Course pages 2011–12

# Computer Graphics and Image Processing

**Principal lecturer:** Prof Peter Robinson**Taken by:** Part IB**Past exam questions****Information for supervisors** (contact lecturer for access permission)

No. of lectures: 16

Prerequisite courses: Algorithms, Mathematical Methods for Computer Science (for one lecture of Image Processing part of the course)

This course is a prerequisite for Advanced Graphics (Part II).

## Aims

To introduce the necessary background, the basic algorithms, and the
applications of computer graphics and image processing. A large
proportion of the course considers the design and optimisation of
algorithms, so can be considered a practical application of the
lessons learnt in the *Algorithms* course.

## Lectures

**Background.**What is an image? What are computer graphics, image processing, and computer vision? How do they relate to one another? Image capture. Image display. Human vision. Resolution and quantisation. Colour and colour spaces. Storage of images in memory, and double buffering. Display devices: the inner workings of CRTs, LCDs, and printers. [3 lectures]**2D Computer graphics.**Drawing a straight line. Drawing circles and ellipses. Cubic curves: specification and drawing. Clipping lines. Filling polygons. Clipping polygons. 2D transformations, vectors and matrices, homogeneous co-ordinates. Uses of 2D graphics: HCI, typesetting, graphic design. [5 lectures]**3D Computer graphics.**Projection: orthographic and perspective. 3D transforms and matrices. 3D clipping. 3D curves. 3D scan conversion.*z*-buffer. A-buffer. Ray tracing. Lighting: theory, flat shading, Gouraud, Phong. Texture mapping. [5 lectures]**Image processing.**Operations on images: filtering, point processing, compositing. Halftoning and dithering, error diffusion. Encoding and compression: difference encoding, predictive, run length, transform encoding (including JPEG). [3 lectures]

## Objectives

At the end of the course students should be able to

- explain the basic function of the human eye and how this impinges on resolution, quantisation, and colour representation for digital images; describe a number of colour spaces and their relative merits; explain the workings of cathode ray tubes, liquid crystal displays, and laser printers;
- describe and explain the following algorithms: Bresenham’s line
drawing, mid-point line drawing, mid-point circle drawing, Bezier
cubic drawing, Douglas and Pucker’s line chain simplification,
Cohen-Sutherland line clipping, scanline polygon fill,
Sutherland-Hodgman polygon clipping, depth sort, binary space
partition tree,
*z*-buffer, A-buffer, ray tracing, error diffusion; - use matrices and homogeneous coordinates to represent and perform 2D and 3D transformations; understand and use 3D to 2D projection, the viewing volume, and 3D clipping;
- understand Bezier curves and patches; understand sampling and super-sampling issues; understand lighting techniques and how they are applied to both polygon scan conversion and ray tracing; understand texture mapping;
- explain how to use filters, point processing, and arithmetic operations in image processing and describe a number of examples of the use of each; explain how halftoning, ordered dither, and error diffusion work; understand and be able to explain image compression and the workings of a number of compression techniques.

## Recommended reading

* Foley, J.D., van Dam, A., Feiner, S.K. & Hughes, J.F. (1990). *Computer graphics: principles and practice*. Addison-Wesley (2nd ed.).

Gonzalez, R.C. & Woods, R.E. (2008). *Digital image processing*. Addison-Wesley (3rd ed). [The second edition (1992) and the first edition (Gonzalez & Wintz, 1977) are as useful for this course.]

* Slater, M., Steed, A. & Chrysanthou, Y. (2002). *Computer graphics and virtual environments: from realism to real-time*. Addison-Wesley.