Linear Diffusion

نویسنده

  • Erkut Erdem
چکیده

The diffusion process can be seen as an evolution process with an artificial time variable t denoting the diffusion time where the input image is smoothed at a constant rate in all directions. Starting from the initial image u(x), the evolving images u(x, t) under the governed equation represent the successively smoothed versions of the initial input image f (x), and thus create a scale space representation of the given image f , with t > 0 being the scale. As we move to coarser scales, the evolving images become more and more simplified since the diffusion process removes the image structures at finer scales. Figures 1 and 2 show example scale space representations sampled at different diffusion times for two different images. In fact, the notion of scale is an essential part of early visual processing, where the main task is to separate the image into relevant and irrelevant parts. ∗[email protected]

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

متن کامل

AN ANALYTICAL SOLUTION FOR DIFFUSION AND NONLINEAR UPTAKE OF OXYGEN IN THE RETINA

A simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. The approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. The computational results for the scaled variables are presented through graphs. The effect of the important parameters (1) d...

متن کامل

Evaluation of Diffusion Anisotropy and Diffusion Shape in Grading of Glial Tumors

Background: The most common primary tumors of brain are gliomas. Grading of tumor is vital for designing proper treatment plans. The gold standard choice to determine the grade of glial tumor is biopsy which is an invasive method.Objective: In this study, we try to investigate the role of fractional anisotropy (diffusion anisotropy) and linear anisotropy ...

متن کامل

Least – Squares Method For Estimating Diffusion Coefficient

 Abstract: Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the ...

متن کامل

LEAST – SQUARES METHOD FOR ESTIMATING DIFFUSION COEFFICIENT

Determining the diffusion coefficient based on the solution of the linear inverse problem of the parameter estimation by using the Least-square method is presented. A set of temperature measurements at a single sensor location inside the heat conducting body is required. The corresponding direct problem will be solved by an application of the heat fundamental solution.

متن کامل

A Statistical Study of two Diffusion Processes on Torus and Their Applications

Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012