Project by Chris Cacciatore Tian Jiang and Kerenne Paul Abstract This project focuses on the use of Radial Basis Functions in Edge Detection in both onedimensional and twodimensional images We will be using a 2D iterative RBF edge detection method We will be varying the point ID: 749358
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Slide1
Radial Basis Functions and Application in Edge Detection
Project by: Chris Cacciatore,
Tian
Jiang, and
Kerenne
PaulSlide2
Abstract
This project focuses on the use of Radial Basis Functions in Edge Detection in both one-dimensional and two-dimensional images. We will be using a 2-D iterative RBF edge detection method. We will be varying the point distribution and shape parameter. We also quantify the effects of the accuracy of the edge detection on 2-D images. Furthermore, we study a variety of Radial Basis Functions and their accuracy in Edge Detection. Slide3
Radial Basis Functions (RBF’s)
Radial Basis Function
RBF’s use the distances between points on a given interval and epsilon( shape parameter) as variables.
Commonly Used RBF’s
Multi-quadratic
Inverse Multi-quadraticGaussian
Multi-quadratic=GaussianExp()This project focuses on Multi-quadratic RBF’s
Slide4
The
- adaptive method for
jump discontinuity
This method
changes the values of the shape parameters depending on
the smoothness of f(x). Using this method allows the accuracy of the approximations to be solely determined on . The Main idea is that disappears only near the center of the discontinuity resulting in the basis functions near the discontinuity to become linear. This causes Gibbs oscillations not to appear in the approximation. Local -adaptive method
Slide5
Gibbs Phenomenon
Example graph for Gibbs phenomenonSlide6
Using the
-adaptive method
Begin by finding the jump discontinuity. This can be done by finding the first derivative/slope at the centers. Coefficients
can also be used. (research how)
Example of simple discontinuitySlide7
Epsilon Variable
Initial image of simple maple leaf in Black/White
Image of maple leaf with epsilon at .1
Program: TwoD_Example1Slide8
Epsilon Variable (cont.)
Epsilon = 2
Epsilon = 0
Note that these two images descend from the same original maple leaf. Image on right is inaccurate
due to round off errors occurring when epsilon becomes to large.Slide9
Epsilon Variable (cont.)
Epsilon = .0001
Epsilon = .001Slide10
In the future…
Research further into how the code used works with RBF’s
Investigate other types of RBF’s and their practicality in edge detection
Improve upon current methods of edge detectionSlide11
References
Vincent Durante,
Jae-Hun
Jung.
An iterative adaptive
multiquadric radial basis function method for the detection of local jump discontinuities. Appl. Numer. Math. 57 (2007) 213-229