Park City Mathematics Institute
Learning the Math of Image Processing
Project Abstract

Drafts of Project Files (password required)

Numbers to Images to Numbers and Back
Dianna Sopala*, Ellie Ratliff, John Mahoney
This activity is intended as an introduction to image processing. Students explore the relationship between gray levels of images and numerical values. This activity also simulates transformations that could be performed on images. We believe this activity is appropriate for grades 7-12. The activity should take 1 to 2 periods and can be done any time during the school year. This activity should not require technology but can be facilitated with calculator access.
 
Which Image is Which? A Truly Visual Representation of Data Using Histograms in Image Processing
Sandra Corbacioglu*
The study of image processing begins with the representation of a black and white image simply as a matrix where each element is an integer ranging from 0 to 255, representing a shade of gray where 0 = black and 255 = white. The integer values can be recorded, tallied and displayed as a histogram.

This activity provides a rudimentary introduction to the field of image processing by showing the relationship between images and their histograms. Students will find the relationship between the characteristics of a histogram and the appearance of the image via a series of matching exercises, ranging from easy to challenging. This activity is appropriate for grades 9 - 12, assuming students have a basic understanding of histograms as a way of representing data.

 
Introduction to Image Processing using Excel
David Metzler*, Melanie Wertz, Marla Mattenson, Zach Korzyk
This project introduces students to the basic ideas and operations of image processing, using Excel and a custom-designed web application. Students first use the web application as a "black box" to do some simple operations on images. They then use the application to download an Excel file with the image data, and investigate the connection between the numbers and the picture. After working on a very small test image to learn how to perform image operations in Excel (or even by hand), they then perform these operations on realistically large images, displaying them by uploading them to the web application. In the last stage of the project, they learn how to use a median filter to remove noise from an image. Parts of the lesson can be used to save time or to avoid using the web, in classrooms with no internet access.
 

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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.