Review of probability

  • Definition of a random variable
  • Definition of a discrete probability space
  • Definition of a probability measure
  • Definition of the mean (first moment).
  • Definition of the variance (second centered moment).

Two Distributions

  • Gaussian or Normal distribution
  • Uniform Distribution 

Transformations of random variables

  • How to transform "Standard Gaussian" or "Standard Normal" random samples to those coming from an arbitrary normal distribution.

MATLAB simulation of random samples.

Random vectors

Gray Level Slicing or Levelset Slicing

Bit Plane Slicing

The difference between gray level slicing and bit plane slicing.

Euclidean Transformations of images

  • Rotation matrices
  • Definition of orthonormal
  • Vector equation for Euclidean transformations.