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LTA Conference 19 June 2013. Creating and Manipulating Images using Maths and a Spreadsheet. http://tinyurl.com/n7u5x6p. Jeff Waldock Department of Engineering and Mathematics, Faculty of ACES. Creating and Manipulating Images using Maths and a Spreadsheet. Jeff Waldock.
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19 June 2013
Creating and Manipulating Images using Maths and a Spreadsheet
Department of Engineering and Mathematics, Faculty of ACES
Students are familiar with digital images, and in post-processing them
Almost all digital photo post-processing uses Mathematics:
Tinting, altering colour balance
SHUMaths students are also very adept with Excel.
… led to a final year case study combining these elements, developing mathematical skills through experiential/action learning.
Digital images are composed of a pixel array, with each pixel itself comprising separate red, greenand bluecomponents
Each of these components can take values between 0and255.
Normally expressed as hexadecimal values – in the form #RRGGBB, so red, for example, is #FF0000.
The most common format for digital photographs is JPG, or JPEG.
An Excel add-in has been created which can:
Students can therefore devise and apply a variety of effects by
- developing a mathematical technique to create the effect
- importingthe image to be processed
- implementingthe effect using existing spreadsheet skills
- exportingthe new image
Contrast / Brightness
The range of mathematics that can be explored in this way is broad:
Brightness: Straight lines.
Contrast: Straight lines and curves. e.g. Image Gamma:
Monochrome, colour casts, tints: Arithmetic
Blur, Sharpen (unsharp mask): Matrices
Translation, shear, stretch: Linear transformations
Distortion (e.g. ripple effect): Geometry, trigonometry
Noise: Random numbers
Colour control: Histograms, Statistics
Morphing: Linear Interpolation
Edge-detection: Finite differences
Filtering: 2-D FFT
The student case study
The Excel Add-in
“We're increasingly surrounded by digitally altered images in everyday life and it was fascinating to see the mathematics behind these"
“I thought that it was really fun, different and something you wouldn’t initially expect to be related to mathematics!”
"The Excel skills that I have gained will be very useful in future employment"
"The way the case study is set up encourages interest and research into the topic"
Can generate images based on mathematical functions: