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.