Mathematics in Everyday Life Gilad Lerman
Department of Mathematics
University of Minnesota Highland park elementary (6th graders)

What do mathematicians do? :

What do mathematicians do? What homework do I give my students? Example of a recent homework: Denoising

What do mathematicians do? :

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

How to obtain a panorama :

How to obtain a panorama By “rotating line camera”
Stitching together multiple images
Your camera can do it this way…
E.g. PhotoStitch (Canon PowerShot SD600)

Experiment with PhotoStitch :

Experiment with PhotoStitch Experiment done by Rebecca Szarkowski Input: 10 images along a bridge

Experiment continued… :

Experiment continued… Experiment done by Rebecca Szarkowski Output: Panorama (PhotoStitch) Output: Panorama (by a more careful mathematical algorithm)

What’s math got to do with it? :

What’s math got to do with it? From visual images to numbers (or digital images) New Topic: Relation of Imaging and Mathematics

Slide 8:

Digital Image Acquisition

From Numbers to Images :

From Numbers to Images Let us type the following numbers
1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6
7 7 7 7 7 7 7 7
8 8 8 8 8 8 8 8
We then color them so 1=black, 8=white
rest of colors are in between

One more time… :

One more time… Now we’ll try the following numbers
1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
4 4 4 4 4 4 4 4
8 8 8 8 8 8 8 8
16 16 16 16 16 16 16 16
32 32 32 32 32 32 32 32
64 64 64 64 64 64 64 64
128 128 128 128 128 128 128 128
We then color them so 1=black, 128=white
rest of colors are in between

Example: Smoothing by averaging Original image on top left
It is then averaged with neighbors
of distances 3, 5, 19, 15, 35, 45

Slide 17:

Example: Smoothing by averaging And removing wrinkles by both….

More Relation of Imaging and Math :

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

Slide 19:

Moon sharpening (continued)

Real Life Applications :

Real Life Applications Many…
From a Minnesota based company…
Their main job: maintaining railroads
Main concern: Identify cracks in railroads,
before too late…

How to detect damaged rails? :

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

Millions of images then collected :

Millions of images then collected

How to detect Cracks? :

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)

Summary :

Summary Math is useful (beyond the grocery store)
Images are composed of numbers
Good math ideas good image processing

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

By: Nikkugupta (30 month(s) ago)

a brilliant ppt