N-Dimensional Signal Processing : Part 2

MRes CVIPGS course, Term 2

Lecturer
Simon Arridge

1. Introduction to Differential Geometry

1.1 Images as functions

  • Definitions
  • Taylor Series expansion and the Koenderick jet
  • Properties of the local Hessian
  • Definition of extrema and saddle points
  • Ridges in n-dimensions
  • Image invarients up to fourth order

    1.2 Curvature

  • Contour curvature
  • Image curvature

    2. Scale Space

    2.1 Linear Scale Space

  • Introduction and background
  • Formal properties
  • Gaussian kernels and their derivatives

    2.1 NonLinear Scale Space

  • Motivation
  • Edge-effected diffusion (Perona-Malik)
  • Classification of Alvarez and Morel
  • Euclidean and Affine shortening flow

    3. Multispectral Images and Statistical Classification

    3.1 Feature Space

  • Introduction
  • Definitions of feature space
  • Clustering

    3.2 Statistical methods

  • Linear and non-linear discriminant functions
  • supervised Learning
  • Unsupervised Learning