Creating and Manipulating Images using Maths and a Spreadsheet

1. 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

2. 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

3. 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.

4. 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

5. 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

6. Creating and Manipulating Images using Maths and a Spreadsheet Jeff Waldock Contrast / Brightness Picturevalues.exe

7. 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

8. Creating and Manipulating Images using Maths and a Spreadsheet Jeff Waldock The student case study The Excel Add-in ImageAnalysis

9. 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"

10. Creating and Manipulating Images using Maths and a Spreadsheet Jeff Waldock

11. Creating and Manipulating Images using Maths and a Spreadsheet Jeff Waldock Can generate images based on mathematical functions:

12. 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