Geometry from Derivatives: from Edges in Images to Volumes of Tubes

Carlton Cross

Dr. Kevin R. Vixie

I will explain how to use derivatives to extract geometric information from shapes and images. I will start by generalizing the usual derivative so that it works on discontinuous functions (thereby helping us find geometry in images and discover Radon measures) and then move on to derivatives of volumes of shapes (thereby enabling us to find volumes of tubular neighborhoods and discover curvature measures).

The challenge will be doing this in a little bit of time using a little bit of calculus. Exploiting the famous {1 picture = 1000 words} formula, we will arrive at our destination just in the nick of time.

Kevin was born in Hinsdale, Illinois, awhile ago. After that he moved around a bit. Then he attended Walla Walla College. There he studied a bit. Then he moved a bit more, moving through various universities and labs until he found that he once again he was only a bit of a distance from Walla Walla (at WSU).

Now he studies things, writes things, teaches things, and makes things in his shop, supported by significant time with his wife Beata, son Levi, dog Obi and cat Charlie ... and with a bit of help from his friends.