When presenting a particular mathematical topic to a group of students it can help their understanding if a familiar illustrative example can be provided.
There is a surprisingly wide range of mathematics involved in manipulating digital images from simple arithmetic (e.g. increasing or decreasing the image brightness) to matrix algebra (applying a filter) to numerical PDEs (image sharpening) to more complex processes such as pattern recognition.
Students are familiar with digital images most likely because of their mobile phone camera and many are also familiar with the post-processing possibilities - either using in-camera tools or through tools such as Photoshop. Many students have a good working knowledge of spreadsheets - particularly Microsoft Excel - as they are widely used as a support tool in their course. This paper describes a tool developed to allow students to make use of their spreadsheet skills in applying the mathematical techniques necessary to implement a variety of image modifications. It is an Excel add-in which decomposes the image to its red green and blue parts putting each into a separate worksheet. It can also recompile a JPG image from the data in these worksheets.
This tool has been used with final year students on the BSc Mathematics degree at Sheffield Hallam University taking a mandatory 20 credit module ‘Advanced Case Studies’. The image processing case study is one of four in the year and lasts six weeks with class contact of 3 hours per week.
Although used here with final year degree students it could equally well be used with students studying mathematics at many levels – from high school level to postgraduate. The important difference will be the examples tackled.
