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Creating and Manipulating Images using Maths and a SpreadsheetLTA Conference19 June 2013Jeff WaldockDepartment of Engineering and Mathematics, Faculty of ACES1

http://tinyurl.com/n7u5x6p 1

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock2Experiential/active learningEngagementMotivationUnderstandingPractical applicabilityContextualises learningEmployabilityBSc Mathematics at SHU is distinctive it emphasises real practical applicationsit emphasises the importance of mathematical modelling2

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock3Almost all digital photo post-processing uses Mathematics:ReflectionRotationChanging brightnessChanging contrastTinting, altering colour balanceBlurringSharpeningRe-sizingEdge-detectionDistortionsPattern detectionStudents are familiar with digital images, and in post-processing themFace recognitionSHUMaths students are also very adept with Excel. led to a final year case study combining these elements, developing mathematical skills through experiential/action learning.3

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock4Digital images are composed of a pixel array, with each pixel itself comprising separate red, green and blue componentsEach of these components can take values between 0 and 255.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 SpreadsheetJeff Waldock5The most common format for digital photographs is JPG, or JPEG.An Excel add-in has been created which can:Import JPG images, placing the red, green and blue components as (decimal) integers in separate worksheets.Resize images to fit the number of columnsRecompile JPG images from the values in the R,G and B worksheetsStudents can therefore devise and apply a variety of effects by- developing a mathematical technique to create the effect- importing the image to be processed- implementing the effect using existing spreadsheet skills- exporting the new image5

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock6Contrast / Brightness

Picturevalues.exe

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Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock7Brightness: Straight lines.Contrast: Straight lines and curves. e.g. Image Gamma: Monochrome, colour casts, tints: ArithmeticBlur, Sharpen (unsharp mask): MatricesTranslation, shear, stretch: Linear transformationsDistortion (e.g. ripple effect): Geometry, trigonometryRotation: MatricesNoise: Random numbersColour control: Histograms, StatisticsMorphing: Linear Interpolation

Edge-detection: Finite differencesFiltering: 2-D FFTThe range of mathematics that can be explored in this way is broad:Images.xlsx7

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock8The Excel Add-inImageAnalysisThe student case study

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Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock9We're increasingly surrounded by digitally altered images in everyday life and it was fascinating to see the mathematics behind these"Student comments:I thought that it was really fun, different and something you wouldnt 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"9

Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock10

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Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock11Can generate images based on mathematical functions:

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Creating and Manipulating Images using Maths and a SpreadsheetJeff Waldock12http://maths.shu.ac.uk/units/55-5767/images/One_colour_grad6.php?w=500&h=3

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