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

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.

Radial Basis Functions Multi-Quadric RBF: (𝑥− 𝑥 𝑗 ) 2 + 𝜖 𝑗 2 Inverse Multi-Quadric RBF: 1 (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 )

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

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

Total Image

Edge Detection with another image Initial image

Epsilon Variable epsilon = 0 epsilon = 0.05 epsilon = 0.1

Epsilon Variable Epsilon=0.2 Epsilon=0.3 → more accurate

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