Mathematics in Everyday Life by Gilad Lerman
Department of Mathematics
University of MinnesotaGilad Lerman
Department of Mathematics
University of Minnesota
Maths in daytoday life by Gilad Lerman Department of Mathematics University of Minnesota
1. Mathematics in Everyday Life
Gilad Lerman
Department of Mathematics
University of Minnesota
Highland park elementary (6th graders)
2. What do mathematicians do?What homework do I give
my students?
• Example of a recent homework: Denoising
3. What do mathematicians do?What projects do I assign
my students?
• Example of a recent project:
Recognizing Panoramas
• Panorama:
• How to obtain a panorama?
wide view of a physical space
4. How to obtain a panorama
1. By “rotating line camera”
2. Stitching together multiple images
Your camera can do it this way…
E.g. PhotoStitch (Canon PowerShot SD600)
18. More Relation of Imaging and Math
Differences of numbers sharpening images
On left image of moon
On right its edges (obtained by differences)
We can add the two to get a sharpened version of the first
20. Real Life Applications
• Many…
• From a Minnesota based company…
• Their main job: maintaining railroads
• Main concern: Identify cracks in railroads,
before too late…
21. How to detect damaged rails?
• Traditionally… drive along the rail (very long) and
inspect
• Very easy to miss defects (falling asleep…)
• New technology: getting pictures of rails
23. How to detect Cracks?
• Human observation…
• Train a computer…
• Recall that differences detect edges…
Work done by Kyle Heuton (high school student at Saint Paul)
24. Summary
• Math is useful (beyond the grocery store)
• Images are composed of numbers
• Good math ideas good image processing