1. Radial Basis Functions and Application in Edge Detection
Chris Cacciatore Tian Jiang Kerenne Paul

2. Abstract
This project focuses on the use of Radial Basis Functions in Edge Detection in both one-dimensional and two-dimensional images.
Use a 2-D iterative RBF edge detection method.
Vary the point distribution and shape parameter.
Quantify the effects of the accuracy of the edge detection on 2-D images.
Study a variety of Radial Basis Functions and their accuracy in Edge Detection.

3. Contents
RBF Matrix Calculation
Approximation

4. Radial Basis Functions
Multi-Quadric RBF:
Sum of all MQ-RBF calculations:

5. RBF Matrix Calculation Mλ = f

6. Lambda coefficients λ = 𝑀 −1 f

7. Interpolation 𝑀 𝑦 λ = f

8. Smooth function without jump
f = cos x, -π<x<π

9. Gibb’s phenomenon
f = x/|x|

10. RBF Approximation with different number of coefficients
f = x/|x|

11. MQ RBF in 2D Edge Detection
Edge map from x-direction
Edge map from y-direction