Difficulty: Introductory | Prerequisites: Basic CS concepts, introductory linear algebra helpful
Big Picture: These topics cover the applied side of computer science, where theoretical foundations meet real-world problems. Computer graphics is about creating and manipulating visual content. Signal and image processing deals with extracting useful information from raw data (audio, images, video). Computational science uses computers to model and solve scientific problems numerically. These areas draw heavily on linear algebra, calculus, and the algorithms covered in earlier units. You do not need deep maths to follow this introductory overview, but familiarity with vectors and matrices will help.
Computer graphics creates and manipulates digital visual content using algorithms. Signal and image processing extracts, transforms, and analyses data in the form of sound, images, and video. Computational science builds numerical models and uses computers to solve scientific problems that are too complex for pen-and-paper analysis.
Computer graphics
The field of creating, manipulating, and rendering digital visual content. It involves the synthesis and processing of image data using algorithms. Think of it as: the science behind everything from video games to medical imaging to CGI in films.
Image processing
Techniques for analysing, enhancing, or transforming digital images. Closely related to computer vision (teaching computers to "see") but focused more on the transformation of image data than on understanding its content.
Signal processing
The analysis, modification, and synthesis of signals such as sound, images, and sensor data. Signals can be carried by electrical, mechanical, or even biological means. Think of it as: the mathematics of cleaning up, compressing, or extracting meaning from raw data streams.
Fourier transform
A mathematical operation that decomposes a signal into its constituent frequencies. Fundamental to signal processing, audio analysis, image compression, and many other applications. The Fast Fourier Transform (FFT) is the efficient algorithm for computing it.
Computational science (scientific computing)
The field concerned with building numerical models and using computers to analyse and solve scientific problems. It combines applied mathematics, computer science, and domain-specific knowledge (physics, biology, engineering, finance).
Computational geometry
The study of algorithms for solving geometric problems, such as finding convex hulls, intersections, and nearest neighbours. Heavily used in computer graphics and geographic information systems.
Computer graphics is concerned with creating, storing, and rendering digital visual content
It involves both the generation of images (rendering) and the processing and analysis of existing images
Core sub-areas include:
Rendering: converting 3D models into 2D images (rasterisation, ray tracing)
Modelling: representing objects and scenes mathematically (polygonal meshes, curves, surfaces)
Animation: making objects move and change over time
Visualisation: turning abstract data into visual representations (scientific visualisation, information visualisation)
Closely related to image processing, computational geometry, and data structures (scene graphs, spatial data structures like octrees and BSP trees)
Heavily applied in video games, film visual effects, medical imaging, CAD, and virtual reality
Information can take the form of text, speech, sound, images, or other multimedia
Signal processing studies algorithms for manipulating these data forms, regardless of the physical medium carrying the signal (electrical, mechanical, or biological)
This is a foundational concept in information processing, which treats computation independently of the data carrier
Key application areas:
Telecommunications: transmitting voice and data reliably
Medical imaging: MRI, CT scans, ultrasound image enhancement
Speech processing and synthesis: voice assistants, text-to-speech
Audio processing: noise cancellation, compression (MP3), equalisation
An important open problem in theoretical CS: what is the lowest possible computational complexity for a fast Fourier transform algorithm?
Also called scientific computing
Concerned with building numerical models and quantitative analysis techniques, then using computers to solve scientific problems
Sits at the intersection of applied mathematics, computer science, and domain expertise
Used wherever problems are too complex for analytical (closed-form) solutions: weather modelling, protein folding, financial modelling, fluid dynamics, astrophysics simulations
Relies heavily on numerical methods, optimisation algorithms, and high-performance computing
Computer graphics powers everything from the interface on your phone to blockbuster film effects to surgical planning tools that let doctors rehearse operations on 3D models. Signal processing is why your phone call sounds clear despite background noise, and why an MRI scan can show soft tissue in detail. Computational science lets climate scientists project temperature changes decades into the future and lets pharmaceutical researchers model how a drug molecule binds to a protein.
Students often think computer graphics is only about video games. It is a broad field that includes medical imaging, scientific visualisation, CAD, and data visualisation.
A common mistake is conflating image processing with computer vision. Image processing transforms images (filtering, enhancement, compression); computer vision tries to understand what is in an image (object detection, scene recognition). They overlap but are distinct.
Students sometimes assume signal processing is only relevant to electrical engineering. It applies equally to biological signals (EEG, ECG), acoustic data, and any domain where data arrives as a continuous or sampled stream.
Computational science is sometimes confused with computer science itself. Computational science is specifically about using computation to solve problems in other scientific domains.
⚠️ Know the distinction between computer graphics (creating/rendering images) and image processing (transforming existing images).
⚠️ Be able to name at least three application areas for signal processing (telecom, medical imaging, speech, audio).
⚠️ Understand what a Fourier transform does conceptually (decomposes a signal into frequencies) even if you are not asked to compute one.
⚠️ Know what computational science is and how it differs from computer science as a discipline.
True or False: Computer graphics is only used in entertainment and gaming.
Fill in the blank: The mathematical operation that breaks a signal into its component frequencies is called the ______.
True or False: Signal processing can be applied to biological signals, not just electrical ones.
Fill in the blank: Scientific computing is also known as ______.
True or False: Image processing and computer vision are the same thing.
Q: What is computer graphics, and what are its main sub-areas?
A: Computer graphics is the field of creating, manipulating, and rendering digital visual content. Its main sub-areas include rendering (converting 3D models to 2D images), modelling (representing objects mathematically), animation, and visualisation (turning data into visual form).
Q: What is the Fourier transform and why is it important in signal processing?
A: The Fourier transform decomposes a signal into its constituent frequencies. This is important because many signal processing tasks (filtering, compression, noise removal) are easier to perform in the frequency domain than in the time or spatial domain.
Q: What is the difference between image processing and computer vision?
A: Image processing focuses on transforming images (filtering, enhancement, compression, edge detection). Computer vision focuses on interpreting and understanding image content (recognising objects, detecting faces, understanding scenes). They share techniques but have different goals.
Q: Define computational science in one sentence.
A: Computational science is the field that builds numerical models and uses computers to analyse and solve scientific problems that cannot be solved analytically.
Q: Name an open problem in theoretical CS related to signal processing.
A: The question of the lowest possible computational complexity for the fast Fourier transform remains unresolved.
Computer graphics relies on data structures (scene graphs, spatial trees), algorithms (rendering, ray tracing), and linear algebra (transformations, projections). Signal processing connects to information theory (Shannon's work underpins how we compress and transmit signals) and to data structures and algorithms (FFT is an algorithm; filter design is an algorithmic problem). Computational science draws on numerical methods, which you will see in applied mathematics courses, and on high-performance computing and parallel algorithms.
Computer graphics, rendering, rasterisation, ray tracing, 3D modelling, animation, visualisation, scientific visualisation, image processing, computer vision, signal processing, digital signal processing, DSP, Fourier transform, fast Fourier transform, FFT, frequency domain, filtering, convolution, computational geometry, computational science, scientific computing, numerical methods, numerical modelling, simulation, high-performance computing, HPC, medical imaging, speech synthesis, audio processing, noise cancellation