CONTENTS 1. Introduction 1.1 Course Outline 1 1.2 Introduction ...

Full Module Title:
MATHS FOR IMAGING 2B
Short Module Title: MATHS 2B
Module Code: 2DPI507 Module Level: 5
Academic credit weighting: 15 credits. Length: 1 semester
School:
Media, Art and Design.
Department:
Photographic and Digital Media
Module Leader:
TBA
Host Course:
BSc(Hons) Photography and Digital Imaging
Status:
Option.
Subject Board:
Pre-requisites:
None.
Co-requisites:
None.
Assessment:
50% examination, 50% coursework.
Summary of Module content:
The Fourier transform and its properties. The discrete Fourier transform. Matrix theory. Monte-Carlo
modelling. Regression.
Module Aims:
• To study in a rigorous manner some important mathematical ideas and procedures necessary for
the advanced study of image formation and image quality.
Learning Outcomes:
On completion of the module the successful student will be able to:
1. Understand and be able to apply Fourier theory to a level appropriate for advanced studies of
image formation, image evaluation, image processing and image modelling.
2. Use eigenvalue and eigenvector methods from matrix algebra.
3. Implement Monte-Carlo modelling techniques appropriate for the study of image formation in a
variety of systems.
4. Use regression methods in analysing data.
Indicative syllabus content:
The Fourier transform and its properties. Theorems (similarity, shift, derivative, Parsevals and others).
Convolution and the convolution theorem. The Dirac comb. The mathematics of sampling and
aliasing.
The discrete Fourier transform (DFT). Cyclic convolution.
Matrix algebra: the characteristic equation. Eigenvalues and eigenvectors and their use.
Analysis of experimental data using regression analysis.
Monte-Carlo methods: Random number generation. Uniform deviates. Transformation and rejection
methods for other distributions. Monte-Carlo modelling and its application to simple imaging systems.
Teaching and Learning Methods:
Illustrated lectures and workshops (appx 24 hrs). Seminars and tutorials (appx 12 hrs).
Assessment Rationale:
The examination will test the students’ ability to define concepts, derive results and relationships,
prove selected theorems, use given equations and formulae for numerical calculations and interpret
the significance of results.(Learning outcomes 1, 2 and 4).
Written coursework will consist of a number of problems requiring a detailed and accurate analysis
with justifications and assumptions, and use of computers for numerical analysis. (Learning outcomes
1 - 4).
DPI_Hbook 71 ©University of Westminster