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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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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

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

  • Experiential/active learning
    • Engagement
    • Motivation
    • Understanding
    • Practical applicability
    • Contextualises learning
    • Employability
  • BSc Mathematics at SHU is distinctive
    • it emphasises real practical applications
    • it emphasises the importance of mathematical modelling
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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

Students are familiar with digital images, and in post-processing them

Almost all digital photo post-processing uses Mathematics:

Reflection

Edge-detection

Distortions

Rotation

Pattern detection

Changing brightness

Face recognition

Changing contrast

Sharpening

Tinting, altering colour balance

Re-sizing

Blurring

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.

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

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.

Colours.exe

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

The most common format for digital photographs is JPG, or JPEG.

An Excel add-in has been created which can:

  • ImportJPG images, placing the red, green and blue components as (decimal) integers in separate worksheets.
  • Resizeimages to fit the number of columns
  • RecompileJPG images from the values in the R,G and B worksheets

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

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

Contrast / Brightness

Picturevalues.exe

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

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

Rotation: Matrices

Noise: Random numbers

Colour control: Histograms, Statistics

Morphing: Linear Interpolation

Edge-detection: Finite differences

Images.xlsx

Filtering: 2-D FFT

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

The student case study

The Excel Add-in

ImageAnalysis

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

Student comments:

“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"

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

Can generate images based on mathematical functions:

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Creating and Manipulating Images using Maths and a Spreadsheet

Jeff Waldock

http://maths.shu.ac.uk/units/55-5767/images/One_colour_grad6.php?w=500&h=3