Geometry of Images

This page is for information related to the VIVE course Geometry of Images

PreTest

Some students are suprised at the level of mathematics needed in this course. Here is a Self Test. Please try this and if you find it difficult, please discuss with me whether to take this module.

Notes

Fourier Transforms and Sampling
Image Derivatives and Edge Detection
Link to Lorenson and Cline paper Marching cubes: A high resolution 3D surface construction algorithm, SIGGRAPH 1987
2D curvature
3D curvature
Partial Differential Equations on Images

Mathematica Examples

I have put the examples from lectures here

Matlab Examples

Week 1 : here is an example of sampling and Fourier Interpolation
Week 2 : here is an example of differentiation using spatial convolution and Fourier filtering
Here is an example of directional edge differentiation in 2D using test image Cameraman
Here is an example of canny edge detection in 3D using synthetic test image

Here are examples of calculating image curvature in 2D and 3D

  • 2D Image curvature function and a script to run this function using some synthetic and standard test images.
  • 3D Voxel curvature using synthetic test image

    PDEs, Scale Space and Anisotropic Diffusion

    A useful link about PDEs in imaging is Weickert's book
    Link to Perona Malik paper P. Perona and J.Malik "Scale-space and edge detection using anisotropic diffusion", IEEE Trans. Patt Anal Machine Intell. 12(7),pages 629-639, 1990.

    Coursework

    This is coursework for 2019 The handin date is Thursday March 7th, 11.55p.m.