodology is proposed to estimate the volume of thyroid gland using SAGT and ultrasound (EFOV) images through four steps: first; modifying Star algorithm with Green’s Theorem (SAGT) to calculate the actual thyroid area instead of measuring the thyroid dimensions manually that avoids using the ellipsoid formula. Second; the neck scanning is systemised in order to minimize the operator experience effect and to create the EFOV image during the registration process. Third; a new edge detection filter suitable to this application is designed that’s based on the extraction and registration of the ultrasound image features to be used with SAGT to calculate the thyroid actual area from US EFOV images. Fourth: applying the summation of area technique to calculate the volume of thyroid gland. The experimental results conducted for the phantom neck showed that the proposed method could perform the volume estimation with accuracy between (96-98) % as compared to the ellipsoid formula that has accuracy between (83-92) %. It’s concluded that, the area calculation of thyroid gland using SAGT, with systemising the neck scanning has shown an improving accuracy for the thyroid gland volume estimation

Nicholas C. Makris - One of the best experts on this subject based on the ideXlab platform.

  • LONG-TERM GOALS 1. Dynamics of clutter
    2016
    Co-Authors: Pi Prof, Nicholas C. Makris
    Abstract:

    The long term goal of this research is to develop a general method to determine the dynamics of clutter observed in sonar imagery such as Ocean Acoustic Waveguide Remote Sensing1 (OAWRS). We aim to use waveguide remote sensing techniques to obtain time varying density images of clutter in a shallow water environment, and use these images to develop a robust technique to invert for clutter dynamics. Currently there is no robust method to determine the dynamics of clutter from density images. Our research aims to ultimately distinguish clutter from intended targets by exploiting the differences in their dynamics. 2. Clutter characterization The long term goal of this research is to develop a GreensTheorem-based full-field model to quantify scattering from man-made cylindrical targets in an ocean waveguide, and use the model to characterize and distinguish returns from such man-made targets from clutter such as fish schools. 3. Hurricane classification The long term goal of this research is to analyze underwater noise measurements in the vicinity of a hurricane to help in surface wind speed estimation.

Edalat A - One of the best experts on this subject based on the ideXlab platform.

  • Extensions of domain maps in differential and integral calculus
    'Institute of Electrical and Electronics Engineers (IEEE)', 2015
    Co-Authors: Edalat A
    Abstract:

    © 2015 IEEE.We introduce in the context of differential and integral calculus several key extensions of higher order maps from a dense subset of a topological space into a continuous Scott domain. These higher order maps include the classical derivative operator and the Riemann integration operator. Using a sequence of test functions, we prove that the subspace of real-valued continuously differentiable functions on a finite dimensional Euclidean space is dense in the space of Lipschitz maps equipped with the L-topology. This provides a new result in basic mathematical analysis, which characterises the L-topology in terms of the limsup of the sequence of derivatives of a sequence of C1 maps that converges to a Lipschitz map. Using this result, it is also shown that the generalised (Clarke) gradient on Lipschitz maps is the extension of the derivative operator on C1 maps. We show that the generalised Riemann integral (R-integral) of a real-valued continuous function on a compact metric space with respect to a Borel measure can be extended to the integral of interval-valued functions on the metric space with respect to valuations on the probabilistic power domain of the space of non-empty and compact sets of the metric space. We also prove that the Lebesgue integral operator on integrable functions is the extension of the R-integral operator on continuous functions. We finally illustrate an application of these results by deriving a simple proof of Greens Theorem for interval-valued vector fields

Massimiliano Giona - One of the best experts on this subject based on the ideXlab platform.

  • Contour Integrals and Vector Calculus on Fractal Curves and Interfaces
    Chaos Solitons & Fractals, 1999
    Co-Authors: Massimiliano Giona
    Abstract:

    Abstract This article develops the definition of contour integrals over fractal curves in the plane by introducing the notion of oriented Iterated Function Systems and directional pseudo-measures. An expression for the contour integral of continuous functions over fractal interfaces is obtained through renormalization. As a result, a vector calculus on fractal interfaces which are boundaries of regular two-dimensional domains is developed by extending Greens Theorem in the plane, also to fractal curves. The use of moment analysis makes it possible to obtain recursive relations and closed-form expressions for contour integrals of algebraic functions. Several physical applications are analyzed, including the properties of double-layer potentials and connections with the solution of the Dirichlet problem on bounded two-dimensional domains possessing fractal boundaries.

Pi Prof - One of the best experts on this subject based on the ideXlab platform.

  • LONG-TERM GOALS 1. Dynamics of clutter
    2016
    Co-Authors: Pi Prof, Nicholas C. Makris
    Abstract:

    The long term goal of this research is to develop a general method to determine the dynamics of clutter observed in sonar imagery such as Ocean Acoustic Waveguide Remote Sensing1 (OAWRS). We aim to use waveguide remote sensing techniques to obtain time varying density images of clutter in a shallow water environment, and use these images to develop a robust technique to invert for clutter dynamics. Currently there is no robust method to determine the dynamics of clutter from density images. Our research aims to ultimately distinguish clutter from intended targets by exploiting the differences in their dynamics. 2. Clutter characterization The long term goal of this research is to develop a GreensTheorem-based full-field model to quantify scattering from man-made cylindrical targets in an ocean waveguide, and use the model to characterize and distinguish returns from such man-made targets from clutter such as fish schools. 3. Hurricane classification The long term goal of this research is to analyze underwater noise measurements in the vicinity of a hurricane to help in surface wind speed estimation.