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COMPM081 - Geometry of Images

This database contains 2016-17 versions of the syllabuses. For current versions please see here.

Code COMPM081 (Also taught as: COMPGV11)
Year 4
Prerequisites Successful completion of years 1 and 2 of the Computer Science programme, including the mathematics course/option, or core courses in computer science and mathematics. Plus Image Processing in Year 3.
Term 2
Taught By Simon Arridge (50%)
Lewis Griffin (50%)
Aims To introduce the generalisation of image processing to n-Dimensional data : volume data, scale space, time-series and vectorial data.
Learning Outcomes To understand the principles of image processing in n-dimensions, time-series analysis and scale space, and to understand the relations between geometric objects and sampled images.

Content:

0. Basic Image Operations
    Fourier Transforms
    Convolution and Differentiation in Fourier Domain Recursive Filters
    Marching Square/ Cubes
    Level Set Methods

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
    - 3D curvature: the Weingarten mapping, Gaussian and mean curvatures

2. Scale Space

    2.1 Linear Scale Space
    - Introduction and background
    - Formal properties
    - Gaussian kernels and their derivitives
    2.2 Non-linear Scale Space
    - Motivation
    - Edge-effected diffusion (Perona-Malik)
    - Classification of Alvarez and Morel
    - Euclidian and Affine shortening flow
    - Numerical methods for computing scale spaces

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

4. Bayesian and Information Theoretic Approaches
    Bayesian Image Restoration
    Markov Random Fields
    Definitions of Entropy and Mutual information
    Deconvolution with image priors (statistical and structural

Method of Instruction:

Lecture presentations with associated class coursework and laboratory sessions

Assessment:

The course has the following assessment components:

  • Written Examination (2.5 hours, 75%)
  • Coursework Section (2 pieces, 25%)

To pass this course, students must:

 

  • Obtain an overall pass mark of 50% for all sections combined
  • Obtain a minimum mark of 40% in each component worth ≥ 30% of the module as a whole.

The examination rubric is:
Choice of 3 questions from 5. All questions carry equal marks