Radial Basis Functions and Application in Edge
Detection
Chris Catiatore, Tian Jiang and Kerenne Paul
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.
Radial Basis Functions
Multi-Quadric RBF: Inverse Multi-Quadric RBF:
Gaussian RBF: ()
Shape Parameter: ε Uses distance between points on
a given interval
Is used as a variable in RBF representation
Epsilon Variable
epsilon = 0 epsilon = 0.05 epsilon = 0.1
epsilon = 0.2 epsilon = 0.3 epsilon = 0
Epsilon Variable
epsilon = 0
epsilon = 2
epsilon = 0.05epsilon = 0.01
epsilon = 0.1 epsilon = 1
Edge map from x-direction
Edge map from y-direction
Edge Map at 0.1 (x-direction and y-direction)
Edge map from x-direction, y-direction and total
Example of Gibbs Phenomenom
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
Future works:• Start using other types of Radial Basis Functions• Research more about matrix involvement in the code• Try to understand more about the code itself and what’s causing the variation in edge maps