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. Radial Basis Functions
Multi-Quadric RBF: (𝑥− 𝑥 𝑗 ) 2 + 𝜖 𝑗 2
Inverse Multi-Quadric RBF: (𝑥− 𝑥 𝑗 ) 2 + 𝜖 𝑗 2
Gaussian RBF: 𝑒 − 𝜖 𝑗 2 (𝑥− 𝑥 𝑗 ) 2 =exp(− 𝜖 𝑗 2 (𝑥− 𝑥 𝑗 ) 2 )

4. Project with Maple Leaf
Initial image
The most accurate image
epsilon = 0.1

5. Epsilon Variable epsilon = 0 epsilon = 0.01 epsilon = 0.05 epsilon = 1

6. Total Image

7. Edge Detection with another image
Initial image

8. Epsilon Variable epsilon = 0 epsilon = 0.05 epsilon = 0.1

9. Epsilon Variable
Epsilon=0.2
Epsilon=0.3 → more accurate

10. What to do:
Get familiar with MATLAB and use it to help analyze the code
Find other factors in the code rather than epsilon to make the image look different
Research further into how the code used works with Radial Basis Function (Multi-Quadric RBF)
Investigate the other two RBFs and their practicality in edge detection